THE`SE ´ecole Ecole´ doctorale des Sciences Exactes et leurs Applications (ED : 211)

pr´esent´eeet soutenue publiquement le 19 avril 2018 Abdelhafid Touil pour obtenir le grade de docteur Sp´ecialit´edoctorale “Physique”

Optical microscopy investigation of gas hydrate nucleation, growth and dissociation processes Etude´ par microscopie optique de la nucl´eation,croissance et dissociation des hydrates de gaz

Jury

Pr´esidentdu jurry : Marc Prat Directeur de recherche IMFT, Toulouse

Rapporteurs : Bertrand Chazallon Professeur Universit´eLille Lionel Mercury Professeur ISTO/CNRS, Orl´eans

Examinateurs : Hannelore Derluyn Charg´eede Recherche LFCR/CNRS Arnaud Desmedt Charg´ede Recherche ISM/CNRS, Bordeaux Noushine Shahidzadeh Professeur University of Amsterdam

Directeur de th`ese: Daniel Broseta Professeur UPPA/LFCR

Laboratoire des Fluides Complexes et leurs R´eservoirs UMR 5150 CNRS-TOTAL-UPPA Pau, France

Remerciements

Les travaux pr´esent´esdans ce m´emoireont ´et´er´ealis´esau sein du Laboratoire des Flu- ides Complexes et leurs R´eservoirs(LFCR), et une partie au sein de l’Institut des Sciences Mol´eculairesde Bordeaux (ISM) dans le cadre dune th`eseco-financ´eepar le CNRS et lA- gence Nationale de la Recherche.

Je tiens tout dabord `aremercier mon directeur de th`eseDaniel Broseta pour mavoir confi´ece travail de recherches si passionnant, ainsi que pour son encadrement infaillible et son soutien tout le long de la th`ese. Il a ´et´eparticuli`erementpr´esentet `al´ecoutelors de mes nombreuses p´erip´etiesscientifiques.

Jai pu travailler dans un cadre particuli`erementagr´eable,grˆace`alensemble des mem- bres du laboratoire LFCR et du l’ISM de Bordeaux. Je pense particuli`erement`aRoss, Ar- naud, Christophe, Guillaume, Hannelore, Manuel, Patrick et Romain qui ont su m’apporter leurs conseils et leurs aides durant ces ann´ees.

Je remercie les rapporteurs Bertrand Chazallon et Lionel Mercury pour leurs lec- tures et corrections de mon manuscrit.

Je souhaite remercier tout le personnel technique et administratif du laboratoire no- tamment Joseph, Fabrice, Eric,´ Laurent, Bertrand, Djamel, Catherine, V´eronique,Blandine et J. Patrick.

Mes remerciements ne seraient pas complets sans une pens´ee`ames coll`eguesdoctor- ants stagiaire et post-doctorants : Abdoul, Daoud, Dyhia, Ez´equiel,Fouad,´ Hacene, Hai, Henry, Julien, Lourdes, Mohamed, Patrick, Romuald, Salem et Yacine.

Je remercie aussi tous les membres de ma famille, mon p`ereet sa femme, mes fr`eres et surs, ma tante Zohra et ma cousine Zahia qui ont toujours ´et´e`ames cˆot´es(mˆemede loin) pendant cette th`eseet qui m’ont toujours encourag´e.

Pour finir, jexprime tout mon amour et mes remerciements pour la femme de ma vie Nawel qui a su mencourager. Je la remercie aussi pour la patience et le soutien dont elle a fait preuve pendant toute la dur´eede cette th`ese.

¸Cafait du bien de dire merci. Encore merci `aCelui quon oublie trop souvent. Abstract

The nucleation, growth and dissociation of gas hydrate across a water – gas meniscus in glass capillaries are investigated by means of video-microscopy and confocal Raman spec- troscopy under controlled temperature, pressure, cooling rate and substrate wettability and geometry. Structure I and II hydrates are examined, with the following guest molecules: CO2, CH4,N2, cyclopentane, and cyclopentane + CO2. By lowering the temperature well below 0 ◦C, i.e., under strong subcooling, all these hydrates but the cyclopentane hy- drate nucleate without forming ice on the liquid water – guest meniscus, which is rapidly covered with a polycrystalline crust. The hydrate then propagates from this meniscus as fast-growing fibers or dendrites in bulk water and as a thin polycrystalline crust, or halo, along the capillary wall. On water-wet substrates, this halo advances on the guest side of the meniscus, fed by a water layer sandwiched between the halo and glass. Symmetrically, on guest-wet (silane-treated) glass, the halo and an underlying guest layer grow on the wa- ter side of the interface. No halo is observed on intermediate-wet glass. The hydrate halo growth and morphology and the thickness of its underlying water (or guest) layer strongly depend on subcooling. Thanks to the small capillary volume and the rapid temperature descent, the metastability limit of CO2 hydrate is approached for various pressures and sub- strate wettabilities. The low subcooling regime is investigated as well: a novel CO2 hydrate morphology is discovered for subcoolings below 0.5 ◦C, which consist of a hollow hydrate crystal originating from the water – guest meniscus and advancing on the guest side along glass, fed by a thick water layer sandwiched between glass and this crystal. A new proce- dure is proposed to determine gas hydrate dissociation conditions in a large temperature and pressure range, including the metastable extension of the three-phase (liquid water – hydrate - guest) down to temperatures well below 0 ◦C. Finally, the mechanisms by which CO2 and cyclopentane synergistically act to form the structure II hydrate are discussed.

Keywords: Gas Hydrate, Microthermometry, Microscopy, Raman spectroscopy, Microflu- idic, wettability, Phase equilibria R´esum´e

La nucl´eation,la croissance et la dissociation des hydrates de gaz au voisinage d’un menisque eau – gaz dans des capillaires de verre sont ´etudi´eespar vid´eo-microscopieet spectroscopie Raman `atemp´erature,pression, mouillabilit´eet g´eom´etriedu substrat contrˆol´ees.Dans ce travail, deux hydrates simples de structure I (hydrate de CO2 et hydrate de CH4), deux hydrates simples de structure II (N2 et Cyclopentane) et un hydrate double (cyclopentane + CO2) sont examin´es.En baissant la temp´eraturebien au-dessous de 0 ◦C, i.e., sous un fort sous-refroidissement, tous ces hydrates, except´el’hydrate de cyclopentane, nucl´eentsans que la glace soit form´ee.L’hydrate forme d’abord une croˆutepolycristalline sur le m´enisque eau-mol´eculeinvit´ee(guest). Ensuite, il se propage rapidement `apartir de ce m´enisque dans l’eau sous forme de fibres ou dendrites et le long de la paroi capillaire sous forme d’une croˆute fine et polycristalline appel´ee” halo ”. Sur un substrat hydrophile, ce halo avance du cˆot´ede la phase invit´ee,aliment´epar une couche d’eau entre le halo et la paroi interne du capillaire. Sym´etriquement,sur un verre hydrophobe (trait´eau silane), le halo et une couche de la phase invit´eese propagent du cˆot´eeau. Aucun halo n’est observ´esur un substrat de mouillabilit´einterm´ediaire.La croissance et la morphologie du halo d’hydrate et l’´epaisseurde sa couche sous-jacente d’eau (ou de phase invit´ee)d´ependent fortement du sous-refroidissement. Grˆaceau faible volume du capillaire utilis´eet `ala vitesse rapide de re- froidissement, la limite de m´etastabilit´ede l’hydrate de CO2 est approch´eepour diff´erentes pressions et mouillabilit´e.Le r´egimedes faibles sous-refroidissements est ´egalement´etudi´e: une nouvelle morphologie d’hydrate de CO2 est d´ecouvertepour des sous-refroidissements inf´erieurs`a0,5 ◦C, constitu´eed’un cristal creux, g´en´er´eeau niveau du m´enisqueeau – guest et avan¸cantdu cˆot´eguest le long du verre, aliment´epar une ´epaissecouche d’eau prise en sandwich entre le verre et ce cristal. Une nouvelle proc´edureest propos´eepour d´etermina- tion des conditions d’´equilibre des hydrates de gaz dans une large plage de temp´eratureet de pression, y compris l’extension m´etastablede la ligne triphasique (eau liquide – hydrate – guest) jusqu’`ades temp´eraturesbien inf´erieures`a0 ◦C. Enfin, les m´ecanismespar lesquels le CO2 et le cyclopentane agissent en synergie pour former l’hydrate de structure II sont discut´es.

Mots-cl´es :Hydrate de gaz , Microthermometrie, Microscopie, Spectroscopie Raman, Mi- crofluidique, Mouillabilit´e, Equilibre´ de phase.

Contents

Contents I

List of Figures V

List of Tables XIII

1 Introduction 1 1.1 R´ef´erences ...... 6

2 Bibliography on clathrate hydrates 9 Introduction ...... 10 2.1 Structural analysis of hydrates ...... 11 2.2 Some physical quantities (hydrate properties) ...... 13 2.2.1 Hydration number ...... 13 2.2.2 Molar volumes ...... 14 2.2.3 Hydrate density ...... 14 2.2.4 Enthalpy of dissociation of gas hydrates ...... 14 2.3 Applications of hydrates ...... 16 2.3.1 Natural gas supply ...... 17 2.3.2 Natural Gas storage ...... 17 2.3.3 Hydrogen storage ...... 17 2.3.4 Gas separation ...... 18 2.3.5 CO2 sequestration ...... 19 2.3.6 Refrigeration ...... 19 2.3.7 Desalination ...... 20 2.3.8 Other gas hydrate applications ...... 21 2.4 Gas Hydrate formation, growth and dissociation ...... 22 2.4.1 Thermodynamics of crystallization ...... 22 2.4.2 Hydrate nucleation ...... 25 2.4.2.1 Primary nucleation ...... 26 2.4.2.2 Secondary nucleation ...... 29 2.4.3 Hydrate growth ...... 30 2.5 R´ef´erences ...... 32

3 Roles of wettability and supercooling in cyclopentane hydrate spreading over a substrate 41 Abstract ...... 42 3.1 Introduction ...... 43 3.2 Materials and Methods ...... 47 3.2.1 Materials ...... 47

I CONTENTS

3.2.2 Experimental configuration ...... 47 3.2.3 Glass wettability and thin layers on the glass ...... 48 3.2.4 Experimental procedure ...... 50 3.3 Results ...... 53 3.3.1 Halo morphologies and initial velocities ...... 53 3.3.2 Strong slowing down of the halo front ...... 60 3.3.3 Substrate wettability effects ...... 61 3.4 Discussion of halo growth mechanisms ...... 64 3.4.1 General considerations ...... 64 3.4.2 Linear regime of halo growth ...... 65 3.4.3 Halo propagation beyond the break point ...... 68 3.5 Conclusions and outlook ...... 71 3.6 R´ef´erences ...... 74

4 CO2 hydrate formation and growth in glass capillaries 81 Abstract ...... 82 4.1 Introduction ...... 82 4.2 Materials and methods ...... 86 4.2.1 Experimental setup ...... 86 4.2.2 Experimental procedure ...... 86 4.2.3 Phase assignement by Raman spectroscopy ...... 89 4.3 CO2 hydrate formation and growth in glass capillaries ...... 90 4.3.1 CO2 hydrate formation and growth under strong supercooling con- ditions...... 91 4.3.2 Raising T towards the CO2 hydrate dissociation temperature. . . . . 98 4.3.3 CO2 hydrate formation and growth under moderate supercooling conditions ...... 102 4.3.4 CO2 hydrate formation and growth under low supercooling condi- tions: evidence for a new morphology and growth process...... 102 4.4 CO2 hydrate nucleation near the metastability limit ...... 109 4.5 Conclusion ...... 112 4.6 R´ef´erences ...... 114

5 Gas hydrate phase diagrams 119 Abstract ...... 120 5.1 Methods of determining hydrate equilibria ...... 121 5.1.1 Abrupt change in the slope of the temperature or pressure . . . . . 124 5.1.2 Electrobalance method ...... 126 5.1.3 Differential Scanning Calorimetry (DSC) ...... 127 5.1.4 Quartz Crystal Microbalance (QCM) ...... 127 5.1.5 Visual observation ...... 128 5.2 Materials and methods ...... 129 5.2.1 Materials ...... 129 5.2.2 Experimental procedure ...... 129 5.3 Results and discussion ...... 132 5.3.1 Simple hydrate dissociation above the ice melting point ...... 133 5.3.1.1 Carbon dioxide hydrate ...... 133 5.3.1.2 Nitrogen hydrate ...... 134 5.3.1.3 Methane hydrate ...... 135 5.3.2 Metastable extension of Lw – H – V below 0 ◦C ...... 137

II CONTENTS

5.3.3 Enthalpy of dissociation and the quadruple points ...... 141 5.3.3.1 Quadruple Points ...... 141 5.3.3.2 Enthalpy of hydrate dissociation ...... 143 5.3.4 Synergy effect in the formation of CO2 + cyclopentane system . . . 147 5.3.4.1 Double hydrate formation and growth ...... 147 5.3.4.2 Double hydrate dissociation ...... 149 5.4 Conclusion ...... 151 5.5 R´ef´erences ...... 152

6 Conclusion and outlook 161 Conclusion and outlook ...... 161 Conclusion et perspectives ...... 165

A Model of cyclopentane hydrate halo growth in a round capillary i A.1 R´ef´erences ...... v

B Using astigmatism in round capillaries to study wetting layers vii Abstract ...... vii B.1 Introduction ...... viii B.2 Refraction in a glass capillary ...... ix B.2.1 Contact angles by measuring a meniscus ...... ix B.2.2 Using a cusp to determine the true internal diameter ...... xi B.2.3 Taking advantage of total internal reflection (tir) ...... xvii B.3 Experimental materials and methods ...... xx B.4 Experimental illustrations ...... xxii B.4.1 CO2-water and CO2-brine contact angles at high temperature or pressure ...... xxii B.4.2 Thin layers revealed by the capillary inner cusp ...... xxvii B.5 Conclusion and outlook ...... xxx B.6 R´ef´erences ...... xxxii

CN2 hydrate growth in glass capillary xxxvii

D Raman shifts of CP in hydrate and liquid state xli D.1 R´ef´erences ...... xliii

E Development of a homemade software xlv

III CONTENTS

IV List of Figures

2.1 The different forms of nucleation...... 25 2.2 Gibbs free energy of homogeneous nucleation as a function of the radius of the nucleus...... 27 2.3 The metastability zone where hydrate nucleation is not spontaneous. This zone is bounded by the three-phase equilibrium (Lw – H – V) line and the metastable limit (see Chapter 4)...... 27 2.4 Schematic of primary nucleation mechanism: homogeneous nucleation of a spherical crustal hydrate in the bulk water (a), heterogeneous nucleation of cap-shaped hydrate crystal on the substrate surface (b) and heterogeneous of lens-shaped hydrate crystal at the water - gas interface (c)...... 28

3.1 Schematic view of a capillary loaded with water and cyclopentane (a), with a zoomed-in view of the meniscus at 0 ◦C in the case of an untreated glass capillary (b), contact angle, θ = 13 ◦, and a silane-treated glass capillary (c), θ = 106 ◦...... 48 3.2 Photographs of a meniscus between water (left) and cyclopentane (right) in a silane-treated capillary at various temperatures from 10 to 19 ◦C, − showing the increase in contact angle with decreasing temperature...... 49 3.3 Typical temperature profile in a CP hydrate formation and dissociation ex- periment. Shading is to better distinguish the different steps. Images (e) and (f) show the hydrate halo creeping on the capillary inner wall, under cyclopentane, with the arrows indicating the growth direction. W: water. CP-E: cyclopentane emulsion in water. FH: first hydrate halo. SH: second hydrate halo...... 51 3.4 Snapshots of hydrate halos grown in cyclopentane to similar distances from the water-cyclopentane meniscus ( 0.45 mm) along the glass capillary wall ≈ at various temperatures or supercoolings. ∆t is the time elapsed since the halos have started advancing from the meniscus. The boxes in the two upper images highlight how the water layer between the hydrate halo and the wall leads slightly on the halo...... 54 3.5 Initial halo velocities Vh as a function of supercooling for the experiments reported in Table 3.1 ...... 56 3.6 Snapshots from experiment 4 showing the hydrate halo growing along the capillary wall, together with the water-vapor and cyclopentane-vapor menisci. At early times (a,b), the halo in cyclopentane and the CP-vapor meniscus both advance in the same direction. At late times, (c-d) (images recentred), when the halo has overrun the CP-vapor meniscus and is continuing its ad- vance along glass in vapor, the CP-vapor meniscus moves in the opposite direction...... 58

V LIST OF FIGURES

3.7 (a ) Halo front position or distance from the water-CP interface as a function of time in experiments 18, 19 and 20; (b ) View of a ’young’ halo (T = 4 ◦C) − with a rough texture visible in transmission; (c) past the break point, this halo decelerates and thins to sub-micron thickness only revealed by the cusps along the inner wall...... 60

3.8 Log-log plot of the halo front position vs. time, both plotted from the break point. The straight line is a t1/2 law...... 61

3.9 Snapshots from an experiment conducted in a silane-treated capillary. (a) The capillary is initially very slightly cyclopentane-wet, contact angle 100 ◦ at the initial supercooling, ∆T = 7 K(T 0 ◦C); (b) Following the first ≈ thermal cycle, cf. figure 3.3 (crust on the meniscus but no halo, data not shown), a halo is formed during the second cycle (see section 3.3.3; (d-f) The CP-vapor meniscus shows rapid consumption of CP by the halo and the associated liquid CP film. Time intervals indicated are between successive images...... 62

3.10 Enlarged view of the halo front with two possible geometries: hemispherical (a) and lenticular, typical of a soft solid with angles determined by Neu- mann’s construction (b) The substrate is strongly water-wet (low contact angle θ)...... 66

4.1 Schematics of the experiment. Top: enlarged view of the capillary, one of its ends being sealed and the other inserted in a stainless-steel tubing connected to the gas vessel with pressure control, here a high-pressure pump . . . . . 87

4.2 (a) CO2 hydrate formation on the meniscus between water and liquid CO2 in a capillary (internal diameter: 200 µm) at 30 bar and Tn 27 ◦C (a). ∼ − (b) Ice formation (6 bar and -32 ◦C)...... 88

4.3 Characterization of the various phases using Raman spectroscopy. The spec- tra of the CO2 hydrate are compared to those of liquid CO2, CO2-saturated liquid water at 22 bar and -20 ◦C and gaseous CO2 at 22 bar and 6 ◦C. . . . 90

4.4 CO2 hydrate formation and growth at 30 bar and Tn 27 ◦C across a ∼ − meniscus between water (left) and liquid CO2 (right). Within less than 1 s (from a to b), the CO2 hydrate has nucleated on the meniscus and coated it with a thin polycrystalline crust. A CO2 hydrate halo then advances along the capillary wall: from b to c: 15 s, and from c to d: 54 s. Fibers growing from the meniscus towards the bulk of the water are apparent in (d). . . . . 93

4.5 CO2 hydrate formation and growth at 10 bar at Tn 31 ◦C across a menis- ∼ − cus between water and gaseous CO2. Within less than 1 second (from a to b), the CO2 hydrate has nucleated on the meniscus and covered it with a thin polycrystalline crust. The CO2 hydrate then propagates on both sides of the meniscus, as a halo spreading on glass on the CO2 side and as fast- growing fibers on the water side. Fiber velocity is estimated in the range of 200 µm/s. From b and c: 3/4 s: from c to d: 1/4 s...... 94

VI LIST OF FIGURES

4.6 Snapshots from two experiments conducted at 14 bar (left) and 24 bar (right) in a silane-treated glass capillary. Left: at 14 bar, CO2 is gaseous from room temperature (a) down to Tn = 28.5 ◦C (b and c, taken 1 and 6 s − following nucleation) and the substrate is intermediate-wet (θ slightly larger than 90 ◦). Right: at 24 bar, CO2 condenses into a liquid at T 15 ◦C ∼ − (d), and hydrate nucleation occurs at Tn = 26 ◦C (d and e, taken 1 and 6 − s following nucleation). A breath figure of water droplets (BF) appears at T 15 ◦C on glass on the CO2 side of the meniscus (e), which disappears ∼ − starting from the meniscus as soon the CO2 hydrate is present on the meniscus. 95

4.7 View of the glass capillary across the water – CO2 meniscus a few seconds after hydrate nucleation at Tn = 26.5 ◦C and p = 14 bar (a). Increasing − T over Tn, here at a rate of 20 K/min, the hydrate-capped meniscus and the halo are pulled (black arrows) towards the contracting water, generating fractures in the halo seen at the tip of the red arrows in (b). The fractures are rapidly healed, filled with a new halo fed by the water layer present between glass and the (old) halo...... 99

4.8 CO2 pocket rushing from the meniscus into water when T is increased from Tn = 34 ◦C (p = 12 bar) to -8 ◦C...... 99 − 4.9 Hydrate fiber recession towards the meniscus when T is raised slowly to the equilibrium temperature. p = 30 bar and T = 5 ◦C (a) and 6.6 ◦C just below Teq (b). Elapsed time between (a) and (b): 45 seconds...... 100

4.10 Schematic diagram of the evolution of CO2 concentration in water near enough from the meniscus during isobaric hydrate formation/dissociation cycle (see text). The scales are arbitrary...... 100

4.11 CO2 hydrate formation and growth at a water – CO2 meniscus at moderate supercooling conditions (p = 30 bar, ∆T 6.5 K), in a capillary where the ∼ hydrate has been formed and dissociated shortly before. Here, the capillary inner diameter is 250 µm...... 103

4.12 CO2 hollow crystal (HC) forming on the water – CO2 meniscus at low supercooling conditions at p = 24 bar and T = 4.9 ◦C (∆T = 0.4 K). First (a and b), there is a hydrate crystal in water (CW) growing slowly towards the meniscus until it touches it (elapsed time from a to b: 112 s). Then (c and d) a hydrate filament (HF) grows rapidly between the meniscus and the hydrate crystal (CW) from the meniscus (elapsed times from b to c: 14 s; from c to d: 6 s). At some point (e and f) the hydrate grows from the filament end along the meniscus itself and evolves into a hollow cylindrical crystal (see Figure 4.13). Elapsed times from d to e: 2s; from e to f: 4 s. . 104 4.13 Experiments of hollow hydrate crystal growth in a capillary at 22 bar and low supercooling. The temperature in the first experiment (images a and b) is 4.6 ◦C (∆T = 0.2 K). The temperature in the second experiment is 4.7 ◦C (∆T = 0.1 K) at the beginning (image c) and then (image d) is decreased to 4.6 ◦C (∆T = 0.2 K). See text. The black arrows indicate water arriving from the rear of the meniscus to the edge of the hollow crystal, and white arrows show the growth direction of the hollow crystal. The picture at the bottom shows a schematic cross-sectional view and a representation of the leading (and growing) edge of the hollow hydrate crystal...... 106

VII LIST OF FIGURES

4.14 Raman mapping along a segment from the center to the inner wall of the capillary at 22 bar and 4.3 ◦C (0.4 K of supercooling). (a) and (b) show the images by reflection microscopy of the hollow hydrate with 10x and 50x zoom respectively. The lines correspond to the best fit of the different intensity ratios...... 108 4.15 FN, the fraction of cooling cycles in which CO2 hydrate nucleation has occurred, as a function of supercooling ∆T = Teq Tn, where Teq = 5.5 − is the equilibrium temperature for CO2 hydrate and Tn is the nucleation temperature for three different cooling rates at p = 24 bar...... 110 4.16 Nucleation temperatures of CO2 hydrate at the water – CO2 interface in a glass capillary. Cooling rate: 20 K/min. The crosses are the values av- eraged over several identical measurements, with nucleation temperatures represented as histograms: for clarity, only four histograms are represented, each corresponding to a given pressure. An enlarged view of the histogram corresponding to P = 24 bar is presented. The lines on the right-hand side are the three-phase Lw – H – V (liquid water – hydrate – CO2-rich vapor) and Lw –H–Lc (liquid water – hydrate – CO2-rich liquid) equilibrium lines, and Q2 is the upper quadruple point of the Lw –H–V–Lcc equilibrium . 111

5.1 pT phase equilibria of a water + guest binary system, in which the guest component has a liquid/vapor transition in the region of interest (at high enough p and T) and there is therefore an upper quadruple point Q2 (see text). Lw, water-rich liquid; I, ice; H, gas hydrate; V, guest-rich vapor; Lc, guest-rich liquid...... 122 5.2 Pressure and temperature changes during a hydrate formation/dissociation experiment by the isochoric presses (see text)...... 125 5.3 The decrease and increase in pressure are monitored and indicate respectively the formation and dissociation of gas hydrate under isothermal process. The gas is rapidly admitted into or vented from the system. This process is repeated in successive approximations until the gap (difference between the hydrate formation and dissociation pressures) reaches 1 – 2 % of the absolute pressure.28 ...... 126 5.4 Typical temperature sequence to determine the gas hydrate dissociation condition at temperatures above than the lower quadruple point Q1. . . . . 130 5.5 A schematic representation of the formation of hydrate crusts on water – gas menisci...... 131 5.6 water – CO2 hydrate – CO2-rich liquid three-phase equilibrium pT conditions in a carbon dioxide + water system. X, Takenouchi et al.43; , Ohgaki et 42 ⃝ al. ; ▲, present study (cf. table 5.5)...... 133 5.7 liquid water – CO2 hydrate – CO2 gas three-phase equilibrium pT conditions in a carbon dioxide + water system: X, Vlahakis et al.44; , Larson.45; , ⃝ ▲ present study (cf. table 5.5)...... 134 5.8 N2 hydrate formation on the water – N2 meniscus at 200 bar and -38.5 ◦C: the meniscus between water and N2-rich vapor (a) was covered within less than one second by a hydrate crust (b), and hydrate needles (or fibers) were observed to grow from the meniscus to bulk water (b)...... 135 5.9 water liquid – N2 hydrate – N2 gas three-phase equilibrium pT conditions in a nitrogen + water system: X, van Cleeff et al.46; , Jhaveri et al.47; ⃝ ▲, present study (cf. table 5.7)...... 135

VIII LIST OF FIGURES

5.10 water liquid – CH4 hydrate – CH4 gas three-phase equilibrium pT conditions in a methane + water system: X, Adisasmito et al.48; , Mcleod et al.49; ⃝ ▲, present study (cf. 5.6)...... 136 5.11 Metastable hydrate boundaries in the pT phase diagram for a H2O + gas system. Q1 is the lower quadruple point where liquid water, ice, hydrate and gas coexist at equilibrium...... 138 5.12 Typical temperature sequence to determine the gas hydrate dissociation condition at temperatures below than the lower quadruple point Q1. . . . . 138 5.13 Supercooled water – CO2 hydrate – CO2 gas three-phase equilibrium pT conditions in a carbon dioxide + water system: , Melnikov et al.62; , ⃝ ▲ present study (cf. 5.5)...... 139 5.14 Supercooled water – N2 hydrate – N2 gas three-phase equilibrium pT condi- 46 tions in a nitrogen + water system: X, van Cleeff and Diepen. ; ▲, present study (cf. 5.7)...... 140 5.15 supercooled water – CH4 hydrate – CH4 gas three-phase equilibrium pT 63 conditions in a methane + water system: X, Melnikov et al. ; ▲, present study (cf. 5.6)...... 140 5.16 The ice birefringence property at -1.5 ◦C and 6 bar of CO2. A polarising filter has been detected when the light pass through the polarising filter and then through the ice ...... 141 5.17 Semilogarithmic plot of the dissociation pressure versus the temperature along three-phase equilibrium in the system H2O + CO2 over all range of studied temperature: , water – hydrate – CO2-rich liquid; water ⃝ ▲ – hydrate – CO2-rich vapor; , supercooled water – hydrate – CO2-ricch △ vapor; X, water – ice – CO2-rich vapor, cf. table 5.5 ...... 142 5.18 Semilogarithmic plot of the dissociation pressure versus the temperature along three-phase equilibrium in the system H2O + N2 over all range of studied temperature: water – hydrate – N2-rich vapor; , supercooled ▲ △ water – hydrate – N2-rich vapor; X, water – ice – N2-ricch vapor, cf. table 5.7142 5.19 Semilogarithmic plot of the dissociation pressure versus the reciprocal tem- perature along three-phase equilibrium Lw – H – V for different hydrate former: ,N2; , CO2; X, CH4...... 144 ⃝ △ 5.20 Snapshots showing CP+CO2 double hydrate growth from water – CP menis- cus: formation of hydrate filaments in bulk water at 5 ◦C and 24 bar, (a); small hydrate crystals ejected from water – CP interface into bulk water at 10 ◦C and 75 bar, (b); hydrate tunnels (or pockets) of CP in the water wrapped by a thin layer of hydrate at 20 bar and 8 ◦C, (c) ...... 148

5.21 Four-phase (Lw –H–LCP –VCO2 ) equilibrium pressure-temperature con- ditions: X, Zhang and Lee74; , Mohammadi and Richon75; , present ⃝ ▲ work (cf. table 5.8). Three-phase (Lw –H–VCO2 ) equilibrium pressure- temperature conditions: □, present work (cf. 5.5)...... 150 A.1 Physical picture of the hydrate halo growing along a glass capillary wall. (a) Growth in the CP phase ; (b) under the CP vapor, after the halo has overrun the CP – vapor meniscus...... i

B.1 Sketch diametral section through a spherical cap meniscus in a (locally) cylindrical glass capillary with internal and external radii Ri and Re. Equation (B.1) relates the contact angle, θ, to the cap height, h, from pole, P, to base, BB′, and the radius at the cap base, Ri...... ix

IX LIST OF FIGURES

B.2 Transmission micrographs of the same meniscus (between pure water, left, and CO2, right, at 500bar, 40 ◦C) with the focus on the pole P (a), and on the base BB’ (b). The prominent cusps on the outer (OC) and inner walls (IC), are due to rays such as those shown in the transverse sections (c), which come into focus in order, on focusing towards the objective, starting beyond the capillary. The capillary inner and outer diameters are here 200 and 330µm. Scale bar in (b): 100µm...... xi B.3 Schematic illustration of the formation of an image of the inside capillary wall by reflection, corresponding to cusp IC when ie +ϕ = π/2, i.e. vanishing, hence minimum deviation, and a ray entering and exiting the capillary parallel to the optical axis, at a distance Ra off it...... xiii

B.4 Relation between the apparent (Ra) and the true internal radius (Ri) of a capillary, from eqn. (B.7), for three values of ng: 1.44,1.46 & 1.48 (arrow). The inset, showing a water-CO2 meniscus (150bar, 25 ◦C), illustrates the apparent wall thinning for a capillary with internal and external diameters 300 and 400µm (tie-line in main figure), scale bar 100µm. The cusps IC (white arrows) render the apparent inner wall readily visible on the CO2 side of the meniscus, despite the presence of water droplets formed on the glass on the right during an earlier stage of the experiment. The cusps are not visible on the water side for reasons explained in section B.2.3...... xvi B.5 How to tune the capillary dimensions to exhibit a fluid by total internal reflection (TIR). The curve shows the limit refractive index of the fluid for TIR on the inner wall, nfl (plotted as nfl/ng), as a function of Ri/Re, for a silica capillary (ng = 1.46) in air. The vertical tie-lines show capillaries used here, with aspect ratios Ri/Re = 100/165 0.61 and 150µm/200µm = 0.75. ∼ Fluids with indices nf below the curve give rise to a brilliant cusp IC, by TIR; those above the line do not (e.g. figure B.4), see the text...... xix

B.6 Micrographs of the water-CO2 meniscus (water on the left) in a silane- treated capillary at increasing pressures at room temperature (22 ◦C). Scale bar: 100µm (in the first vignette)...... xxiii

B.7 Pressure dependence of the contact angle of water-CO2 in (a) a hydrophobic, 17 silane-treated capillary at 22 ◦C (filled and open data from ref. and this work, respectively) and (b) a hydrophilic, untreated capillary at different temperatures: 40 ◦C (circles), 100 ◦C (triangles), 150 ◦C (squares), 205 ◦C (diamonds). Error bars are shown only for the latter isotherm...... xxiv

B.8 Pressure dependence of a 8M LiCl brine-CO2 contact angle on untreated ∼ glass at : 40 ◦C ( ), 100 ◦C ( ), 150 ◦C ( ), 205 ◦C ( ). Full symbols ⃝ △ □ ⋄ correspond to water-advancing angles (see text)...... xxv B.9 Using the contrast of cusp IC to highlight growth of thin films: (a) Growth of a thin but visible film of polycristalline cyclopentane hydrate, initiated at the water-cyclopentane meniscus on the left at 4 ◦C; (b-c) Views 60 − and 102s later (capilllary recentred). Although the halo is tenuous to the point of invisibility in the transmission image, the cusps IC clearly show up its progression to the right and thickening. Scale bar in (a): 200µm. . . . xxix

C.1 Raman shifts showing the N–N stretching vibrations in the N2 hydrate and nitrogen gas at the same pressure and temperature (230 bar and -10 ◦C). . xxxviii

X LIST OF FIGURES

C.2 N2 hydrate formation on N2 gas bubble at 240 bar and -38 ◦C: the water – N2 interface is covered in less than 14 of second by hydrate crust. Hydrate needles then grow from the interface to bulk water...... xxxix C.3 N2 hydrate formation and growth in bulk water at moderate supercooling conditions: (a), P = 15 bar, T = 15 ◦C, ∆T 6 ◦C; (b), P = 25 bar, − ≈ T = 22 ◦C, ∆T 4 ◦C, in a capillary where the hydrate has been formed − ≈ and dissociated shortly before...... xl C.4 N2 hydrate halo growth along the glass capillary wall in N2 gas phase from supercooled water – N2 gas meniscus at 50 bar and -15 ◦C (the subcooling ∆T 3.4 ◦C). This halo is fed by the underlying water. Elapsed time from ≈ (a) to (b) 7 s and from (b) to (c) 21 s ...... xl

D.1 Raman shifts showing the cyclopentane stretching vibrations in the CP hy- drate and liquid CP at ambient pressure and 5 ◦C...... xlii E.1 Graphical user interface of an application for video, temperature and pressure acquisition...... xlviii E.2 Representative diagram of the input and output data linking different parts of the experimental setup described in Chapters 3 and 4 ...... xlix E.3 Representative diagram of the input and output data linking different parts of the experimental setup reported in ongoing thesis Dyhia Atig LFCR . . . l E.4 Graphical user interface of an application for video, temperature acquisition li

XI LIST OF FIGURES

XII List of Tables

2.1 Most common hydrate structures known to date (sI, sII and sH) formed from five types of cages presented here. The simplest type of cage is the pentagonal dodecahedron (512). It is found in all three structures, while the other types of cages are found only in one of the structures. Depending on the size ratio of the guest molecule, different structures are favored. Rc is the radius of cavity in A,˚ Nc is the number of cages, Cn is the coordination 3 number and Nw is the number of water molecules per unit cell...... 12 2.2 Parameters for Kamaths correlation (1984)3,8 used to calculate the enthalpy of dissociation of pure gas hydrates (∆H = a + bT) in [cal/gmol gas]. H is hydrate, Lw is water, V is guest-rich vapor and I is ice...... 16 2.3 Different driving forces used for hydrate nucleation.3 ...... 24

3.1 Summary of initial halo velocities and contact angles measured in glass capillaries for various supercooling conditions...... 55 3.2 Halo, CP-vapor and water-vapor meniscus velocities in the direction of halo growth, measured before (Vh, VCPv and Vwv) and after the CP-vapor menis- ′ ′ ′ cus is overrun by the hydrate halo (Vh, VCPv and Vwv), * not determined. . 57

5.1 different three-phase equilibrium examined in the present study: Lw, water- rich liquid; I, ice; Lw∗ , supercooled water; V, guest-rich vapor; Lc, guest-rich liquid; LCP cyclopentane liquid; H, simple hydrate; DH, double hydrate. . . 132 5.2 Lower quadruple point, Q1 of the CO2 and N2 hydrates determined graph- ically based on the intersection between Lw – I – V and Lw – H – V and upper quadruple point, Q2 of the CO2 hydrate corresponds to the intersec-

tion between Lw –H–LCO2 and Lw –H–VCO2 lines ...... 143 5.3 Best linear fit parameters of the data reported in figure 5.19, R2 the coeffi- cient of determination ...... 143 5.4 Enthalpies of dissociation of simple hydrate and quadruple point, z is the compressibility factor obtained from www.peacesoftware.de/einigewerte 68 C web site.∆Hd∗ calculated using Kamath’s correlation (1984) , T0 = 0 ◦ . . 145 5.5 Experimental dissociation pressures for CO2 hydrates formed from water – CO2 meniscus in glass capillary...... 146 5.6 Experimental dissociation pressures for methane hydrates formed from water – CH4 gas meniscus in glass capillary...... 146 5.7 Experimental dissociation pressure for N2 hydrates formed from water – nitrogen gas meniscus in glass capillary...... 147 5.8 Dissociation Temperatures of CP + CO2 double hydrate at Different Pressures151

XIII LIST OF TABLES

XIV Chapter 1

Introduction

Gas hydrates are non-stoichiometric crystalline solids made up of cages of water molecules trapping ’guest’ molecules (hydrate formers) at low enough temperature and/or high enough pressure. They have long been a laboratory curiosity. For decades, the transport of hydro- carbons has been the main incentive for investigating gas hydrates. In fact, the plugging of the flow lines (tubing, pipelines, valves, etc.) with gas hydrates causes serious environmen- tal and economic damages. Hydrates are materials with multiple potential applications, such as separation and transport of gases, secondary refrigeration, desalination, etc. It should be noted that many of these applications are of great environmental interest.

Research activity in this field is still in its infancy in many domains. One of them is the kinetics of hydrate formation, growth and dissociation. The kinetics of hydrate formation are characterized by very strong metastability effects. On the one hand, when the system (water + hydrate former) is cooled to a temperature below the hydrate dissociation temperature, the nucleation of hydrates is not observed during a long period. This waiting time, which is called the induction time, can be reduced by means of stirring, impurities, or by increasing subcooling or pressure. The water from a recent melting of hydrate or ice exhibits a memory effect, which results in faster hydrate nucleation and lower subcoolings are required. On the other hand, it is well known that there exists a metastability limit for the liquid water-ice transition, in the range of -40 ◦C at ambient pressure, which is approached during experiments carried out in small volumes under high cooling rates.1 Previous work carried out with CO2-rich aqueous fluid inclusions indicates that upon rapid cooling the 2,3 CO2 hydrate forms prior to ice. There thus exists another metastability limit beyond which the hydrate forms spontaneously. To the best of our knowledge, how to approach this metastability limit and how it depends on, e.g., pressure or substrate wettability, have

1 CHAPTER 1. INTRODUCTION never been explored experimentally.

Gas hydrates usually nucleate at a water – guest interface, and then rapidly spread over the interface as a thin polycrystalline film, the crust, whose morphology and growth have been thoroughly investigated over the past two decades.4–13 A few observational studies in water-wet (glass or silicon) micromodels have shown complex growth processes, including nucleation at water – guest interfaces followed by growth over the water films wetting the substrate.14–16 In these micromodels, and more generally in sediments, the presence of curved substrates with different wettabilities can strongly impact the existence and growth rate of these hydrate films.

Another important feature, still poorly understood, is the so-called ’self-preservation’ or ’anomalous stability’ of gas hydrates.17,18 This occurs when the gas hydrate is brought outside its stability region, particularly at low temperatures (below 0 ◦C) and pressures, where it remains stable over a long period of time.

Advances in these issues will stem from insights at scales intermediate between the two extremes of the spatial scales that have been accessed so far: above the few nanometers accessed by molecular dynamic simulations, and below the few millimeters accessible by experiments in conventional reactors equipped with see-through windows. The favorite tool for investigating these scales is optical video-microscopy, which has however been sparingly used. In this experimental approach, the main difficulty is the measurement cell, typically built around two parallel sapphire or glass windows,19 and its temperature and pressure control system, which should at the same time be thin enough to fit between the condenser and the objective and resist high pressures. The experimental approach adopted in this PhD thesis overcomes this difficulty by using glass (transparent) capillaries acting as optical pressure cells, and a commercial cooling-heating stage allowing their precise handling under the optical microscope or Raman spectrometer. This experimental setup, which includes a proper pressure control, has been used in the research presented in this manuscript to examine many of the issues cited above: the propagation of gas hydrates over substrates, their nucleation and growth behavior in confined and small volumes, their anomalous stability in liquid water at sub-zero temperatures, and their dissociation. In all these investigations, the observations start at and near the meniscus separating the water and guest phases in the capillary, because it is where the gas hydrate appears when the system is driven into its stability region, and from which it then expands into the bulk

2 CHAPTER 1. INTRODUCTION phase(s) and over the substrate.

This experimental approach has been introduced about one decade ago by some ”fluid inclusionists”, the researchers who infer the formation conditions of geological sedi- ments from the analysis, mainly by microthermometry and spectroscopic techniques (such as Raman spectroscopy), of the fluids, most often gas-bearing aqueous liquids, enclosed in the small cavities (called inclusions) present in these sediments.20 Microthermometry is the recording with the microscope of the phase changes - freezing and melting if there is a solid phase - which take place in these inclusions during heating or cooling. The obser- vation upon cooling of hydrate freezing, which usually occurs prior to the freezing of the remaining aqueous solution to ice, is the sign that some gas is present in the aqueous fluid, most often a CO2- or a CH4-rich gas. Sealed glass capillaries filled with fluids, e.g., water and CO2, or water and CH4, are model fluid inclusions. Sealed glass capillaries at one of their end - that filled with the aqueous phase - while the other end is connected to the gas-filled pump with pressure control, are employed in the experiments presented in this manuscript. These capillaries can be considered as part of a pore network, and be viewed as model (cylindrical) pores. This study is thus expected to provide insights into how gas hydrates behave in sediments.

In another scientific area, capillaries and, more generally, microfluidic systems or re- actors, are very versatile systems allowing small fluid volumes to be handled with precise temperature control, where the reactions are accelerated through enhancement of heat and mass transfers. An order-of-magnitude assessment of the times needed for reaching thermal and phase equilibria can be made here, taking as an example the round capillaries of radii in the range of 100 µm used in this thesis. An upper bound of the time required for this 2 capillary and its content to adjust to an imposed outside temperature is tth R /Dth < a ∼ few seconds, considering the lowest thermal diffusivity Dth among the materials involved: 7 2 silica, water, gas, ice, hydrate and low-molecular-weight oils, that is, Dth 10− m /s for ∼ the latter materials. The times required to reach liquid/liquid or liquid/gas phase equilib- rium are longer, since the involved mass diffusion coefficients are much smaller, typically by 2 orders of magnitude, than thermal diffusivities, but they are still much lower than ∼ those needed in conventional cells, where in practice equilibrium cannot be reached without imposing strong convection (by agitation). Phase equilibrium involving a solid (hydrate) phase requires still longer times, because water and guest diffusion coefficients in the hydrate

3 CHAPTER 1. INTRODUCTION

11 2 21 phase are extremely low - below 10− m /s, but nevertheless equilibrium is approached much more rapidly than in conventional (i.e., macroscopic) cells.

In these capillaries and microfluidic devices, capillarity and wettability play a major role, used in the first place for loading the fluids in these systems. They control fluid distribution within the pore volume, such as the shape of a meniscus between two fluids; they may also trigger the nucleation and direct the growth of a new phase. Substrate wettability can be controlled to a large extent, e.g., by means of silane chemistry. Glass capillaries are commercially available in a variety of external and internal diameters (from the µm to the mm) and shapes. Square and rectangle capillaries have the advantage of providing distortion-free images.

This thesis is divided into four chapters:

Following a short bibliography on gas hydrates, their relevant properties and possible applications and a theoretical basis on their nucleation are reported in the next chapter (Chapter 2),

The use of cyclopentane (CP) as the guest phase is appealing experimentally because the CP hydrate forms at ambient pressure and is stable for temperatures below Teq=7 ◦C. In addition, the CP hydrate is considered a proxy of natural gas hydrate and it has been widely used in many scientific researches. This has motivated the optical microscopic study presented in Chapter 3. This chapter describes how a thin layer (halo) of CP hydrate spreads from the water/guest meniscus over a substrate in the simplest of pores - round glass capillaries as a function of supercooling and substrate wettability. This Chapter has recently been published as an article in Langmuir.22

The refraction effects in round capillaries can be a ”helpfrom a hindrance”for detecting very thin (submicron) layers: this feature, which is detailed in Appendix B at the end of this text, has proven to be very fruitful in our study of hydrate halos propagating over glass substrates. This Appendix has also been published as an article in Langmuir.23

The formation of common gas hydrates requires however pressures above the ambient, in addition to low enough temperatures. The experimental system and procedures are adapted to this requirement, and are described in Chapter 4. This Chapter, also written in the form of an article, reports an experimental study of CO2 hydrate formation and growth from the water-CO2 meniscus in a capillary, the morphological evolution when supercooling

4 CHAPTER 1. INTRODUCTION is varied and how the different phases can be identified by Raman spectroscopy. In addition to morphological aspects, this chapter addresses the gas hydrate primary nucleation process and the metastability limit beyond which the hydrate forms spontaneously. Preliminary results have been obtained with other common hydrates, such as N2 hydrates, which are reported in Appendix C.

Chapter 5 deals with the hydrate dissociation behavior of CO2,N2, CH4 and CP+CO2 hydrates. A method is presented for the determination of thermodynamic equilibria (hy- drate – liquid – vapor) in a wide range of pressure and temperature including the metastable extension down to temperatures below 0 ◦C. The effect of gas and pressure on the ice melt- ing points, the quadruple points and the enthalpies of hydrate dissociation are investigated.

The mechanisms by which CO2 and CP synergistically act to form a structure II hydrate are elucidated.

A software has been built for handling and managing the videomicrographes, in which the pressure, temperature information is stored, this software, which has been used through- out this thesis, is described in Appendix E.

5 CHAPTER 1. INTRODUCTION

1.1 R´ef´erences

[1] F. Caupin, “Escaping the no man’s land: Recent experiments on metastable liquid water,”Journal of Non-Crystalline Solids, vol. 407, pp. 441 – 448, 2015. 7th IDMRCS: Relaxation in Complex Systems. 1

[2] E. Roedder,“Studies of fluid inclusions; [part] 2, freezing data and their interpretation,” Economic Geology, vol. 58, no. 2, p. 167, 1963. 1

[3] P. L. F. Collins,“Gas hydrates in co 2 -bearing fluid inclusions and the use of freezing data for estimation of salinity,”Economic Geology, vol. 74, no. 6, p. 1435, 1979. 1

[4] C. J. Taylor, K. T. Miller, C. A. Koh, and E. Dendy Sloan Jr., “Macroscopic investi- gation of hydrate film growth at the hydrocarbon/water interface,” Chem. Eng. Sci., vol. 62, no. 23, pp. 6524 – 6533, 2007. 2

[5] B. Peng, A. Dandekar, C. Sun, Y. Luo, W. Pang, and G. Chen,“Hydrate film growth on a surface of a gas bubble suspended in water,”J. Phys. Chem. B, vol. 111, pp. 12485– 12493, 2007.

[6] C.-Y. Sun, G.-J. Chen, C.-F. Ma, Q. Huang, H. Luo, and Q.-P. Li,“The growth kinetics of hydrate film on the surface of gas bubble suspended in water or aqueous surfactant solution,”Journal of Crystal Growth, vol. 306, no. 2, pp. 491 – 499, 2007.

[7] K. Saito, A. K. Sum, and R. Ohmura, “Correlation of hydrate-film growth rate at the guest/liquid-water interface to mass transfer resistance,”Indust. Eng. Chem. Res., vol. 49, no. 15, pp. 7102–7103, 2010.

[8] C. Y. Sun, B. Z. Peng, A. Dandekar, Q. L. Ma, and G. J. Chen, “Studies on hydrate film growth.,”Annu. Rep. Prog. Chem., Sect. C: Phys. Chem., pp. 77–100.

[9] M. Kishimoto and R. Ohmura,“Correlation of the growth rate of the hydrate layer at a guest/liquid-water interface to mass transfer resistance,”Energies, pp. 92–100, 2012.

[10] P. U. Karanjkar, J. W. Lee, and J. F. Morris, “Surfactant effects on hydrate crystal- lization at the wateroil interface: Hollow-conical crystals,” Crystal Growth & Design, vol. 12, no. 8, pp. 3817–3824, 2012.

6 CHAPTER 1. INTRODUCTION

[11] M. Kitamura and Y. H. Mori, “Clathrate-hydrate film growth along water/methane phase boundaries– an observational study,”Cryst. Res. Tech., vol. 48, no. 8, pp. 511– 519, 2013.

[12] S. L. Li, C. Y. Sun, B. Liu, Z. Y. Li, G. J. Chen, and A. K. Sum, “New Observations and Insights into the Morphology and Growth Kinetics of Hydrate Films,” Scientific Reports, vol. 4, pp. 1–6, 2014.

[13] D. Daniel-David, F. Guerton, C. Dicharry, J.-P. Torr´e,and D. Broseta,“Hydrate growth

at the interface between water and pure or mixed co2/ch4 gases: Influence of pres- sure, temperature, gas composition and water-soluble surfactants,” Chem. Eng. Sci., vol. 132, pp. 118 – 127, 2015. 2

[14] B. Tohidi, M. Clenell, R. Anderson, R. Burgass, and A. Biderkab, “Visual observation of gas-hydrate formation and dissociation in synthetic porous media by means of glass micromodels,”Geology, vol. 29, p. 867, 2001. 2

[15] D. Katsuki, R. Ohmura, T. Ebinuma, and H. Narita, “Formation, growth and ageing of clathrate hydrate crystals in a porous medium,” Philosophical Magazine, vol. 86, pp. 1753–1761, 2006.

[16] L. Hauge, L. Gauteplass, M. Hoylanda, G. Ersland, A. Kovcsek, and M. Ferno,“Pore- level hydrate formation mechanisms using realistic rock structures in high-pressure sil- icon micromodels,”International Journal of Greenhouse Gas Control, vol. 53, pp. 178– 186, 2016. 2

[17] S. Takeya, T. Ebinuma, T. Uchida, J. Nagao, and H. Narita, “Self-preservation effect and dissociation rates of ch4 hydrate,”Journal of Crystal Growth, vol. 237-239, pp. 379 – 382, 2002. The thirteenth international conference on Crystal Growth in conj unction with the eleventh international conference on Vapor Growth and Epitaxy. 2

[18] L. A. Stern, S. Circone, S. H. Kirby, and W. B. Durham, “Anomalous preservation of pure methane hydrate at 1 atm,”The Journal of Physical Chemistry B, vol. 105, no. 9, pp. 1756–1762, 2001. 2

[19] E. A. Smelik and H. E. King,“Crystal-growth studies of natural gas clathrate hydrates using a pressurized optical cell,” American Mineralogist, vol. 82, no. 1-2, pp. 88–98, 1997. 2

7 CHAPTER 1. INTRODUCTION

[20] I.-M. Chou,“Optical cells with fused silica windows for the study of geological fluids,” Raman spectroscopy applied to Earth sciences and cultural heritage, no. January 2012, pp. 227–247, 2012. 3

[21] S. R. Davies, E. D. Sloan, A. K. Sum, and C. A. Koh,“In situ studies of the mass trans- fer mechanism across a methane hydrate film using high-resolution confocal raman spectroscopy,” The Journal of Physical Chemistry C, vol. 114, no. 2, pp. 1173–1180, 2010. 4

[22] A. Touil, D. Broseta, N. Hobeika, and R. Brown,“Roles of wettability and supercooling in the spreading of cyclopentane hydrate over a substrate,”Langmuir, vol. 33, no. 41, pp. 10965–10977, 2017. PMID: 28910532. 4

[23] N. Hobeika, P. Bouriat, A. Touil, D. Broseta, R. Brown, and J. Dubessy,“Help from a hindrance: Using astigmatism in round capillaries to study contact angles and wetting layers,”Langmuir, pp. 5179–5187, 2017. 4

8 Chapter 2

Bibliography on clathrate hydrates

Contents Introduction ...... 10 2.1 Structural analysis of hydrates ...... 11 2.2 Some physical quantities (hydrate properties) ...... 13 2.2.1 Hydration number ...... 13 2.2.2 Molar volumes ...... 14 2.2.3 Hydrate density ...... 14 2.2.4 Enthalpy of dissociation of gas hydrates ...... 14 2.3 Applications of hydrates ...... 16 2.3.1 Natural gas supply ...... 17 2.3.2 Natural Gas storage ...... 17 2.3.3 Hydrogen storage ...... 17 2.3.4 Gas separation ...... 18

2.3.5 CO2 sequestration ...... 19 2.3.6 Refrigeration ...... 19 2.3.7 Desalination ...... 20 2.3.8 Other gas hydrate applications ...... 21 2.4 Gas Hydrate formation, growth and dissociation ...... 22 2.4.1 Thermodynamics of crystallization ...... 22 2.4.2 Hydrate nucleation ...... 25 2.4.3 Hydrate growth ...... 30 2.5 Références ...... 32

9 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

Introduction

Gas clathrates are solid compounds formed by the inclusion of guest molecules in cavi- ties of a crystal lattice of a species, called a host molecule, different from the guest molecule.

Important guests include CO2,N2, CH4 and other low-molecular-weight hydrocarbons. The intermolecular interaction between the guest molecule and the host is of the van der Waals type. Gas hydrates are a subfamily of gas clathrates in which the cages of the crystal lattice are formed of water molecules. When in addition to water the trapped molecule participates in cage formation, we speak of semi-clathrates: an example is the TBAB (Tetra-n-Butyl + [1] Ammonium Bromide) semi-clathrate, (C4H9)4N Br− ·qH2O , where the bromide anions (Br – ) participate in the cage building, whereas the N+ cation is located at the center of four cages containing in their cavities the four butyl groups (C4H9). Certain types of or- ganic molecules, such are hydroquinone,1 can build crystal lattices and trap molecules such as CO2 or CH4. In this work, we will be interested mainly in gas hydrates.

Clathrate hydrates are polyhedra of water molecules, linked together by hydrogen bonds. Each polyhedron cage may contain a small molecule, typically gaseous under normal conditions, but hydrates can also be formed with molecules that are liquid at ambient conditions, such as cyclopentane. Generally, hydrates are non-stoichiometric compounds; the cavities may or may not be occupied by the guest molecules. The hydrate formation can be schematized as follows:

ϕ nH2O + M M(H2O)n (2.1) −−−→ where M is the guest molecule, n is the number of moles of water per mole of guest molecules (this is the hydration number) and ϕ is a vapor or liquid phase. It is called a simple hydrate when the cavities are occupied by the same type of guest molecule, and double or mixed hydrate when the cavities are occupied by two or more types of guest molecules.

The hydrate cage is stabilized by van der Waals forces between the water molecules and the trapped molecule. Hydrates usually form at relatively low temperatures (below

20 ◦C) and moderately high pressures, even though some hydrates are formed at atmospheric

[1]q is the number of water molecules per molecule of TBAB in a clathrate unit cell, which are of two types, A, q = 26 and B, q = 38.

10 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES pressure, such a cyclopentane hydrate.

2.1 Structural analysis of hydrates

The cages are more or less regular polyhedra, which can be described in a simple way

mi using the nomenclature of Jeffrey (1984). A polyhedral cage ni is composed of indexed faces i, characterized by their number of sides ni (or edges) and by the number of times mi they intervene in the three-dimensional volume of the cage. Thus, a cage denoted 51262 is made up of 12 pentagonal faces and 2 hexagonal faces. There are several types of cages, of which 5 are the most common and best known: 512, 51262, 51264, 435663 and 51268. Table 2.1 summarizes the geometrical properties of these cages and gives a three-dimensional representation. The oxygen atoms are located at the apex of the polyhedra and the lines represent a bond O H O, meaning that each hydrogen atom has a molecular bond specific − − to the water molecule and a hydrogen bond with the oxygen atom of a neighboring water molecule. X-ray analysis2,3 of the crystals of different hydrates allowed to identify the following three structures: structure I (denoted sI), structure II (denoted sII) and structure H (denoted sH). Table 2.1 shows also the geometry of the various cages encountered in each of the structures I, II and H, and their arrangement to form the corresponding primitive cell.

Structure sI: The crystalline cell has two types of cages: 2 small and 6 large cages. The small cages, denoted 512, have 12 pentagonal faces, hence their name pentagonal dodecahedron. Large cages are tetradecahedra. They have 12 pentagonal faces and 2 hexagonal faces. The large cages are denoted 51262. The sI-type cell is a cubic structure with edge size 12.03 A,˚ which contains 46 molecules of water.

Structure sII: It has 16 small and 8 large cages. The small cages are of type 512 as for the structure sI. The large cages are hexadecahedra denoted 51264. These cages have 12 pentagonal faces and 4 hexagonal faces. The primitive cell of type sII is a cubic structure with edge size 17.3 A,˚ which contains 136 molecules of water.

Structure sH: It is a rare structure in the natural state. It has three types of cages: three cages of type 512, two cages of type 435663 and a large cage of type 51268. The primitive cell of type sH is a hexagonal structure of lattice parameters a = 12.26A˚ and c = 10.17A,˚ it comprises of 34 molecules of water.

11 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

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Table 2.1: Most common hydrate structures known to date (sI, sII and sH) formed from five types of cages presented here. The simplest type of cage is the pentagonal dodecahedron (512). It is found in all three structures, while the other types of cages are found only in one of the structures. Depending on the size ratio of the guest molecule, different structures are favored. Rc is the radius of cavity in A,˚ Nc is the number of cages, Cn is the coordination number and Nw is the number of water molecules per unit cell.3

In general, the size and geometry of guest molecules determine the nature of the crystal structure of the hydrate formed. The structure can be characterized by the size and configuration of guest molecules, which determines the ability to enter and to adjust to the shape and size of the cage.

The techniques used to characterize the sI, sII and sH hydrates (crystallographic stud- ies, X-ray analyzes) are also used with the semi-clathrates formed with tetraalkylammonium + – and other quaternary ammonium salts (TBAX = (C4H9)4N X−, with X is a bromide B, chloride, fluoride, nitrate ion, etc.). Semi-clathrates formed with TBAB at atmospheric pressure are of two main types, called type A (tetragonal structure), which is preferen- tially encountered at a high concentration of TBAB (greater than about 20 % by weight), and type B (orthorhombic structure), which is formed at a lower concentration of TBAB. Morphologically, the ”A”type is often in the form of a column, while the ”B”type has an indefinite form composed of thin crystals.

12 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

2.2 Some physical quantities (hydrate properties)

The study of hydrate properties and the characteristics of their formation and de- composition allowed the development of new technologies. The study of hydrate properties began with the arrival of modern measurement techniques. The most widely used tech- niques at the molecular level are X-ray diffraction, NMR (Nuclear Magnetic Resonance) and vibrational spectroscopy (IR, Raman), etc.

2.2.1 Hydration number

The hydration number of a given hydrate is the number of molecules of water per guest molecule.

number of water molecules n = (2.2) hyd number of guest molecules

The lowest value of this ratio corresponds to a perfectly stoichiometric hydrate struc- ture, i.e. all cavities are occupied by the guest molecules. For example, methane or carbon dioxide can occupy the 8 cavities (2 small and 6 large cages) of the sI hydrate, and therefore the lowest (or stoichiometric) value nhyd is equal to 46/8 = 5.75. The hydration number will be at least 136/24 = 5.67 in a sII hydrate and 34/6 = 5.67 also in structure sH. In reality hydrates are non-stoichiometric compounds, the occupancy rate of the cavities is less than 1, and the above values are the lower limit for the real hydration number. It is essential to determine the hydration number to get an idea about the composition of a hydrate. The occupancy rate is a function of the temperature, pressure, size and shape of guest molecule. The hydration number of a real hydrate can be written as follows:

number of water molecules per unit cell n = (2.3) hyd C N i j=1 i=1 νiθj ∑ ∑ i where νi represents the number of i-type cages per water molecule, θj the fractional filling (occupation) of cage i by a type j molecule, C the number of gas compounds in the hydrate phase and N the number of types of cages in the elementary cell.

13 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

2.2.2 Molar volumes

H w The molar volume of the water in the hydrate, denoted vm− , is the volume occupied by one mole of water molecules in the hydrate phase, i.e.

H w VcellNa vm− = (2.4) Nw

23 where Na denotes the Avogadro constant (Na = 6.02·10 molecules/mol), Vcell is the volume of the elementary cell, and Nw the number of water molecules in the elementary cell.

H g The molar volume of trapped gas in the hydrate, denoted vm− , is calculated as follows:

H g H w · (2.5) vm− = vm− nhyd

2.2.3 Hydrate density

The hydrate density also depends on the occupancy of the cavities. The expression of the real hydrate density is as follows:

Mg Mw + nhyd ρH = H w (2.6) vm− where Mw is the molar mass of the water, Mg the average molar mass of the trapped guests calculated in this way,

i i νiθj Mg = xjMj = Mj i (2.7) j j ∑k i νiθk ∑ ∑ ∑ ∑ i with Mj and xj are respectively the molar mass and the molar fraction of the guest j, θj the fractional occupancy of cage i by a type j molecule.

2.2.4 Enthalpy of dissociation of gas hydrates

The enthalpy of formation/dissociation corresponds to the amount of heat released/absorbed during the formation/dissociation reaction. The most reliable method for determining the

14 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES enthalpy of dissociation of hydrates is calorimetry.4–7 The enthalpy of dissociation ∆H may be determined indirectly from the univariant slope of the phase equilibrium line (ln(p) against 1/T) using the Clausius–Clapeyron equation:

dlnp ∆H = (2.8) 1/T − zR where p is the equilibrium pressure, T the equilibrium temperature, ∆H the dissociation enthalpy, z the compressibility factor and R = 8.31J/Kmol the universal gas constant. If the compressibility factor is assumed to be constant, this equation can be used to calculate the enthalpy of dissociation from commonly available (p, T) data. Although this equation is hard to apply to mixed guests, it is still used to get a first approximation of the enthalpy of the dissociation of these hydrates.

There is a correlation of Kamath (1984),3,8 which makes it possible to calculate the enthalpy of dissociation of the pure gas hydrates as a function of temperature. The correlation is written as follows:

∆H = a + bT (2.9)

Table 2.2 gives the values of the coefficients a and b for each gas for determining the dissociation enthalpy of simple gas hydrates into liquid water + vapor or ice + vapor.

In chapter 5, the dissociation enthalpies of the hydrate into water and guest-rich vapor are determined for CO2,N2 and CH4 simple hydrate using the ClausiusClapeyron equation.

15 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

3 Gas T (◦C) a·10− b Phases

CH4 0 to 25 13.52 -4.02 Lw-H-V

-25 to 0 6.53 -11.97 I-H-V

C2H6 0 to 14 13.25 -15.00 Lw-H-V

-25 to 0 8.46 -9.59 I-H-V

C2H8 0 to 5 -37.75 250.09 Lw-H-V

-25 to 0 7.61 -4.90 I-H-V

CO2 0 to 11 19.20 -14.95 Lw-H-V

-25 to 0 9.29 -12.93 I-H-V

N2 0 to 25 6.19 18.37 Lw-H-V

-25 to 0 4.93 -9.04 I-H-V

H2S 0 to 25 6.78 31.45 Lw-H-V

-25 to 0 8.49 -7.81 I-H-V

Table 2.2: Parameters for Kamaths correlation (1984)3,8 used to calculate the enthalpy of dissociation of pure gas hydrates (∆H = a+bT) in [cal/gmol gas]. H is hydrate, Lw is water, V is guest-rich vapor and I is ice.

2.3 Applications of hydrates

Clathrate hydrates were a laboratory curiosity in the beginning of the 19th century. 9 Their discovery is attributed to Davy (1811) for his work on the hydrates of Cl2 well before the term clathrate hydrate was invented.Three major focus areas are currently driving the research on gas hydrates, namely, flow assurance, natural gas hydrates in sediments, and innovative technological applications exploiting hydrate formation.

During the extraction and transport of hydrocarbons in subsea pipelines, if the required low temperature and high pressure conditions are met, a massive impermeable plug of gas hydrate can form from the dispersed water droplets in oil. This causes a real economic and environmental problem.10 For this reason, hydrates have been considered as a nuisance,

16 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES and the purpose of flow assurance is to avoid hydrate formation.

Gas hydrates and semi-clathrates are now regarded as a promising solution for various industrial processes, they can be used for the transport and storage of natural gas and other gases, for the capture, separation and purification of various gases (such as {CO2), but also as a refrigerating fluid for air conditioning and finally for desalination of seawater.

2.3.1 Natural gas supply

It is known that large amounts of methane are stored in the form of hydrates in the ocean depths. This quantity is estimated at about 2·1022 m3 which is a considerable potential source of energy.11 Natural gas hydrates form within porous sediments containing water and at least 5 to 10 % methane gas. Their stability depends on the concentration of methane as well as the pressure in the medium, this is why the gas hydrate stability zone is located at depths of more than 500 meters where p > 50 bar, i.e. above the equilibrium pressure at 3 – 5 ◦C.

2.3.2 Natural Gas storage

Natural gas hydrates are also a subject of research and development with the aim of storing the gas in the form of hydrates, since much more methane can be trapped in the hydrate than in the gaseous state (about 160 – 170 times the volume of the gas at standard conditions). Natural gas hydrates can be transported at temperatures much higher than the temperature required for liquefying natural gas (-161 ◦Cat atmospheric pressure).

2.3.3 Hydrogen storage

Hydrogen is considered a potential energy for the future. However, storage remains a weak point in the hydrogen industry. Whether in the form of ultra-high-pressure gas or cryogenic liquid, hydrogen storage is expensive, presents significant risks and is limited by a very low density. The ”solid”storage of hydrogen, in the form of metal hydrides[2], in adsorbed form in nanoporous materials or in the form of gas hydrates is a very active field of research.

[2]https://fr.wikipedia.org/wiki/Hydrure

17 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

Hydrogen in fact forms a hydrate of structure sII at high pressures. In the presence of some thermodynamic promoters, this formation pressure can however be reduced con- siderably. The THF H2 mixed hydrate is formed at a pressure of 50 bar at 7 ◦C and the − ∼ concentration of THF in the solution does not modify the amount of H2 stored in the hy- drate. Other organic promotors (acetone, propylene oxide, 1,3-dioxane, 2,5-dihydrofuran) have the same performance as THF with respect to hydrogen storage and enthalpy of dissociation.12

2.3.4 Gas separation

The ability of clathrate hydrates to trap certain gases is equivalent to that of ad- sorption of the best activated carbons and zeolites, membrane separation and cryogenic separation.13,14 The advantage of hydrate separation techniques, compared with conven- tional techniques such as amine absorption or adsorption, is mainly to consume less energy.

The separation method is based on the selective partition of the CO2 component of a fuel or flue gas mixture between the solid hydrate crystal phase and the gaseous phase upon hydrate crystal formation. The significant difference in required formation pressure between different gas hydrates forms the basis for gas separation processes. For example, at 2.5 ◦C, the minimum pressure required to form pure CO2 and pure H2 hydrate are 16 and 3660 bar respectively, and therefore the hydrate formed from a mixture of CO2 and H2 will preferentially contain CO2.

A two-stage hydrate formation process combined with a membrane separation unit can separate a gas mixture initially from 40% CO2 and 60% hydrogen to a gas containing 15 98% CO2 and 96% H2 in the remaining gas. Other studies have shown the possibility of 16 application of hydrates as a means of recovering CO2 from gas mixtures such as (CO2/N2) or (CO2/CH4), since CO2 is the main occupant of hydrate cavities. The addition of an additive such as propane, THF or TBAB makes it possible to reduce the operating pressure without affecting the separation rate obtained. The reader can refer to the reviews of Babu et al14 and Ma et al13 for more details.

18 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

2.3.5 CO2 sequestration

The concentration of CO2 in the atmosphere is constantly increasing due to its emission by the various industries. Approximately 32 billion tons of CO2 were released into the [3] atmosphere in 2015 . CO2 sequestration reduces these quantities by storing CO2 so that it cannot be dispersed into the atmosphere. Two options are possible: geological sequestration or ocean sequestration.

Geological sequestration requires a sufficiently stable and deep underground reservoir, drilling rigs, and high-pressure pumps, which involves high costs and energy consumption. Ocean sequestration, which is debated because of possible environmental impacts, consists in injecting and trapping CO2 into the ocean depths.

Conditions such as temperature at ocean depths (4 ◦C), hydrostatic pressure (50 bar at 500 m deep water) and CO2 hydrate density which is higher than that of seawater, allow the sequestration of CO2 in hydrate form.

The sequestration of CO2 in natural geological or oceanic environment can only be considered in the form of pure CO2 hydrate, since any addition of an additive in large quantities is prohibited for economic as well as environmental reasons, even though certain additives have the advantage of lowering the formation pressure of these hydrates.17 The acidification due to the increase of CO2 concentration in seawater should also be considered.

2.3.6 Refrigeration

The Montreal (1987) and Kyoto (1997) protocols aim to prohibit the industrial use of chlorofluorocarbons (CFCs) and hydro-chlorofluorocarbons (HCFCs) for their serious effects on the ozone layer. In this context, secondary refrigeration processes are intended to greatly reduce the use of these refrigerants in industrial refrigeration.

Conventional refrigeration systems use the same fluid to produce cold, in a compres- sion - condensation - expansion - evaporation loop (Carnot cycle), and to distribute this cold to the points of use.

Secondary refrigeration consists of producing cold in a centralized and confined refrig-

[3]http://www.iea.org/newsroom/news/2016/march/decoupling-of-global-emissions-and-economic- growth-confirmed.html

19 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES eration unit, while the transfer to the points of use is carried out by a secondary loop using a refrigerating fluid that is neutral and respects the environment. This solution minimizes the risk of leakage of the refrigerant and avoids direct contact with users. The use of TBAB semi-clathrate and CO2 hydrate slurries as a diphasic refrigerant has shown promising re- sults in refrigeration and air conditioning.18 This solution offers two advantages. On the one hand, the hydrates have high enthalpies of dissociation, which makes it possible to increase the energy efficiency of the process. On the other hand, the phase transition tem- perature depends strongly on the gas (CO2) pressure (or TBAB concentration in water). It is possible to adjust these parameters in order to adapt the cold production and distribution temperature to the needs of various applications (food preservation, pharmaceuticals, air conditioning, etc.).

2.3.7 Desalination

Several countries suffer from a shortage of drinking water due to population growth and water requirements for industrial and agricultural activities. Conventional water desali- nation/treatment processes such as distillation or reverse osmosis require high maintenance costs, this is why studies are being carried out to check the desalination potential of seawater by processes of hydrate formation and dissociation. By using a proper hydrate formation promoter, the total cost of the produced potable water drops drastically and makes the hydrate formation/dissociation process attractive.19

The process of desalting water through hydrate formation/decomposition involves evacuating the remaining water after forming the hydrate. This remaining water contains more salt, and the salt is known as a hydrate inhibitor. The clathrate hydrate can then be dissociated and pure water phase can be produced while the released guest may be recycled in the hydrate formation unit.

Processes for the formation of CO2 hydrates from seawater are being studied and 20 could have a double advantage; the production of drinking water and the storage of CO2.

Hydrates made up with guests other than CO2 are good candidates for desalination of seawater.21 Propane, for example, appears to have been selected for its formation condi- tions by the Koppers company, which develops a pilot for propane hydrate formation from seawater. This process appears to convert 40 % of the initial water to drinking water.22 A

20 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES particular interest of using an appropriate refrigerant such as R-22 is that the hydrate is 23 formed at lower pressures, below 8 bar, for a temperature up to 14.4 ◦C.

2.3.8 Other gas hydrate applications

The use of gas hydrates in biotechnology applications is relatively new and promising, particularly in controlling enzymes in biological systems, recovery of proteins, and drug delivery systems. Concentrating orange, apple and tomato juices through CO2 hydrate is an efficient technology for food industry.24–29

Hydrates may be present in several places where thermodynamic conditions are favor- able, such as in drilling muds, oil deposits, wet natural gases, inside the Earth’s crust and in the Universe (Mars and Saturn). Their presence in these places involves other applications that are under study and development.

For more details on gas hydrate applications, the reader may refer to reviews of Eslamimanesh et al.30 and Kouh et al.31

21 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

2.4 Gas Hydrate formation, growth and dissociation

The development of sustainable hydrate management strategies in oil and gas flowlines, as well as in the various applications detailed above, requires to expand our basic knowledge of the interactions between water and hydrate formers. This is why studying hydrate formation is necessary and very important.

Generally, hydrate formation is a series of two processes, nucleation and then stable growth.32–36 Gas hydrate nucleation and growth have been investigated experimentally using different techniques and mathematical formulations have been derived to describe the acquired data.37 At the molecular level, nucleation processes which are characterized, on the one hand by small length and time scales and on the other hand by its stochastic nature, are very difficult to be determined and studied experimentally. For this reason, there have been increasing efforts to obtain this information using molecular simulations.38 Due to the stochastic and time-dependent nature of clathrate hydrate nucleation and growth, there is still a lot of ongoing scientific discussion pertaining to these issues. In the next sections, the theoretical background of hydrate nucleation and growth are presented.

2.4.1 Thermodynamics of crystallization

A solute is the minority chemical species that is dissolved in the liquid, called a solvent. The solubility of a solute is its maximum amount that is dissolved in a fixed volume of solvent at a given temperature and pressure. When this maximum is reached, the solution (liquid solvent + solute) is saturated.

By definition, a system is in thermodynamic equilibrium when the free molar Gibbs free energy G is minimal at a given temperature T and pressure p, that is to say:

m dG = Vdp SdT + µidni (2.10) − i ∑ with V the molar volume, S the molar entropy, m the number of solute species, ni and

µi are the number of moles and chemical potential of solute i respectively. If we consider the transformation of a solute from a solubilized state (L) to a solid state (S), at constant pressure and temperature,

22 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

m L L + S S dGT,p = (µi dni µi dni ) (2.11) i ∑ In a closed system, the number of moles of a given species remains constant, hence the following condition holds at equilibrium:

µL µS = 0 (2.12) eq,i − eq,i

The chemical potential µi of component i governs the interchanges between phases as well as the chemical transformations. Out of equilibrium, the solute prefers to migrate L S where its chemical potential is the lowest. For a given solute, if ∆µi = µ µ < 0, then the i − i L S system is under-saturated and the solute is solubilized in the liquid. If ∆µi = µ µ > 0, the i − i system is in the state of supersaturation and tends to return to the equilibrium condition by crystallizing the solute. The difference in chemical potentials ∆µi is thus the driving force of crystallization. In this case, the concentration of the solute, called Cexp, is then necessarily higher than the solubility at equilibrium Ceq under the same conditions of temperature and pressure. The supersaturation governs the nucleation and growth processes and determines the purity, morphology and size of the crystals. The driving force of crystallization, equal to the deviation from the equilibrium of the chemical potential as the expression below:

aL L L exp,i µ µ = RTln = RTexp lnS (2.13) exp,i − eq,i L aeq,i

L L where R, aexp,i and aeq,i are respectively the gas constant, the solute activities in the liquid phase at experimental condition and at thermodynamic equilibrium, S is the supersaturation. At low concentration, assuming that the ratio of activities tends to 1, supersaturation is expressed in different ways:

• ∆C = Cexp Ceq: absolute supersaturation (frequently used in industry), −

• S = Cexp/Ceq: the supersaturation ratio,

• σ = (Cexp Ceq)/Cexp: relative supersaturation or degree of supersaturation −

A correct definition of supersaturation is the basis for the modeling of nucleation and growth kinetics. However, its expression remains unclear in the hydrate research domain.

23 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES and many expressions derived from the initial definition of driving force are used (see Table 2.4.1).

Investigators Year Driving force

32 Vysniauskas and Bishnoi 1983 Teq Texp − Skovborg and Rasmusse34 1994 µH µL exp,w − exp,w Natarajan et al.35 1994 (fG fG )/fG exp − eq exp

Christiansen and Sloan 1995 ∆gexp

Kashchiev and Firoozabadi39 2002 ∆µ supersaturation

40 Anklam and Firoozabadi 2004 ∆gexp

41 Arjmandi et al. 2005 Teq Texp −

Table 2.3: Different driving forces used for hydrate nucleation.3 H Teq and Texp are respectively the equilibrium and experimental temperatures; µexp,w and L µexp,w are the chemical potential water molecules, respectively, in the aqueous phase and G G the hydrate phase; feq and fexp are respectively the equilibrium and experimental fugacities of guest molecules in vapor phase; gexp is the molar Gibbs free energy during the hydrate formation.

Christiansen and Sloan (1995) proposed a driving force for isothermal path equal to the molar changes of the total Gibbs free energy during the hydrate formation,

m fG H w eq,i ∆gexp = ∆Gexp/nw = (pexp peq)(v v ) + RTexp xi ln (2.14) − − G i fexp i ∑ , where vw and vH are the molar volumes of the aqueous phase and the hydrate phase G G respectively, feq,i and fexp,i are the gas fugacities of component i in the gas mixture at equilibrium and during crystallization. xi = ni/nw is gas fraction and ni and nw are the number of moles of water and gas consumed respectively. An interesting virtue of this driving force expression is that it can be applied to multicomponent gases.

The driving force for hydrate formation is a function of pressure, temperature, and gas composition. For a given guest molecule and pressure, the driving force can be expressed as the supercooling (commonly called subcooling in the literature on gas hydrates), defined as

24 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

∆T = Teq Texp (2.15) −

where Teq is the hydrate dissociation temperature at this pressure and Texp the system temperature.

The study of Tohidi and his coworkers41 on the relationships between supercooling and the driving force shows that for pure gas + water systems and over a wide pressure range, supercooling is a good representative of driving force. The same study shows also that, at a constant degree of supercooling, the pressure has no significant effect on the driving force above a certain pressure range.

2.4.2 Hydrate nucleation

The appearance of a solid requires the creation of nuclei which constitute the embryos of future crystals. Hydrate nucleation takes place under several mechanisms that can be classified into two groups. The first concerns the so-called primary nucleation, which takes place spontaneously in an aqueous solution free of hydrate. The second is the so-called secondary nucleation, which is achieved through the active participation of neighboring hydrate crystals (see Figure 2.1).

�����������

������������������ �������������

����������� ���������

�������������������� ������������������� ��������������

��������������

Figure 2.1: The different forms of nucleation.

25 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

2.4.2.1 Primary nucleation

Primary nucleation is the appearance of the first hydrate crystal able to grow further to macroscopic sizes. When the aqueous solution is supersaturated with gas, the chemical potential of dissolved gas is higher than that of the enclathrated gas. This difference in chemical potentials promotes aggregation of water and gas molecules to form a hydrate nucleus. Two approaches leading to nucleation can then be considered. The first consid- ers that the solvated molecules condense abruptly to form a stable or unstable aggregate according to its size. The second approach considers that nucleation consists of a series of condensations: the nucleus grows as entities are added and remain invisible to the experi- menter.42 Until this nucleus reaches a critical size, the nucleus remains unstable: it forms and dissolves rapidly and has a very short lifetime. It is according to this last approach that Volmer and Weber (1926) built the basis of their model.3 The birth of these nuclei involves the creation of a volume and therefore a surface that surrounds this volume, which involves two antagonistic Gibbs free energies. Their resultant ∆G achieves, as the process progresses, a maximum ∆Gcr, which corresponds to the creation of a hydrate germ of crit- ical size rcr (Figure 2.2). If we assume that the germ is spherical and of radius r, its Gibbs free energy is written:

3 2 4 r ∆G = ∆Gsurface + ∆Gvolume = 4πr γ π kBTlnS (2.16) − 3 vm where vm is the molecular volume equal to the ratio of molar volume of hydrate phase and the Avogadro constant, γ is the surface tension between hydrate crystal and water, S is the ratio of supersaturation, kB is Boltzmann constant.

At the beginning of the process, i.e. for small nuclei, r < rcr), the term ∆Gsurface, proportional to the square of nucleus’ radius, dominates so that the nucleus tends to shrink and dissolve. Then, as aggregation of nuclei increases with increasing supersaturation

(or driving force), the term ∆Gvolume, proportional to the cube of the nucleus’ radius, counteracts the effect of ∆Gsurface until reaching the critical value ∆Gcr. At this stage, the hydrate germ is in unstable equilibrium. It grows or dissolves depending on whether an entity is added (r > rcr) or removed (r < rcr), because in both cases there is a decrease of the Gibbs free energy of the system. The derivative of Gibbs free energy is null at r = rcr). There is thus a metastable zone in which the nucleation is not spontaneous (see Figure

26 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

"#$%&'()

∆

"(% .(% . ∆ /"

"*+,$-)

∆ Figure 2.2: Gibbs free energy of homogeneous nucleation as a function of the radius of the nucleus.

2.3). The limit of this zone will be discussed in Chapter 4.

������������ ���������� �������������

�����������

Figure 2.3: The metastability zone where hydrate nucleation is not spontaneous. This zone is bounded by the three-phase equilibrium (Lw – H – V) line and the metastable limit (see Chapter 4).

The nucleation is homogeneous if hydrate nuclei are created in the bulk of water. It is heterogeneous if the nuclei appear on the surface of a solid phase with physical or chemical nature different from that of hydrate crystal (such as the reactor wall, agitator, and impurities in water) or at the water - gas interface (see Figure 2.4). The presence of a third phase lowers the interfacial energy necessary to overcome in nucleation phenomenon

and thus reduces ∆Gcr. When we consider the system free energy, it is more favorable to form hydrate on a two-dimensional surface than a three-dimensional nucleus in bulk water phase.37

The water - gas interface remains the most likely place where the initial hydrate pri-

27 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

���

� �������� � �������� � ���������

Figure 2.4: Schematic of primary nucleation mechanism: homogeneous nucleation of a spherical crustal hydrate in the bulk water (a), heterogeneous nucleation of cap-shaped hydrate crystal on the substrate surface (b) and heterogeneous of lens-shaped hydrate crystal at the water - gas interface (c).

mary nucleation can take place. Indeed, the supersaturation is maximum, which promotes the formation of hydrate crystals. Many authors confirmed experimentally this initial nu- cleation site.3 The agitation then disperses the first hydrate crystals in the liquid water giving the impression that the nucleation occurs in its bulk. After this primary nucleation, hydrate crystals continue to arise both at the gas-liquid interface and in the bulk of water by secondary nucleation (see below).

Due to the significant metastability exhibited by the system (water + hydrate former) when cooled to a temperature below the equilibrium hydrate formation temperature, the nucleation of hydrates is not observed during a certain period (Figure 2.3). This time interval separating the moment when the aqueous solution is in supersaturated state from that in which the first hydrate nuclei of critical size appears is called the induction or lag time. Several factors can reduce this waiting time such as stirring speed, reactor wall, and impurities in water, increasing supercooling or pressure.38,43

Water from a recent hydrate dissociation results in faster nucleation of the hydrate and lower supercoolings are required: this phenomenon is called the memory effect.44 Three attempts to explain the memory effect have been proposed:45

• The dissociation of the hydrates results in a rapid increase in gas content in water, which makes the solution supersaturated with possibly nanoscopic bubbles which then serve as a nucleation site.46,47

• After dissociation of the hydrate, some partial hydrate cages or polyhedral clusters persist for a long time. Further lowering temperature, these residual structures can

28 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

agglomerate and form new nuclei.48–50

• In the case of heterogeneous nucleation, the hydrates can alter and leave imprints on the soft surface bearing hydroxyl groups, surface water, and the hydrate surface (hydrated or hydroxylated silicon or iron oxides). After dissociation, these imprints are nucleation sites of the hydrate.51

Although its fundamental reasons are not yet well defined, the memory effect has a very important practical role, because it can be used to facilitate hydrate formation. In our experiments, we have benefited greatly from this effect in the study of the propagation of hydrate films on the substrate called halos (see Chapter 3) and in the rapid determination of hydrate phase diagrams (Chapter 5). However, in the study of nucleation, we had to eliminate this effect by maintaining the system at a temperature well above the equilibrium and for a sufficiently long time in order to eliminate any memory effect (see Chapter 4).

Primary nucleation is typically dominant only during the startup phase of a non-seeded crystallization process,

2.4.2.2 Secondary nucleation

The exact mechanism of this generation is not well defined. It gives rise to divergent interpretations: microattrition, dislocations, energies locally dissipated by collisions. We can distinguish three types of secondary nucleation: apparent (surface), true (catalytic), and contact.52

Apparent secondary nucleation occurs when the hydrate particles are already present in aqueous solution (seed crystallization). These are small fragments removed (torn) from the surface of particles larger than the critical size. These are therefore stable, and become new centers of hydrate growth.

Catalytic nucleation involves mechanisms where the nuclei are created by interaction between a hydrate crystal and water. The presence of hydrate crystals disrupts the equilib- rium of the nuclei present in the aqueous solution and allows aggregates smaller than the critical radius rcr to evolve towards a stable nucleus.

Finally, secondary contact nucleation is caused by the collision of a growing hydrate crystal with another solid surface, such as the stirrer, reactor walls or a second hydrate

29 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES crystal.

Makongo and his coworkers53 observed by using photomicrographs crystals of methane hydrate nucleate on the water – methane interface. Near each primary hydrate crystal, other secondary crystals appear. Below these secondary crystals, additional crystals appear and grow in the bulk of water. The crystals retained their boundaries which allowed the experimenters to determine their number, size and orientation and to develop a model for secondary nucleation.

2.4.3 Hydrate growth

After nucleation, the hydrate nuclei evolve spontaneously towards a thermodynami- cally more stable state corresponding to an increase in their size by incorporation of water and guest molecules and this as long as the supersaturation remains sufficient. The hydrate forms and grows rapidly laterally along the water - guest-rich fluid interface but also much more slowly perpendicularly to this interface. Numerous results have been collected on lateral growth rate as a function of supercooling and guest molecule. The measurement of lateral growth rate of hydrate films is somewhat easier than that of thickening rate.54–70 Although considerable efforts have been devoted to theoretically interpreting and model- ing the experimental kinetic data,33,34,56,57,60,71–81 the mechanisms of crystal growth, in general, are still not well known.

The hydrate crystal growth is controlled by the combination of three transfer pro- cesses, each characterized by its own kinetics. Growth is usually assumed to take place in the aqueous phase.

• Transport of the gas molecules to the surface of hydrate crystal (diffusion step),

• Integration of gas molecules into the crystal lattice (integration step, which includes several sub-steps),

• Release and dissipation of crystallization heat.

The crystallization of the hydrates is exothermic and this heat must thus be dissipated away from the growing hydrate surface. If the temperature exceeds the equilibrium temper- ature, and the heat dissipation is not fast enough, it can limit the overall growth rate. In

30 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES crystallization, it is generally considered that heat transfer is very rapid.72 The global rate of hydrate crystal growth is limited by the slower of the two processes. When mass transfer (by diffusion) is the limiting process, the crystal growth takes place in a ”diffusional”mode. However, if the integration of the solute into hydrate lattice is the limiting process, then the hydrate growth takes place in an integration mode or in a ”chemical”regime.3

Scientists tend to explain crystal growth with theories based on thermodynamic equi- librium. In the crystallization industry for the purpose of using these hydrates in several applications as described above, kinetics (growth rates) are more important to investigate. In general, it is assumed that the crystal growth step presents a layer-by-layer process, by this way gas and water molecules will bond in a most energetically favorable site on the forming crystal surface.82 The theory of surface energy is based on the assumption that the shape of a growing crystal minimizes its surface energy. The theory of diffusion assumes that the solute molecule is deposited continuously on the face of the crystal with a velocity proportional to the difference in concentrations between that in the liquid and that at the liquid-crystal interface. Until now, it is considered that hydrates may grow as: a single crystal, a film at the water - guest-rich phase interface or multiple crystals in a stirred system. The most important models, based on the kinetics of growth, the mass transfer and the heat transfer processes, have been recently reviewed by Ribeiro and Lage,83 Sun et al.84 and Mochizuki and Mori.72

31 CHAPTER 2. BIBLIOGRAPHY ON CLATHRATE HYDRATES

2.5 R´ef´erences

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40 Chapter 3

Roles of wettability and supercooling in cyclopentane hydrate spreading over a substrate

Contents Abstract ...... 42 3.1 Introduction ...... 43 3.2 Materials and Methods ...... 47 3.2.1 Materials ...... 47 3.2.2 Experimental configuration ...... 47 3.2.3 Glass wettability and thin layers on the glass ...... 48 3.2.4 Experimental procedure ...... 50 3.3 Results ...... 53 3.3.1 Halo morphologies and initial velocities ...... 53 3.3.2 Strong slowing down of the halo front ...... 60 3.3.3 Substrate wettability effects ...... 61 3.4 Discussion of halo growth mechanisms ...... 64 3.4.1 General considerations ...... 64 3.4.2 Linear regime of halo growth ...... 65 3.4.3 Halo propagation beyond the break point ...... 68 3.5 Conclusions and outlook ...... 71 3.6 Références ...... 74

41 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE Abstract

We use transmission optical microscopy to observe cyclopentane hydrate growth in sub- mm, open glass capillaries, mimicking cylindrical pores. The capillary is initially loaded with water and the guest fluid (cyclopentane) and thus possesses three menisci, that between water and cyclopentane (CP) in the middle, and two menisci with the vapors at the ends. At temperatures T below the equilibrium temperature Teq 7 ◦C, the hydrate nucleates on the ≈ water-CP meniscus, rapidly coating it with an immobile, polycrystalline crust. Continued movement of the other two menisci provides insights into hydrate growth mechanisms, via the consumption and displacement of the fluids.

On water-wet glass, the subsequent growth consists of a hydrate ’halo’ creeping with an underlying water layer on the glass on the CP side of the meniscus. Symmetrically, on CP-wet glass (silane-treated), a halo and a CP layer grow on the water side of the interface. No halo is observed on intermediate wet glass.

The halo consists of an array of large monocrystals, over a thick water layer at low supercooling (∆T = Teq T below 5 K), and a finer, polycrsystalline texture over a thinner − water layer at higher ∆T. Furthermore, the velocity varyies as ∆Tα, with α 2.7, making ≈ the early stages of growth very similar to gas hydrate crusts growing over water – guest interfaces. Beyond a length in the millimetre range, the halo and its water layer abruptly decelerate and thin down to sub-micron thickness. The halo passes through the meniscus with the vapor without slowing down or change of texture. A model of the mass balance of the fluids helps rationalize all these observations.

42 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE 3.1 Introduction

Gas hydrates are non-stoichiometric crystalline solids made up of cages of water (host) molecules trapping ’guest’ molecules at low enough temperature or high enough pressure.

Important guests include CO2,N2, CH4 and other low-molecular-weight hydrocarbons. Long considered a nuisance because they may plug natural gas pipelines, they are now viewed as promising materials for applications as diverse as gas storage and separation, secondary refrigeration and waste or salted water treatment. The stability of hydrate- bearing sediments is controlled by that of the natural gas hydrates present, as is gas recovery from those sediments. In many of these situations or applications, substrates are present and play an important yet poorly understood role, which motivates the present microscopy study of the spreading of the model system, cyclopentane (CP) hydrate, in the simplest of pores - round glass capillaries.

Gas hydrates usually nucleate at a water-guest interface, and then rapidly spread over the interface as a thin polycrystalline film, the crust, whose morphology and growth have been thoroughly investigated over the past two decades.1–10 The transport of water and guest molecules is extremely slow across this crust, which thus thickens very slowly.1 Gas hydrates may also expand from this crust into the bulk of the aqueous or the guest-rich phase.11–14

In what follows, it will be useful to keep in mind the salient features of this process. For given guest molecule and pressure, the driving force is supercooling (commonly called subcooling in the literature on gas hydrates), ∆T = Teq T, where Teq is the hydrate − dissociation temperature at this pressure and T the system temperature. Supercooling is the equivalent of the salt supersaturation of strongly salted aqueous solutions, which drives salt crystallization.15 With increasing supercooling, the crystallites are smaller, resulting in a smoother crust, and the rate of lateral growth over the water-guest interface increases 2,5,8,9 strongly. The rate also increases when the guest is more soluble in water, e.g. CO2 10 hydrate crusts advance faster over water than CH4 hydrate crusts at similar ∆T, pointing to the role played by guest solubility in water.4,6

Solid substrates promote gas hydrate formation.16–21 For example, hydrophobic sub- strates promote nucleation at the mineral-water-guest contact line and subsequent growth of gas hydrate, possibly because of local gas enrichement and ordering of the water molecules

43 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE very near the substrate.21 But hydrophilic particles, such as glass beads or other oxide par- ticles, are also known to accelerate conversion into hydrate, as inferred from macroscopic measurements, such as gas consumption or heat release,16,17 rather than by direct obser- vations. The roles of the wettability, surface area and size distribution of solid particles, or of pore size distribution in the case of mesoporous particles, are still poorly understood.

Some progress was made in experiments conducted on model substrates, starting with flat substrates. It is a common observation that gas hydrate creeps on glass or sapphire windows, above the contact line of the water-guest interface.22–24 Beltr´anand Servio25 coined the term ”halo”for gas hydrate growing on solid substrates. These authors observed methane hydrate halos creeping out of the contact line of water drops sitting on flat glass under methane, just after completion of a hydrate crust over the drop surface, and then radiating widely, thus propagating hydrate formation to the neighboring drop – the ”bridge effect”.

Viewed growing over a flat substrate, such hydrate halos are hard to detect by trans- mission microscopy, and Beltr´anand Servio plausibly assumed that the water needed for halo growth (feed water) was drawn from the drop to the halo front by capillarity in a thin gap between the glass and the halo, in a manner similar to the so-called ’bottom-supplied creeping’ process by which some salt crystallites grow on glass walls from a reservoir of saturated aqueous solution such as a sessile drop.26–29

Phase contrast and fluorescence microscopy already provided a more detailed view of cyclopentane hydrate halo growth on flat glass.30 Feed water was shown to be already present on the substrate in the form of a precursor film or droplets, and to come from the overlying guest phase by ’fog’ settling and antisublimation. Substrate wettability was also shown to strongly impact the existence and growth rate of these halos: rapid lateral growth was observed under the guest fluid over water-wet (hydrophilic) substrates, vs. no growth over hydrophobic silane-treated glass,30 in agreement with previous observations by Jung 31 32 21 and Santamarina and by Esmail et al. Nguyen et al recently observed CO2 hydrate growing from the contact line along a hydrophobic glass-water interface.

In practical situations solid substrates are curved, with radii of curvature or pore sizes ranging from tens of microns in highly-permeable sediments, to nanometers in some mesoporous particles used as hydrate promoters.33 A few observational studies in water-

44 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE wet (glass or silicon) micromodels with pore or channel dimensions in the 10-100 µm-range showed complex growth processes, including nucleation at water-guest interfaces followed by growth over the water films wetting the substrate.34–36 These processes control the filling of the pore space by gas hydrates, and ultimately the flow and mechanical (macroscopic) properties of the hydrate-bearing porous medium.37 They also influence mineral–hydrate adhesion.38

Here, we report optical transmission microscopy of cyclopentane (CP) hydrate halos creeping out of the water–cyclopentane meniscus in open round glass capillaries, with the purpose of understanding how substrate wettability and supercooling influence the spread- ing of a hydrate on a solid substrate. CP is very sparingly soluble in water and similarly to natural gas, it forms a structure II hydrate, stable at temperatures below Teq 7 ◦C and ≈ at atmospheric pressure, which considerably eases its handling. For these reasons it has been widely used in many fundamental studies and considered a proxy of natural gas hy- drates.39,40 There are indeed many similarities between both hydrates, but also differences, notably when the nature of the guest phase, liquid or vapor, is involved.41 We therefore draw the reader’s attention to the due caution called for before carrying over all conclusions of studies of CP hydrate to the more common gas hydrate systems.

The experimental configuration has many advantages from both fundamental and practical standpoints. From a fundamental standpoint, round glass capillaries mimic model (cylindrical) pores, and therefore insights into how hydrates grow and fill the porous space in highly-permeable sediments are to be expected. From a practical standpoint, glass capillaries are available at low cost in a large range of shapes (round, square, rectangle, etc.) and sizes, from microns to millimetres. Their wettability can be easily adjusted, e.g. in this study by means of silane chemistry. They are relatively good conductors of heat, so that their interior rapidly adjusts to a change in external temperature, and they are available with good optical quality. In round capillaries, refraction effects provide a ”help from a hindrance”for detecting ultra-thin (submicron) films such as the halo, provided the capillary section is appropriately chosen.42

The Materials and Methods section (cf. 3.2) presents the round glass capillaries and how their wettability was altered by silane treatment and characterized by contact angle measurement, as well as the experimental configuration and procedure. The Results section presents the morphologies and growth rates of cyclopentane hydrate halos advancing either

45 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE over water-wet or over cyclopentane-wet, i.e. hydrophobic capillaries, as a function of temperature. The proposed mechanisms of halo growth are then discussed and compared to the much better characterized mechanisms of gas hydrates growing over water-guest interfaces. Some remaining questions and prospects are addressed in the ”Conclusions and outlook”section.

46 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE 3.2 Materials and Methods

3.2.1 Materials

10 cm-long cylindrical capillaries in fused silica (hereafter loosely called ”glass”) were used as received from VitrotubesTM. The inner and outer diameters, ID = 2R = 200 µm and OD = 330 µm, ensure that even ultra-thin (submicron) hydrate of water layers lying against the inner wall of these capillaries are readily revealed by simple transmission microscopy (cf. 3.2.3). We used deionised water (resistivity > 18 MΩ cm, PureLab Classic from ELGA Labwater) and cyclopentane (98%+ purity, Aldrich).

In some experiments, the capillaries were rendered hydrophobic (oil-wet) by a silane 43 2 treatment adapted from Dickson et al. A solution of 10− M dichloro-dimethyl-silane in dry cyclohexane (both Aldrich) was introduced by capillary rise and left for one hour under inert N2 atmosphere. Unreacted silane was removed by rinsing repeatedly in pure dry cyclohexane. Finally the capillaries were washed in absolute ethanol and dried at 110 ◦C for 30 min.

3.2.2 Experimental configuration

Capillaries were loaded with pure water and cyclopentane by plunging one end through the interface of these two liquids in a beaker; cyclopentane climbs by capillarity first, fol- lowed by water. The two liquids each occupy a few millimeters separated by the water- cyclopentane meniscus. A vapor-water and a cyclopentane-vapor meniscus are thus also present (see Figure 3.1). Unless otherwise specified, the capillary is left open on both sides. The lengths of the liquid columns can be adjusted by controlling the residence times of the capillary end in each phase or by evaporation after loading.

It might be thought that when being displaced by the water in the loading process, some cyclopentane could remain on the capillary wall, e.g. as a thin residual film between the water and the glass. In this case, high apparent contact angles, θ, of the water-cyclopentane meniscus with the wall (figure 1), would have been noted, as well as a strong hysteresis, or difference between the values of θ when the meniscus is moving in one direction or the other. We did not observe these features (see next section). In addition, the contact angles of the water-vapor meniscus with the wall were observed to be similar in a capillary loaded

47 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE

with water alone, that was then dried and loaded through cyclopentane, as above.

��� θ � ����� ����� �� �����

������������ ��������������� �����������

����� �� ����� �� � ��� ���

Figure 3.1: Schematic view of a capillary loaded with water and cyclopentane (a), with a zoomed-in view of the meniscus at 0 ◦C in the case of an untreated glass capillary (b), contact angle, θ = 13 ◦, and a silane-treated glass capillary (c), θ = 106 ◦.

Capillaries loaded with water and cyclopentane were placed in a heating-cooling stage (Linkam CAP500, with LINKSYS temperature control software). An important feature of this stage is a rack and pinion that slides the capillary up to 2.5 cm along its axis in a narrow groove cut in a silver slab that ensures good thermal homogeneity. The capillary is viewed through a small hole at the centre of the slab and centred on the optical axis. Temperature

is controlled to within ±0.2 ◦C in the interval of interest, from about 40 ◦C to 20 ◦C. The − microscope, an Olympus B50, is used here in transmission mode. Camera images (Ueye UI 3360), the time and the temperature (from LINKSYS) are stored in video format by means of a home-made software application developed in C++ with the QT suite.

3.2.3 Glass wettability and thin layers on the glass

Most of the observations reported here were carried out in the vicinity of the meniscus between water and cyclopentane (figure 1), which was checked at the start and the end of each cycle of hydrate formation. Its shape is a spherical cap, unaffected by gravity, because 1/2 it is much smaller than the capillary length, (σwg/g∆ρ) 4.5 mm, where σwg 51 ≈ ≈ mN/m44 and ∆ρ 0.25 g/cm3 are the interfacial tension and density difference between ≈ liquid water and cyclopentane, and g is the acceleration due to gravity. In each experiment,

48 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE glass wettability was assessed from the contact angle of the meniscus with the glass wall, θ, measured in the water phase (Figure 3.1a), inferred from h, the height of the meniscus cap (negative for angles larger than 90 ◦), and R=ID/2, the internal radius of the capillary:

R2 h2 tanθ = − (3.1) 2Rh

In the untreated glass capillaries used in this study, θ is observed to be small, denoting strong preferential wetting by water, figure 3.1(c) These angles are reported for each experiment in Table 1. In the silane-treated glass capillaries, θ is slightly above 90 ◦, and increases slightly with decreasing temperature, from θ 100 ◦ at T = 0–10 ◦C, figure 3.1(c), to 124 ◦ ≈ at 10 ◦C and 150 ◦ (cyclopentane-wet) at 20 ◦C, figure 3.2 Note that refraction enlarges − − the apparent capillary inner diameter and that the contact angle cannot be deduced by merely drawing a tangent on an image of the meniscus at the contact line. See the Annex B for the correction of this aberration.

w CP

T = 10 °C 0 °C -10 °C -19 °C θ = 103 ° 104 ° 124 ° 147 °

Figure 3.2: Photographs of a meniscus between water (left) and cyclopentane (right) in a silane-treated capillary at various temperatures from 10 to 19 ◦C, showing the increase in − contact angle with decreasing temperature.

Importantly, refraction produces bright reflections (cusps) on the inner wall of the capillary when the conditions are met for total internal reflection of the impinging light rays. These conditions were provided by Hobeika and coworkers42: the refractive index n of

49 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE the material lying against the inner wall must not exceed a certain limit that depends only on the refractive index of the glass wall, ng, and on the ratio of the inner to outer diameters, ID/OD. This limit refractive index can be calculated from the laws of refraction and is found to be 1.36 with our values of ng 1.46 and ID/OD=200/330=0.606. Therefore, in ≈ contact with water or cyclopentane hydrate (n 1.33–1.36), the inner wall appears as a ≈ bright cusp, whereas it is barely visible when covered with cyclopentane (n 1.41) due to ≈ the very weak internal reflection. The bright cusps for n < 1.36 remain bright provided the thickness of the material lying against the wall exceeds the penetration depth of the illuminating light, 140 nm for the glass-water-hydrate system of interest. When the layer ≈ thickness decreases below this penetration depth, so does the intensity of the bright cusp, which however remains visible for thicknesses commensurate with this depth.42 Thus, a 100 nm film of water or hydrate intruding between the cyclopentane and the glass is ≈ conspicuous due to its associated cusps.

3.2.4 Experimental procedure

The capillary loaded with water and cyclopentane is submitted to cycles of tempera- ture variation around the equilibrium temperature Teq=7 ◦C, while video-recording hydrate formation and growth at T < Teq and dissociation at T > Teq. Remember here that direct hydrate formation from liquid water and CP would require extremely long waiting times, especially with the small volumes involved. In practice, it is necessary to pass through ice for forming hydrate for the first time. Accordingly, the temperature sequence in all experi- ments is as shown in figure 3, which also shows snaphots of the water-CP meniscus in the case of a water-wet capillary:

i) The sample is cooled from TR 20 ◦C, inset figure 3.3(a), until the sudden for- ≈ mation of ice (initiation to completion in less than 1 s) occurring at TI 20 to 40 ◦C; ≈ − − the ice has a grainy, polka-dotted texture due to air or CP inclusions; rapid ice growth from the inner wall to the center of the capillary induces some displacement and deformation of the water-CP meniscus, in the form of a protuberance pointing towards the CP, inset (b)

ii) When T is raised to slightly above 0 ◦C, the ice is seen to melt and a distinct solid of CP hydrate rapidly forms as a crust at the interface between CP and melt water, keeping

50 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE

��� ��� �� ���� � ��

��� ��� ∆������� � � � �� ����

�� ��� ��� �

����������� ���

�� ���

� � �� ��� �� ����

Figure 3.3: Typical temperature profile in a CP hydrate formation and dissociation experiment. Shading is to better distinguish the different steps. Images (e) and (f) show the hydrate halo creeping on the capillary inner wall, under cyclopentane, with the arrows indicating the growth direction. W: water. CP-E: cyclopentane emulsion in water. FH: first hydrate halo. SH: second hydrate halo.

roughly the same shape as that of the ice-CP interface just before ice melting. Subsequent hydrate growth is controlled by substrate wettability and supercooling, inset (c)

iii) The CP hydrate is next melted by raising the temperature to above Teq = 7 ◦C, which gives rise to an emulsion of CP droplets in water; these droplets rise buoyantly to the top of the capillary, inset (d)

iv) Shortly after hydrate dissociation, a second formation is triggered at the water-CP

meniscus (and from the emulsion) by lowering T to below Teq, to a given supercooling 45 ∆T = Teq T. By virtue of the memory effect, there is no need to go through the − ice formation and melting steps. Once the meniscus is covered with a hydrate crust, the spreading of the halo onto the substrate is controlled by supercooling and by substrate wettability, see insets (e) and (f) for water-wet glass.

Carrying out this second hydrate formation and growth allows these processes to be

investigated in the absence of ice, in supercooled water down to 10 ◦C, or a supercooling − of 17 K. The absence of ice was attested by the fact that on warming the samples, there

51 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE was no change in the texture of the solid phase until reaching the dissociation temperature of CP hydrate ( 7 ◦C). The sequence of hydrate melting (iii) and formation and growth ≈ at a different supercooling, ∆T,(iv), can be repeated.

The growth processes that follow the completion of the hydrate crust on the water- cyclopentane meniscus are presented and discussed in the next section. In addition to observing the neighborhood of what initially is a meniscus between liquid water and CP, the positions of the two other menisci with the vapors may be followed. Unlike the water- cyclopentane meniscus, they are mobile and their motion, much slower than that of the halo, provides information on the consumption of water and CP and on the mechanisms of hydrate halo growth.

52 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE 3.3 Results

All experiments except those in the last subsection were carried out in untreated, hence water-wet, glass capillaries.

3.3.1 Halo morphologies and initial velocities

In water-wet capillaries, the hydrate halo is observed to systematically advance along the capillary wall on the guest (cyclopentane) side of the meniscus (see Figures 3.3 through

7). Its morphology and lateral velocity Vh depend very strongly on the supercooling ∆T, as illustrated in Figure 3.4, which gathers snapshots of hydrate halos grown to the same distance from the contact line, 0.45 mm, at ∆T from 2.8 to 13 K. We focus first on ≈ morphologies, then on lateral velocities.

Halo morphologies For the mildest supercoolings, e.g. for ∆T = 2.8 K in Figure 3.4, the halo consists of an assemblage of large, plate-like or polygonal crystals. Contrary to the intimate contact between the halo and the glass in our observations of propagation on a flat substrate, the poor tiling of the wall by the large crystals leaves a wide gap between the hydrate halo and the glass. Spreading of the halo on the cyclopentane side is fed by a layer of water flowing through this gap, as is attested by observation of occasional migration of small hydrate crystals or cyclopentane emulsion droplets, see movie M1 in the Supporting Information.[1] The water layer is thicker at lower supercooling. The contact line of the water layer in the gap with the glass wall lies constantly slightly ahead of the edge of the halo (boxes in the top panel of figure 3.4) and the contact angle, θ, is similar to that in the absence of the hydrate halo, see previous section.

On increasing supercooling (decreasing T), the hydrate halo advances as an assem- blage of small crystallites that nucleate at numerous locations at the halo front (secondary nucleation events),46 hence growing each to smaller size and giving rise to a smoother halo, similar to what is observed for hydrate polycrystalline crusts formed along water-guest in- terfaces.2,8–10,47 The hydrate halo grows closer to the glass wall, and the liquid water layer sandwiched between the halo and this wall is too thin to be visible under our microscope

[1]The Supporting Information is available free of charge on the ACS Publications website at http:// pubs.acs.org/doi/suppl/10.1021/acs.langmuir.7b02121/suppl_file/la7b02121_si_002.avi

53 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE

�������∆������� ���∆��������� �������∆����� ���∆��������

��������∆����� ���∆������� ��������∆����� ���∆�������

��������∆���������∆������� ��������∆� ���� ���∆�������

Figure 3.4: Snapshots of hydrate halos grown in cyclopentane to similar distances from the water-cyclopentane meniscus ( 0.45 mm) along the glass capillary wall at various temperatures ≈ or supercoolings. ∆t is the time elapsed since the halos have started advancing from the meniscus. The boxes in the two upper images highlight how the water layer between the hydrate halo and the wall leads slightly on the halo.

54 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE

(see Figure 3.4). However, due to the proper choice of capillary dimensions, the hydrate halo and the water layer cause a bright cusp on the inner wall (see subsection 3.2.3), so that their presence and lateral advance along the glass can be precisely monitored.

Qualitative evidence for halo thickening with time could be obtained by subtracting images of the same growing halo captured at different times. Hydrate halos have been shown from previous high-resolution microscopy investigations in our laboratory to thicken very slowly, at a rate in the order of a few nanometers per second for cyclopentane hydrate 30 at T 0–1 ◦C. ≈

Halo lateral velocities Vh In all experiments, these velocities are observed to be con- stant from the moment the halo emerges from the meniscus up to a distance of 1 to ≈ 5 mm. Beyond this distance, an abrupt decrease in velocity is observed to occur at the lowest temperatures investigated (T = 6, 4, 2 ◦C and, occasionnally, 0 and 1 ◦C): this − − − feature is further presented in the next section.

At temperatures above 0 ◦C we did not observe any significant differences between the velocities of the first and second hydrate halos: in other words, the presence of tiny water droplets on the capillary wall left by the melting of a previous hydrate halo had no or little effect on velocities.

∆TVh θ ∆TVh θ Exp K µms ◦ Exp K µms ◦ 1 2.8 0.3 11 11 6.6 5.2 19 2 4.0 0.7 21 12 6.6 5.4 8 3 5.0 1.9 19 13 7.0 4.1 14 4 5.7 2.8 11 14 7.0 5.4 16 5 5.7 3.5 13 15 7.0 5.4 20 6 6.0 3.6 18 16 8.0 7.9 24 7 6.0 3.7 16 17 9.0 8.7 32 8 6.0 4.0 21 18 9.0 11.6 13 9 6.1 4.3 15 19 11 14.6 18 10 6.3 5.2 15 20 13 21.0 13

Table 3.1: Summary of initial halo velocities and contact angles measured in glass capillaries for various supercooling conditions.

The ’initial’ velocities are reported as a function of supercooling ∆T in Table 3.1 and graphically in Figure 3.5 Halo velocities Vh increase with ∆T much faster than linearly. A α 1 α power-law fit of the data, Vh = A∆T , yields α 2.7 and A 0.024 µms− K− , with ∆T in ≈ ≈ 55 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE

K.

�����

���� ��� �� ��������∆��

����������� ���

��� � �� ��� ∆������

Figure 3.5: Initial halo velocities Vh as a function of supercooling for the experiments reported in Table 3.1

This power law, as well as the morphological evolution of the halo with supercooling, are very similar to what has been observed for polycrystalline gas hydrate crusts growing laterally along water-guest interfaces (for a review, see ref5). In particular, the lateral velocities of these crusts V have been observed to increase with ∆T as a power law with

an exponent logV/log∆T in the range of 2.5, whether the guest fluid is methane, CO2, ethylene, propane or a mixture of these compounds.2,3,10 This behavior has been accounted for2 by means of a heat transfer model,48 which predicts the product of the crust lateral velocity and the crust thickness to be proportional to ∆T3/2, and the assumption2 that the initial crust thickness is inversely proportional to ∆T, consistent with the observations by Li et al.47 We argue below (next section) that there are strong similarities between the growth processes of a hydrate crust over a water-guest interface and that of a hydrate halo over a water-wet substrate, on condition that enough water is supplied to the halo front by the water layer traveling along with the halo, sandwiched between it and the substrate.

Cyclopentane hydrate halos have previously been observed by high-resolution mi-

croscopy, and their velocities measured at T = 0– 1 ◦C, in a different configuration: a water drop sitting on flat glass under cyclopentane, with the hydrate halo creeping out of the con- tact line on glass.30 The radial velocities were considerably smaller (two to five times) than

the velocities measured here (Vh 3.6–5.4 µms, see table 3.1), and primarily depended on ≈ 56 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE the sources of water contributing to halo growth, either the water present on the substrate as precursor films and breath figures or droplets left by the melting of a previous halo, or present in the cyclopentane as a ’fog’ and as dissolved molecules.30 In this earlier study, no or little evidence was found of water being drawn out of the drop by capillarity between the halo and the substrate. One possible reason for such a difference is the geometry of the substrate, which here is curved and leaves more room for water to flow between the halo and the substrate. Another reason is that the bulk water in our open capillaries remains on one side in contact with the atmosphere and therefore at constant pressure, unlike when water escapes through the contact line from a water drop sitting on flat glass and entirely enclosed by a hydrate crust.

In a few experiments (#3 to 7 in Table 3.1), the movements of the water-vapor and cyclopentane-vapor menisci were monitored along with that of the halo. They highlight the volumes of water and cyclopentane incorporated into the hydrate halo and its underlying water layer, both advancing with a velocity Vh along the capillary wall. Figure 3.6 shows snapshots obtained in one of those experiments. When the hydrate halo and the water layer are advancing in liquid cyclopentane, these two menisci are observed to move in the same direction as that of halo growth, albeit at much lower rates Vwv and VCPv, cf. Table 3.2

Halo in cyclopentane Halo in vapor ∆T Vh VCPv Vwv ∆T V′ V′ V′ Exp K µms µms µms h CPv wv Exp K µms µms µms 3 5.0 1.86 0.33 0.42 4 5.7 2.71 -0.20 0.26 4 5.7 2.82 0.37 * 5 5.7 4.31 -0.35 0.48 5 5.7 3.47 0.33 * 6 6.0 3.21 -0.13 * 6 6.0 3.59 0.12 * 7 6.0 3.53 -0.45 * 7 6.0 3.69 0.48 *

Table 3.2: Halo, CP-vapor and water-vapor meniscus velocities in the direction of halo growth, measured before (Vh, VCPv and Vwv) and after the CP-vapor meniscus is overrun by the hydrate ′ ′ ′ halo (Vh, VCPv and Vwv), * not determined.

The movement of the water-vapor meniscus corresponds to water being incorporated in the hydrate halo and in its accompanying water layer. Recalling that this structure II hydrate contains one CP molecule per 17 molecules of water, it will be realised that the amount of CP incorporated into the hydrate is very small. The at first sight paradoxical movement of the CP-vapor meniscus in the same direction as the water-vapor meniscus is due to displacement of CP by the advancing hydrate and its underlying water layer.

57 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE

�������� ������ t = 0 ���� ����� �� ���

t = 165 s ���

����� ������ t = 55 min ���

t = 64 min ���

Figure 3.6: Snapshots from experiment 4 showing the hydrate halo growing along the capillary wall, together with the water-vapor and cyclopentane-vapor menisci. At early times (a,b), the halo in cyclopentane and the CP-vapor meniscus both advance in the same direction. At late times, (c-d) (images recentred), when the halo has overrun the CP-vapor meniscus and is continuing its advance along glass in vapor, the CP-vapor meniscus moves in the opposite direction.

58 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE

Monitoring the advance of the two menisci necessitated prolonged observation, raising the question of how evaporation might influence the velocities of menisci. CP is much more volatile than water due to the 20-fold difference in vapor pressures. Indeed, in separate experiments without the hydrate, we evaluated the drift in the CP-vapor meniscus to be

0.04 µms at T = 1–2 ◦C. The drift in the water-vapor meniscus was much smaller. ≈ Taking account of this effect, the data of experiment 3 (see Table 2) show that the vapor-water and the cyclopentane-vapor menisci advance at approximately the same rate, 0.42 vs. 0.37(= 0.33 + 0.04) µms. The first figure, 0.42 µms, would have been somewhat lower, had the effect of the small amount of water left on the substrate in the form of a film or small droplets been taken into account. However, we were not able to quantify this effect. As a first conclusion, the two velocities Vwv and VCPv can be considered as approximately equal when corrected for the water left on the substrate for the former and for CP evaporation effects for the latter.

A simple mass balance model of halo growth in a round capillary is developed in the Annex A, in which concentric cylinders of hydrate and water advance along the glass wall at a rate Vh. The layers are thin compared to the capillary radius, eh/R , ew/R 1 and ≪ their thicknesses are simply related to Vh, Vwv and VCPv. This model predicts VCPv to be very slightly less than Vwv due to the small quantity of CP incorporated in the hydrate, in agreement with experimental observations. Determination of the thicknesses of the hydrate and water sleeves would require resolving very small differences between VCPv and Vwv, less than experimentally feasible in typical situations. However, order of magnitude bounds can be inferred (cf. annex A), which are consistent with the data reported in Table 2.

The hydrate halo advances faster than the CP-vapor meniscus, so that it finally overruns it, as recorded in snapshots (c-d) in figure 3.6, and in movie M2 of the Supporting

[2] ′ < Information. At this moment, the CP-vapor meniscus changes direction, i.e. VCPv 0 in table 3.2, while the hydrate halo keeps advancing under the vapor with approximately the same texture and velocity. The consumption of CP takes place in fact on the other side of the CP-vapor meniscus, and it is reasonable to assume that CP also forms a layer over the hydrate halo conveying CP molecules to the halo front. The above model can be extended to describe these features (cf. annex A).

[2]The Supporting Information is available free of charge on the ACS Publications website at http:// pubs.acs.org/doi/suppl/10.1021/acs.langmuir.7b02121/suppl_file/la7b02121_si_003.avi

59 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE

3.3.2 Strong slowing down of the halo front

In the experiments conducted at high supercooling (at ∆T = 13, 11 and 9 K), we observed an abrupt transition in halo advance, from the constant velocity regime above to strong deceleration. Occasionally, we also observed some slowing down of the halo past some propagation distance in experiments conducted at supercoolings between 6 and 9 K.

Figure 3.7 shows how sharp may be the transition between these regimes. Measuring time, t, and position, l(t), from the break point, the rates of growth are very similar at all three temperatures and furthermore are compatible with a square root law: l(t) t1/2, ∝ 1/2 1/2 figure 3.8 The best fit of our data is l(t) = Bt , with B = 17 µms− .

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Figure 3.7: (a ) Halo front position or distance from the water-CP interface as a function of time in experiments 18, 19 and 20; (b ) View of a ’young’ halo (T = 4 ◦C) with a rough texture − visible in transmission; (c) past the break point, this halo decelerates and thins to sub-micron thickness only revealed by the cusps along the inner wall.

Past the break point the overall thickness of the halo and its accompanying water layer also decreases, to the extent that they are only detectable from the bright cusps on the inner wall, figure 3.7(b-c), and figure B.9 in Annex B These cusps arise because cyclopentane is replaced on the wall by the hydrate halo and its water layer, whose lower

60 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE

�����

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� � �� ��� ���� ����� ��������������������������� Figure 3.8: Log-log plot of the halo front position vs. time, both plotted from the break point. The straight line is a t1/2 law.

refractive indices (1.33–1.36 vs. 1.41) ensure total internal reflection (and hence a bright cusp) on the inner wall, see the section above. The decrease in intensity at the advancing edge signals tapering to a thickness below the penetration depth of the light rays, which we have estimated to be 140 nm (cf. Annex B). ≈ In next section, we analyze these results in more detail, and discuss the possible causes and mechanisms of the sudden decrease in the velocities and overall thickness of the halo and its accompanying water layer.

3.3.3 Substrate wettability effects

As reported in table 3.1, contact angles θ were observed to vary only slightly from

one capillary to another, all in the interval 8–24 ◦, except for experiment 17 (32 ◦).

It is interesting to note that experiments 17 (θ 32 ◦) and 18 (θ 13 ◦), conducted ≈ ≈ at the same temperature (T = 2 ◦C), exhibited a significant difference in halo velocities, − respectively 8.7 and 11.6 µms, with a higher velocity on the most water-wet substrate. This prompted us to carry out experiments with silane-treated glass capillaries (see Materials and Methods). These substrates are intermediate-wet at ambient temperature, with contact

angles slightly above 90 ◦; and increasingly cyclopentane-wet at lower temperatures (θ ≈ 124 ◦ at T = 10 ◦C, see figure 3.2). − Figure 3.9 illustrates one of these experiments. Submitting the silane-treated capillary to the same protocole as above, we noted the formation of ice at temperatures somewhat

above those in the untreated glass, e.g. TI = 20 ◦C in figure 3.9 vs. -30 to -40 ◦C in − ≈ 61 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE

untreated capillaries. This trend in ice nucleation temperatures with substrate wettability is consistent with observations by other workers.49 It may be due to some ordering of the water molecules in the liquid phase near hydrophobic surfaces.21 On warming to slightly

above 0 ◦C, we observed ice melting and the build-up of a polycrystalline hydrate crust at the interface between the melt water and cyclopentane. This crust did not evolve, even after 10’s of minutes (images not shown). In particular no halo was seen. Warming further

to slightly above 7 ◦C triggered dissociation of the hydrate and formation of an emulsion near the meniscus, figure 3.9(c) The emulsion converted into hydrate as T was lowered

below Teq. Upon decreasing T stepwise, we finally observed at T = 0 ◦C a hydrate halo creeping on the inner wall on the water side of the meniscus, figure 3.9(b-c)

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Figure 3.9: Snapshots from an experiment conducted in a silane-treated capillary. (a) The capillary is initially very slightly cyclopentane-wet, contact angle 100 ◦ at the initial supercooling, ∆T = 7 K(T 0 ◦C); (b) Following the first thermal cycle, cf. figure 3.3 (crust on the meniscus ≈ but no halo, data not shown), a halo is formed during the second cycle (see section 3.3.3; (d-f) The CP-vapor meniscus shows rapid consumption of CP by the halo and the associated liquid CP film. Time intervals indicated are between successive images.

Direct evidence for cyclopentane consumption and incorporation into the growing hydrate halo is shown in the snapshots figure 3.9(d-f), from an experiment conducted at

low temperature (T = 10 ◦C, ∆T = 17 K): the CP-vapor meniscus is seen retreating and − ultimately disappearing when reaching the hydrate crust separating the bulk water and CP

62 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE phases. Comparing figures 3.9(b) and 3.9(e), we see from the disappearence of the bright cusp on the water side that the halo is accompanied by a thick film of CP (> 140 nm, the optical penetration depth). This is evidence that CP wets the hydrate to some extent, otherwise it would not imbibe the narrow space between the silane-treated glass and the halo, as we further discuss in the next section.

Substrate wettability thus plays a key role in CP hydrate spreading, controlling the direction of halo growth. Halo grows on the water side of the water-CP meniscus if the substrate is wetted by the guest fluid (here, cyclopentane), and on the guest side if the substrate is water-wet. If the substrate is intermediate-wet, there is no halo.

We also measured halo velocities, which were found in the range of 0.4 to 1.5 µms for ∆T = 12 to 17 K, with no sign of halo deceleration over distances of a few mms. These values are considerably smaller than the initial halo velocities measured in the opposite direc- tion, on hydrophilic, untreated capillaries (at ∆T = 11 and 13 K, see previous section). The slower spreading compared to untreated glass capillaries, probably is due to the difference in wettability: the silane-treated capillaries used here are only weakly CP-wet, 180 θ 60– − ≈ 70 ◦ at the temperatures of interest, compared to the strongly water-wet untreated glass,

θ 8 – 24 ◦. ≈

63 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE 3.4 Discussion of halo growth mechanisms

Substrate wettability controls the direction of growth of the CP hydrate halo from the water-guest interface. It grows on the side of the fluid that is less wetting to the substrate, helped by a layer of the more wetting fluid sandwiched between the halo and the substrate, which conveys the wetting fluid to the halo front. In this section, we attempt to give more substance to this physical picture and to shed light on the mechanisms of hydrate halo growth on a substrate.

We first draw out the implications of the strong resemblence of spreading of the halo with the growth of a gas hydrate crust at an interface between bulk water and the guest fluid, observed both for water-wet glass (see section 3.3.1) and CP-wet glass (see previous section). Finally we will discuss the strong deceleration after the halo has travelled a certain distance over the substrate.

3.4.1 General considerations

The two substrates involved here differ both in roughness and wettability. The glass wall is smooth and its wettability with respect to the water and guest fluid has been characterized, by means of contact angle measurements (see above). The wettability of the hydrate halo has not been characterized, since contact angle measurements would require planar and smooth hydrate surfaces.50 Gas hydrates are often assumed to be prefentially wet by water in presence of the guest fluid. Our observations suggest that for CP hydrate, this wetting preference is not strong but moderate. Prior to halo growth, the hydrate crystals are observed to form on the water-CP meniscus, where they then remain and keep growing; and sometimes in the emulsion at the rear of the meniscus, where they grow towards the water-CP meniscus until they touch it, and then continue to grow from this point of contact (data not shown). CP hydrate crystals, once formed on the water-CP meniscus, are observed to continue their growth over this interface, facing water on one side and cyclopentane on the other: a strong wetting preference (for water) would rather lead to crystal expulsion in the water phase, as is observed at water-oil interfaces with other types of crystal-forming systems, e.g. fat crystals.51–53 Finally, we must remember the ability of liquid cyclopentane to imbibe the narrow space between silane-treated glass and the hydrate halo (see previous section), which would not be possible if the hydrate were

64 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE strongly water-wet.

Readers are referred further to the large body of work recently reviewed by Zanini and Isa54 and by Binks55, addressing how the wettability, shape and deformability of particles determine their presence at oil-water interfaces, and how deeply they are located in one of these two phases, e.g. they are immersed deeper in the more-wetting phase, and ulti- mately how the corresponding oil-water emulsions (Pickering emulsions) behave. A further complexity arises here because hydrate particles grow over the interface, fed by molecules coming from both sides.

3.4.2 Linear regime of halo growth

Schematic pictures of the advancing hydrate halo are proposed in figure 3.10, which shows the two geometries, hemispherical and lenticular, quite generally considered in the literature for particles at water-oil or water-air interfaces, as well as for gas hydrate crusts growing over the interface between bulk water and bulk guest fluid.2,48,56,57 The lentic- ular geometry, stricly speaking that of a deformable or ”soft”halo, has been considered and analyzed by some authors57 in relation to water-oil emulsions stabilized (or not) by gas hydrates. The features that we discuss next do not depend much on the particular geometries, unlike other features such as emulsion stability.44 The angles α, β and γ at the hydrate-water-guest contact line (see figure 3.10) obey respectively the Young equation

σhg σhw = σwgcos(γ) (3.2) − and Neumann’s contruction

sin(β) sin(α) sin(γ) = = (3.3) σwg σhw σhg where the equilibrium interfacial tension between the aqueous phase and guest fluid, σwg, is known ( 51 mN/m with CP as guest fluid), but not that between hydrate and guest ≈ fluid, σhg, and that between hydrate and the aqueous phase, σhw (see the recent reviews by Aman et al.58 and by Maeda59). In the absence of surfactant adsorbing on the hydrate,

σhg > σhw and, therefore, in the hemispherical configuration, cos(γ) > 0 or 0 < γ< 90 ◦. As discussed above, we expect γ to be quite large: the hydrate is not strongly wet by water.

65 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE

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���� �� �� ����������� �� ���� �� � � � �� � ������������ ����� � � �� ��� � Figure 3.10: Enlarged view of the halo front with two possible geometries: hemispherical (a) and lenticular, typical of a soft solid with angles determined by Neumann’s construction (b) The substrate is strongly water-wet (low contact angle θ).

For simplicity, we consider here a water-wet substrate, but the arguments below may easily be transposed to a situation where the substrate is CP-wet, using a diagram like figure 3.10 with the water and guest phases exchanged.

Figure 10 highlights how the water-wet character of the glass substrate is responsible for the existence, ahead of the halo front, of a water-guest interface concave towards the guest phase, provided the contact angle θ is small enough. This interface is formed by the leading edge of the water layer, extending ahead of the halo front, with an interfacial area increasing with the water-wet character of the substrate, i.e. smaller θ. Its radius of curvature is similar to that of the water-CP meniscus in the absence of the hydrate halo, i.e. R/cos(θ), cf. the boxes in figure 3.4, and thus much greater than the thicknesses of the halo and water layers. Figure 3.10 is not to scale in this respect.

The extended water-guest interface ahead of the halo front resembles that between a bulk aqueous phase and a guest fluid, where a polycristalline gas hydrate crust is advancing, a situation widely investigated over the past two decades, most attention being paid to crust morphology and velocity. The crust front is often modelled as hemispherical, figure 3.10(a), a larger part of the crust being immersed in water when the water-wet character

66 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE of the hydrate increases. Provided water arrives fast enough here through the water film between the glass and the hydrate, the two situations are similar, and the insights gained from the above investigations are directly applicable to halo fronts advancing over water-wet substrates. Physical modeling2 has dealt with either the heat transfer at the crust front,2,60 where the heat generated by hydrate formation is evacuated by conduction, or with the diffusive mass transfer of guest molecules to the crust front,1,4,6 driven by the gradient in guest-concentration in the water phase. Here, we remember that guest solubility in the liquid water equilibrated with the guest fluid far from the growing front, is higher than the solubility in the water equilibrated with the hydrate, at the front.

The heat and mass transfer processes are inter-related, as recently analyzed rigorously by Mochizuki and Mori,61 who derived the temperatures and guest concentrations in water and temperatures around the front and for the lateral growth rate of the crust. They found, at least for methane hydrate crusts under typical conditions, that the temperature at the crust front, Th, is nearly unperturbed, i.e. Th T. The rate of lateral growth of the crust ≈ is controlled by the diffusive supply of the guest substance to the crust front, an effect due to the fact that thermal diffusivity is more than two orders of magnitude larger than the mass diffusion constant of guest molecules in water.13

This analysis can be transposed to hydrate halo growth on a water-wet substrate, considering that the thermal diffusivities of water and quartz or silica are not so different. The concentration of guest molecules in the water near this interface is C = C(T), the equilibrium concentration of a (metastable) guest-saturated water phase at temperature T, see figure 3.10 This concentration is higher than in the aqueous phase at the halo front,

Ch = C(Th), corresponding to a liquid water-hydrate equilibrium at the temperature Th T. ≈ [3]

As a preliminary conclusion, a hydrate propagating as a halo over water-wet sub- strates under the guest fluid should obey similar laws and therefore, as is indeed observed experimentally, have similar morphology and lateral growth rate to those of hydrate crusts propagating over water-guest interfaces, provided the water layer between the substrate and the halo conveys enough liquid water to the halo front. The strikingly similar exponents of the power-law dependence of the rate of spreading on the supercooling (see above, section

[3]From the scarce data available, 62 cyclopentane solubility in water very slightly increases with decreas- ing T, and it is likely that cyclopentane solubility in liquid water equilibrated with cyclopentane hydrate decreases with decreasing T, as is the case with the most common sparingly soluble hydrate-formers.

67 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE

3.3.2) is an illustration of this analogy.

3.4.3 Halo propagation beyond the break point

A full treatment of the complicated, coupled, convective fluid mass and heat flows in our system would require sophisticated numerical methods, like those deployed by Mochizuki and Mori in their analysis of the rate of growth of gas hydrate crusts at water-guest in- terfaces.61 Such a numerical analysis is beyond the aim and scope of this chapter, but a crude, qualitative argument provides insight into the second regime of halo propagation.

The above section 3.3.2 reports experiments in which the CP hydrate halo, after having propagated with a constant lateral velocity, strongly decelerates past some distance or time. This deceleration is simultaneous with the thinning of the water layer, see figure 3.8, resulting in strong viscous resistance to water transport, quantified by a pressure drop given by the plane-Poiseuille expression:

lv µw (3.4) ∆Pvisc = 12 2 ew where ew is the thickness of the water layer (supposed to be constant), v is the average water velocity, l the length of the hydrate halo and µw the viscosity of water. The pressure drop balances the Laplace pressure jump across the water-CP interface at the edge of the water layer, ∆PL σwgcos(θ)/R. The velocity v is somewhat larger than Vh = dl/dt, ≈ because part of the liquid water arriving at the front readily transforms into hydrate and is incorporated into the halo. The mass flux of water flowing between the halo and the glass wall, 2πRewρwv, remains in part liquid, with thickness ew and density ρw, or mass

flux 2πRewρwVh, and in part is incorporated into the hydrate halo front, with thickness eh and density ρw,h, or mass flux 2πRehρw,hVh, leading to:

ehρw,h v = (1 + )Vh (3.5) ewρw

3 where the density of water in the hydrate is ρw,h=0.785 g/cm , assuming that all large cavities in the structure II hydrate are occupied by cyclopentane molecules. Equating ∆PL to ∆Pvisc, the following differential equation is obtained

µ e ρ w + h w,h (3.6) 12 2 (1 )ldl/dt = σwgcos(θ)/R ew ewρw

68 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE which is integrated as a Lucas-Washburn law

σwgcos(θ) 1/2 l(t) = ew t (3.7) √6Rµw[1 + (ehρw,h)/(ewρw)]

In the last equation all quantities under the square root sign are known except the ratio eh/ew, which however has a very limited influence on the value of the prefactor of 1/2 t . For values eh/ew varying between 2 and 0, this prefactor lies in the range of 170ew to

270ew, to be compared with the value obtained by fitting the experimental points in figure 1/2 3.8 with a square-root law, i.e. 17 µms− . The resulting value of ew, in the range of 0.1 µm, is consistent with the observation by optical microscopy reported above (section 3.3.2), that the thickness of the hydrate halo and its underlying water is commensurate with the light ray penetration depth ray, 140 nm. Here, the halo length l has been counted from the break point, which amounts to neglecting the viscous pressure drop generated by water flow in the (thicker) layer till the break point.

The agreement between experimental observations and the predictions of this very simple model is rather surprising considering the assumptions made. The viscous Poiseuille regime does not set in immediately, but is preceded by a regime of linear (constant-velocity) advance, a feature also observed at early times for Poiseuille imbibition flows in capillaries. Another assumption is the constant value of the contact angle θ while the halo and its water layer are advancing along the glass substrate. A further assumption, embodied in the 2 plane Poiseuille permeability value, ew/12, is that of a water layer with uniform thickness ew or, equivalently, a smooth halo surface.

In some experiments where we sealed the capillary on the water side rather than leaving it open, we observed the hydrate halo to slow down faster than in open capillaries, and later the hydrate crust between water and cyclopentane to break down. The liquid cyclopentane then entered the water phase and formed channels through the water zone, quickly wrapped with a hydrate crust (data not shown). Cavitation in the water zone, with bubbles of vapor, was occasionnally observed, signalling again a strong pressure drop in the water as compared to the guest phase. The latter cavitation phenomenon looks like that recently observed with strongly salted water sealed in thin capillaries by salt crusts formed by evaporation.63

At this point it is indeed worth mentioning again the analogous process of salt creeping

69 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE from the edges of an evaporating drop of salted water on a hydrophilic substrate.27,29 The situation when brine flows between the substrate and the crystallites is referred to as bottom supplied creeping. The evaporation of the water, itself related to the water vapor pressure or humidity above the salt front, is the driving force for this phenomenon,26 just as the transfer of guest molecules in liquid water is that for the growth of gas hydrate halos on water-wet substrates.

In concluding this section we may speculate that the break point between the two regimes of growth corresponds to viscous drag in the water sleave superseding molecular diffusion at the crystal interface, as the rate-determining process.

70 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE 3.5 Conclusions and outlook

Understanding gas hydrate growth over solid substrates is important for a variety of natural or industrial processes, involving for instance sedimentary materials or the particles considered for gas storage or separation or for water treatment, whether mesoporous or not. This behavior has been little investigated by direct microscopy observations, unlike gas hydrate growth over water-guest interfaces, which has been a dominant topic in gas hydrate research over the past two decades.

The experiments presented here provide a coherent physical picture of cyclopentane hydrate growth behavior over solid (glass) substrates under various supercooling and sub- strate wettability conditions. Water-wet (bare glass), guest-wet (silane-treated glass at low temperature), and intermediate-wet (silane-treated glass above 0 ◦C) substrates have been considered, and the range of supercooling conditions extended from 2.8 to 17 K.

The experiments consisted in triggering hydrate formation on the meniscus between the host (water) and guest (cyclopentane) fluids in open glass capillaries with controlled wettability and then, once this meniscus was covered with a hydrate crust, in observing susbsequent hydrate growth under the optical transmission microscope. This growth, which occurs as a halo emerging from the edges of this hydrate crust and creeping on the glass substrate, depends both on substrate wettability and supercooling.

Substrate wettability controls the direction of growth of the CP hydrate halo on the substrate: towards the guest side of the water-guest meniscus, i.e. under the guest phase, when the substrate is water-wet, and vice-versa, when the substrate is guest-wet. There is no hydrate halo growing on intermediate-wet glass. The mechanisms for hydrate halo growth are similar whether the substrate is water-wet or guest-wet: in both cases there is a liquid layer of the fluid that wets the glass substrate flowing between the substrate and the hydrate halo and conveying the water or guest molecules to the halo front.

Supercooling has also an important role, which has been investigated in detail in the case of water-wet substrates. Initially, the effects of supercooling on halo morphology and velocity are similar to those observed for gas hydrate crusts growing laterally at water- guest interfaces. At low supercooling (high temperature), the halo morphology is rough and composed of large monocrystals that leave considerable space for liquid water to flow

71 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE between the halo and glass. At high supercooling (low temperature) the halo is smooth and grows very close to the glass wall: the water layer between the halo and glass is thin. The halo lateral velocity, which is steady in the early stages of halo growth, strongly increases with supercooling, in a manner similar to what is observed for gas hydrate crusts growing at water-guest interfaces.

This similarity can be explained as follows. In the early stages of halo growth, there is no limitation for the transport, through the wetting fluid layer, of fluid molecules from the bulk water at the rear of the water-guest meniscus to the halo front. Because its leading edge has a low contact angle with the substrate, this layer advances ahead of the halo front (see Figure 3.10) and has therefore a large area of contact with the other phase: the configuration is very similar to that of a gas hydrate crust advancing along an interface between bulk water and bulk guest, where the transfer processes occurring near and at the crust front are the limiting factors for growth. This similarity has been clearly demonstrated to hold in water-wet capillaries, and the experimental demonstration remains to be carried out in guest-wet capillaries.

Here, different to gas hydrate crusts growing at water-guest interfaces, there is a limiting factor to halo growth, flow of water between the glass and the hydrate sleeve. Past some distance, the halo decelerates and its underlying water layer thins down to sub- micron thickness; it is so thin (and long) that a strong resistance to the flow of water is exerted. This phenomenon has been observed only for the strongest supercoolings (or lowest temperatures). While a clear understanding of why and for what conditions this sudden change occurs has still to be reached, the measured halo velocities and thicknesses can be reconciled within a very simple approach adapted from the Lucas-Washburn model.

An extension of these investigations to more common gas hydrates is underway. In fact, the experimental setup and procedure lends itself relatively easily to adaptation to a water–gas system under pressure, as we have shown in recent work on contact angles inferred 42 from micrographs of the water-CO2 meniscus in a microcapillary. Here, the situation was particularly challenging, in that tenuous hydrate halos with thicknesses as low as a few tens of nanometers were present and advancing on the glass. Their visualization turns out to be possible in cylindrical capillaries with a standard transmission microscope. Better insight into hydrate crystal morphologies and inhibiting or promoting mechanisms of surfactants or other additives (such as asphaltenes) will require minimization of refraction effects, and

72 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE therefore use of square or rectangular capillaries, in combination with higher-resolution microscopy. Future work will also focus on the effects of the substrate curvature on halo growth.

73 CHAPTER 3. ROLES OF WETTABILITY AND SUPERCOOLING IN CYCLOPENTANE HYDRATE SPREADING OVER A SUBSTRATE 3.6 R´ef´erences

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[8] M. Kitamura and Y. H. Mori, “Clathrate-hydrate film growth along water/methane phase boundaries– an observational study,”Cryst. Res. Tech., vol. 48, no. 8, pp. 511– 519, 2013. 43, 53

[9] S. L. Li, C. Y. Sun, B. Liu, Z. Y. Li, G. J. Chen, and A. K. Sum, “New Observations and Insights into the Morphology and Growth Kinetics of Hydrate Films,” Scientific Reports, vol. 4, pp. 1–6, 2014. 43

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[61] T. Mochizuki and Y. H. Mori, “Simultaneous mass and heat transfer to/from the edge of a clathrate-hydrate film causing its growth along a water/guest-fluid phase boundary,”Chemical Engineering Science, vol. 171, pp. 61 – 75, 2017. 67, 68

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80 Chapter 4

CO2 hydrate formation and growth in glass capillaries

Contents Abstract ...... 82 4.1 Introduction ...... 82 4.2 Materials and methods ...... 86 4.2.1 Experimental setup ...... 86 4.2.2 Experimental procedure ...... 86 4.2.3 Phase assignement by Raman spectroscopy ...... 89

4.3 CO2 hydrate formation and growth in glass capillaries ...... 90

4.3.1 CO2 hydrate formation and growth under strong supercooling con- ditions...... 91

4.3.2 Raising T towards the CO2 hydrate dissociation temperature. . . . . 98

4.3.3 CO2 hydrate formation and growth under moderate supercooling conditions ...... 102

4.3.4 CO2 hydrate formation and growth under low supercooling condi- tions: evidence for a new morphology and growth process...... 102

4.4 CO2 hydrate nucleation near the metastability limit ...... 109 4.5 Conclusion ...... 112 4.6 Références ...... 114

81 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES Abstract

We design and implement an experimental methodology which allows gas hydrate formation and growth processes to be investigated across/near a water – gas interface under an unprecedented control of temperature, pressure, and pore wettability and geometry. By means of video-microscopy and confocal Raman spectroscopy, these processes are monitored across a water – CO2 meniscus in a glass capillary acting as a high-pressure optical cell, in a range of supercooling conditions never accessed so far. Because CO2 hydrate forms upon chilling prior to ice, nucleation is investigated under very high supercooling, near the metastability limit. The hydrate starts forming on the meniscus between liquid water and

CO2, which is rapidly coated with a polycrystalline crust, and then hydrate growth proceeds on both sides of the meniscus: as fast-growing fibers or dendrites on the water side and as a hydrate halo creeping over the glass substrate on the gas side. With silane-treated glass (wetted by liquid CO2 but intermediate-wet with gaseous CO2), the halo creeps over glass as well, but on the water side of the meniscus when the CO2 is liquid, and there is no halo when the CO2 is gaseous. Hydrate nucleation is investigated near the metastability limit as a function of pressure, cooling rate and substrate wettability. The morphological changes that occur in the capillary when the supercooling is varied are described. At low supercooling (less than 0.5 K), a novel hydrate growth process is discovered, which consists of a hollow hydrate crystal originating from the meniscus and advancing on the guest side along glass, fed by a thick water layer sandwiched between glass and this hollow crystal.

4.1 Introduction

Gas hydrates are non-stoichiometric crystalline solids made up of cages of water molecules trapping a large amount of a different kind of (’guest’) molecules, such as CO2,

N2, CH4 and other low-molecular-weight alkanes, etc. Interest in gas hydrates is growing, motivated by their unique gas storage capacity, guest selectivity, heat of formation/melting (comparable to that of ice), and by their ubiquitous presence on Earth – in permafrost and in deep marine sediments. How their formation and growth mechanisms are influenced by confinement and substrate wettability is of utmost interest for understanding situations and designing applications involving gas hydrates and solid substrates.

82 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

Gas hydrate research is still in its infancy in many domains. One of these is the kinetics of hydrate formation and dissociation: the so-called memory and self-preservation effects, and the mechanisms by which additives (surfactants, particles, polymers, etc.) promote or inhibit hydrate formation, are still unsettled issues. Advances in these issues will stem from insights at scales intermediate between the two extremes of the temporal and spatial scales that have been accessed so far, namely above the few nanoseconds and nanometers accessed by molecular dynamic simulations, and below the few seconds and micrometers accessible by experiments in conventional reactors equipped with see-through windows. The favorite tool for investigating these scales is indeed optical video-microscopy, but the statement made two decades ago by Smelik and King (1997) that optical microscopy has not been fully exploited in hydrate research still holds true today. While a few efforts in that direction have been carried out since Smelik and Kings pioneering work,1 observation modes others than transmission or reflection are just starting being implemented, providing new insights into hydrate formation and dissociation processes.2,3 Reasons for this lack of investigations are the stringent conditions on the thickness of the sample cell and cell holder, such as approaching the objective to within a few mms of the sample and maintaining a total thickness less than a few cms, while controlling pressure and temperature. In the aforementioned references as well as in a few other studies,4–6 the optical pressure cell consists of two glass or sapphire see-through windows.

The fluid inclusion thermometric studies that have been carried out for over half a century provide hints as to how CO2 hydrates form, grow and dissociate across the meniscus between a water and CO2 phases enclosed in a small quartzitic cavity when submitted to cooling/heating sequences. Inclusions with dimensions often less than a few µms enclosing a liquid, most often an aqueous liquid, are ubiquitous in Earth’s sediments, and their study by microthermometry and by microanalytical techniques (such as laser micro-Raman spectroscopy) provide invaluable clues as to the history over geological times of these sediments.7 Microthermometry consists in recording with the microscope the phase changes – freezing and melting if there is a solid phase – which take place in these inclusions during heating or cooling. Upon cooling, the aqueous phase in these inclusions remains a

(supercooled) liquid well below 0 ◦C, i.e., over a large range of temperatures T < Teq or supercoolings ∆T = Teq T: this strong metastability, often observed over a range larger − than 30 K, is typical of first-order phase transitions in small systems. Contrary to what is observed with water + cyclopentane system,8 a ”double freezing”, of gas hydrate first, then

83 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES of ice a few ◦C below is observed when the inclusion is chilled well below 0 ◦C. These two temperatures, assimilated to the temperatures of primary nucleation of ice and gas hydrate, are the sign that some gas is present in the aqueous fluid inclusion, most often a CO2- or a 9–13 CH4-rich gas. Apart from their higher nucleation temperature as compared to ice, gas hydrates have distinctive growth features: they nucleate and grow at interfaces between the aqueous and guest phases, and then grow further into the bulk water as tiny dendrites, as well as along the mineral boundaries.9,10 These features are however difficult to interpret when both ice and gas hydrate are present, but also when inclusions have complex shapes, that generate refraction effects, in which the pressure cannot be controlled.9,14

The present investigation considerably extends to common gas hydrates the previ- ous work on cyclopentane hydrate (see Chapter 3).8 The cyclopentane is well known for forming hydrate at ambient pressure and temperatures below 7 ◦C. This hydrate forms at the interface between water and cyclopentane by first freezing the water into ice, and then melting the ice. These experiments conducted in open glass capillaries revealed that, following the rapid coverage of the meniscus by a polycrystalline hydrate crust, this crust continues growing along the glass substrate in a manner and with a morphology that depend strongly on supercooling (the distance to equilibrium conditions) and substrate wettability. Indeed, common gas hydrates require high enough pressures to be formed. Their nucleation and subsequent growth at and near the water-guest meniscus, which are the subjects of this investigation, are then monitored under the microscope at different pressure and tem- perature (or supercoling) conditions and in some experiments under the confocal Raman spectrometer for unambiguous phase assignment.

Capillaries are the simplest among the microfluidic systems (micro-reactors) used for processing or crystallizing various materials (e.g., nano- and micro-particles),15,16 and have many of their advantages, The round glass capillaries are model fluid inclusions and their cavity has a simple - cylindrical - shape,17 with therefore tractable refraction effects.18 In this work, the capillaries are sealed at one of their ends - that filled with the aqueous phase - and the other end is connected to a pump with pressure controll and filled with the CO2. In this study, the focus being on the gas hydrate, the temperature descent is halted as soon as it appears on the meniscus: ice formation is therefore avoided, which ensures a better observation of how the CO2 hydrate phase forms, grows and evolves, especially when temperature is subsequently raised. The other important difference with

84 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES the ordinary inclusions is the fact that the pressure is controlled in the proposed experimental configuration.

In another scientific domain, capillaries and, more generally, microfluidic systems, are versatile tools allowing small fluid volumes to be handled with precise temperature control, hence, a small amount of time is needed for reaching thermal and phase equilibria. As an example, the silica capillaries of outer and inner diameters OD = 330 µm and ID = 2R = 200 µm used in the present work, loaded with low-molecular-weight oils, have an upper 2 bound of the time required to adjust to an imposed outside temperature, tth R /Dth ∼ < a few seconds, considering the thermal diffusivity of low-molecular-weight oils, Dth ∼ 7 2 19 10− m /s. The times required to reach liquid/liquid or liquid/gas phase equilibrium are longer, since the involved mass diffusion coefficients are much smaller, typically by 2 orders ∼ of magnitude, than thermal diffusivities. Phase equilibrium involving a solid (hydrate) phase requires still longer times, because water and guest diffusion coefficients in the hydrate phase 11 2 20 are extremely low - below 10− m /s. These times are still much lower than those needed in conventional cells, where in practice equilibrium is reached by imposing strong convection (by agitation).

In these capillaries and microfluidic devices, capillarity and wettability play a major role, they control fluid distribution within the pore volume, such as the shape of a meniscus between two fluids; they may also trigger the nucleation and direct the growth of a new phase. Substrate wettability can be controlled to a large extent, e.g., by means of silane chemistry.8,18 Glass capillaries are commercially available in a variety of external and internal diameters (from the µm to the mm) and shapes. Square and rectangle capillaries have the advantage of providing distortion-free images,

The outline of this chapter is as follows. In section 4.2, the experimental setup and procedure used to observe how the CO2 hydrates form and grow from the water-CO2 meniscus, and the identification of the different phases by confocal Raman spectroscopy, are presented. Section 4.3 describes the formation, starting with primary nucleation, and the subsequent hydrate growth of the CO2 hydrate on both sides of the meniscus, and how the morphology of the hydrate depends on supercooling, which can be varied from high values (more than 30 K) to below 0.5 K. A focus is made in Section 4.4 on these high values (reached because of the small sample dimensions and high experimental cooling rates), assimilated to the metastability limit beyond which the CO2 hydrate forms spontaneously.

85 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

Finally, the Conclusions section summaries the results.

4.2 Materials and methods

4.2.1 Experimental setup

The experimental setup is schematically depicted in Figure 4.1. Unless otherwise speci- fied, the capillaries used in this study are round capillaries (VitrotubesTM) made up of fused silica (referred to as cleared fused quartz), with nominal internal and external diameters equal to respectively 200 and 330 µm and a length equal to 10 cm. The procedure starts with filling the capillary with the aqueous solution of interest (here, distilled water) over a length of 10 mms, flame-sealing one of its end and then centrifuging it in order to displace ∼ the aqueous phase towards the sealed end of the capillary. The capillary is then placed in a heating-cooling stage (Linkam CAP500) that allows accurate control of its position along its axis. One important element in this stage is a silver block with a rectangular slot, where the capillary is inserted and which ensures a good thermal homogeneity over a length of ∼ 5 cm. Temperature is determined to within ±0.2 K in the interval of interest, from about

-40 ◦C to 20 ◦C. The silver block and its slot have a central hole, which is positioned in the optical axis of the microscope (an Olympus B50, used in the transmission mode) and/or of a Raman microspectrometer (see next subsection). The open end of the capillary is inserted and glued (with cyanoacrylate or epoxy adhesives) inside a stainless-steel tube (outer diam- eter 1/16), itself connected to a high-pressure pump (ISCO DM65) containing the CO2 at the chosen pressure. Pressure is checked with a digital manometer (Keller LEO2). The air initially present in the capillary is eliminated by moderate pressurizing with gas, followed by a waiting time of several hours (to allow the air to spread into gas) and purging through the 3-way valve nearest to the capillary (Figure 4.1). The pump, the camera (Ueye UI 3360) and the temperature controller are driven by a home-made software application developed with Qt C++ language.

4.2.2 Experimental procedure

The observations are carried out in the vicinity of the meniscus between the water- and

CO2-rich phases. This meniscus is spherical, typical of a fluid/fluid interface, with water

86 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

Water Gas 200 µm 350 µm 1/16 “

Fused silica capillary 330 µm Stainless steel tubing

Optical microscope with camera + Raman spectroscopie �����������������

gas Valve High-pressure Heating-cooling stage pump

Temperature controller

Liquid nitrogen dewar

Figure 4.1: Schematics of the experiment. Top: enlarged view of the capillary, one of its ends being sealed and the other inserted in a stainless-steel tubing connected to the gas vessel with pressure control, here a high-pressure pump

strongly wetting the silica capillary walls, i.e., the contact angle in water is low. Some experiments are conducted with silane-treated glass capillaries, and the contact angle is indeed much higher.

The initial temperature, T = 15 to 20 ◦C, is well outside the hydrate stability domain. In the case of previous hydrate presence in the capillary, the system is left at the initial temperature for a long enough time (a few minutes) in order to avoid any subsequent memory effect. This effect describes the easier hydrate formation that occurs when the aqueous phase has contained ice or gas hydrate shortly before. CO2 bubbles occasionally appear on the water side of the meniscus upon hydrate dissociation, but then disappear by Ostwald ripening, allowing independent hydrate formation/dissociation experiments to be carried out with the same capillary in a limited amount of time. This feature is exploited for characterizing the CO2 hydrate nucleation behavior (see section 4).

All experiments are carried out at constant pressure and start by chilling the cap- illary (loaded with water and the guest phase) at a constant rate, usually 20 K/min and occasionally 5 and 1 K/min, until the appearance of the solid (crystal) phase(s), ice and/or hydrate (primary nucleation). The water CO2 meniscus is observed to move during the

87 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

temperature descent, witnessing variations in water densities with temperature. At moder-

ate pressure (above 14 bar and below the CO2 liquid/vapor equilibrium pressure at initial ∼ temperature, i.e., 60 bar), the CO2, initially gaseous, condenses into a CO2-rich liquid, ∼ whereas it remains liquid for pressures above 60 bar and gaseous below 14 bar all over the temperature descent.

The descent is stopped as soon as the solid phase appears: due to the small sample

volume and rapid cooling rate, this occurs for strong supercooling ∆T = Teq T, where − Teq is the equilibrium melting temperature of the solid phase at the pressure of the ex- periment, typically ∆T 30 K or more. In most instances, this solid phase is only made ∼ up of CO2 hydrate, which starts forming on the water – CO2 meniscus as detected by an abrupt deviation from its initially spherical shape and a change in texture witnessing the presence of a polycrystalline crust (Figure 4.2a); this moment is identified as the primary

nucleation of the CO2 hydrate. However, in some instances, especially at low pressure (a few bar, typically), the bulk water transforms into ice, which forms on the inner wall and propagates rapidly (within less than a second) from the inner wall to the center of the capillary. Ice has a grainy, polka-dotted texture due to the presence of gas inclusions, and

volume expansion causes the protrusion of ice into the CO2 side of the meniscus (Figure 4.2b). The experiments in which ice is observed to form upon cooling prior to (or along with) hydrate are not considered in this work.

�������� ��� ��� ����� ����� ��� ��� ������ ��� ���

Figure 4.2: (a) CO2 hydrate formation on the meniscus between water and liquid CO2 in a capillary (internal diameter: 200 µm) at 30 bar and Tn 27 ◦C (a). (b) Ice formation (6 bar ∼ − and -32 ◦C).

88 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

4.2.3 Phase assignement by Raman spectroscopy

Complementary to optical microscopy, confocal Raman spectroscopy provides in-situ information as to the nature and composition of various phases such as gas hydrates.21 Raman spectra acquisitions at different locations in the capillary are performed with a HRevo microspectrometer (Horiba Jobin Yvon, Villeneuve d’Ascq, France) using a 532.18 nm wavelength laser as excitation source. The aperture of the confocal hole is chosen at 100 µm to optimize the signal/noise ratio with respect to the focusing-collecting optics and to allow the focusing of the incident laser beam on µm-size part of the sample with a 50X objective (Olympus). Thanks to the 800-mm focal distance and to the dispersion of scattered signal with a holographic grating of 600 lines/mm, the resulting spectral resolution 1 is 2 cm− (Half-Width at Half-Maxima) with a Peltier-cooled CCD detector (Andor, Belfast, UK).

As an example, Figure 4.3 displays the Raman spectra acquired on both sides of the meniscus, i.e., in the water-rich and CO2-rich phases, and on the meniscus itself with its hydrate crust, for an experiment conducted at 22 bar, in which the CO2 hydrate has been formed at -26.5 ◦C, and then the temperature raised and stabilized at -20 ◦C: under these conditions, the CO2 is liquid. Three spectral regions are highlighted: the low-wave-number 1 region (100 – 500 cm− , Figure 4.3b) witnessing intermolecular H2O external or ”O–O” 1 modes, the intermediate region (1200 – 1500 cm− , Figure 4.3a) probing the CO2 Fermi resonance bands of the symmetrical stretching mode ν1 and the harmonic of the bending 22 1 mode 2ν2, and the high-wave-number region (2800-3800 cm− , Figure 4.3c) of water O–H stretching modes. The positions of the peaks in the intermediate region (Figure 4.3a) vary slightly with the environment of the CO2 molecules, whether enclathrated in the hydrate cages, dissolved in (supercooled) liquid water, in the CO2-rich liquid or in the CO2-rich gas (the latter obtained by heating to 6 ◦C): in particular, the two Fermi resonance bands 1 1 of the enclathrated CO2 are shifted towards lower frequencies (1280 cm− and 1384 cm− ) 1 1 in comparison to the CO2 molecules in the gas phase (1289 cm− and 1391 cm− ). The difference between the CO2 in the hydrate and the CO2 in liquid water resides in the width of the bands and in the relative intensities of the two Fermi resonance bands (see Figure 4.3a). Another possibility of differentiating the aqueous phase from the hydrate consists in analyzing the intermolecular low-frequency region (Figure 4.3b), where the lattice modes indicate the existence of a solid phase, hydrate or ice. The lattice mode of a gas hydrate

89 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

1 23,24 has a lower vibrational frequency (212 cm− ) than that of ice : the hydrogen bonds of a hydrate crystal are distorted and weakened compared to those of hexagonal ice (Ih), in which water molecules form perfect tetrahedral sites. The reverse behavior is expected at high wave numbers (O–H stretching), since the distortion of the hydrogen bonding network leads to the strengthening of the O–H bonds, with respect to the water phase (Figure 4.3c).

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Figure 4.3: Characterization of the various phases using Raman spectroscopy. The spectra of the CO2 hydrate are compared to those of liquid CO2, CO2-saturated liquid water at 22 bar and -20 ◦C and gaseous CO2 at 22 bar and 6 ◦C.

4.3 CO2 hydrate formation and growth in glass capil- laries

This section presents and discusses the optical microscopy observations of CO2 hydrate

formation and growth across the water – CO2 meniscus, with a focus on the extreme - strong and mild - supercooling conditions accessible and never investigated so far. We start with primary hydrate nucleation, which in capillaries occurs for very strong supercooling conditions, and then continue by observing hydrate growth on both sides of the meniscus. We then describe in detail how hydrate growth interacts with the glass substrate and the

changes in CO2 hydrate morphology and structure that occur when temperature is raised.

We present in the end of this section CO2 hydrate growth experiments carried out under the

90 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES mild supercooling conditions (less than 0.5 K) allowed by the very fine temperature control of our experimental setup and procedure. All experiments are carried out under constant pressure (isobaric conditions), which is varied over a large range - from a few bar to near 200 bar.

4.3.1 CO2 hydrate formation and growth under strong supercool- ing conditions.

These are the conditions reached when forming the hydrate for the first time (primary nucleation), here by decreasing T at a steady rate (20 K/min in most experiments) from the initial value of 15 – 20 ◦C to the temperature Tn of spontaneous freezing-out of the CO2 hydrate (assimilated to the primary nucleation of the hydrate). At Tn, the meniscus suddenly deviates from sphericity and changes texture (Figure 4.2a): because of the oblique view on the meniscus and the relatively low speed of our camera (< 4 fps), the precise location of hydrate nucleation cannot be observed, and the advance of the hydrate polycrystalline crust front on the meniscus is too fast for being detected. At Tn the temperature descent is stopped, and the ensuing hydrate growth processes are monitored on both sides of the meniscus, which remains immobile as long as T is kept constant. Hereafter, we report first on the experiments carried out in untreated (i.e., water-wet) glass capillaries, and then on the experiments in the same capillaries rendered CO2-wet by silane treatment. We defer to section 4.4 the presentation and discussion of the observed variability in the temperatures

Tn inherent to the nucleation process, together with the influence of pressure, cooling rate and wetting conditions.

Water-wet glass capillaries. Most of our experiments have been carried out with water- wet (i.e., untreated) glass capillaries. Snapshots from two of these experiments are displayed in Figures 4.4 and 4.5, which show the nucleation and subsequent growth of the CO2 hydrate observed on and across a meniscus between liquid water and, respectively, liquid CO2

(p = 30 bar) and gaseous CO2 (p = 10 bar), just before (snapshots a) and after (snapshots b to d) CO2 hydrate nucleation has occurred on the meniscus, at Tn = 27 ◦C (liquid CO2) − and Tn = 31 ◦C (gaseous CO2). These temperatures correspond to supercoolings in excess − of 30 K.

Meniscus coverage by the hydrate crust appears to be instantaneous at the frequencies of our camera (< 4 fps). At the same time (or immediately after, i.e., within 1/4 s) the

91 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES meniscus has been covered with the crust, two remarkable features become apparent:

(i) CO2 hydrate fibers expands at a very high velocity (> 100 µm/s) from the hydrate- capped meniscus into the bulk water, i.e., on the water side of the meniscus. They are not or are barely visible right after the hydrate crust has been formed on the meniscus, and become increasingly contrasted with elapsed time (compare snapshots c and d in Figures 4.4 and 4.5). It is reminded here that the refractive indices of 14 water and CO2 hydrate are very close and the volume fraction occupied by these hydrate fibers is very small, in the order of a few percent, as they are grown from the

CO2 initially dissolved in the supercooled liquid water.

(ii) A CO2 hydrate halo is seen advancing over glass from the contact line of the ≪ ≫ meniscus, on the CO2 side of the meniscus. This halo is thicker near the contact line than at its leading edge (see snapshots 4.4c and 4.4d). Its initial velocity is 10 µm/s, and it slows down after having propagated over a few 10 s to 100 s of ∼ µms on glass, until coming to near-complete arrest

Non-water-wet glass capillaries. A few experiments have been carried out in glass capillaries rendered non-water-wet by silane treatment. The treatment procedure is identical to that used in our laboratory with the same capillaries for studying contact angles of glass 18 – water – CO2 systems and cyclopentane hydrate growth across the water – cyclopentane 8 meniscus. The former study revealed a strong effect of CO2 pressure and state (gaseous or liquid) on substrate wettability at room temperature: the treated glass is intermediate- wet in presence of gaseous CO2 (i.e., at low pressure), with a contact angle (in water) θ in the range of 90 – 100 ◦; this angle increases with p and jumps to 160 ◦ above the ∼ CO2 saturation pressure ( 60 bar at room temperature), i.e., the treated glass becomes ∼ CO2-wet in presence of liquid CO2.

The same wetting behavior is indeed observed at the lower temperatures of interest here. Two hydrate nucleation and growth experiments have been conducted in these treated capillaries, one at a p = 14 bar and the other one at p = 24 bar, in such a way that the

CO2 remains gaseous all the way down to the hydrate nucleation temperature Tn in the experiment conducted at 14 bar, and condenses into a liquid before reaching Tn in the other experiment (conducted at 24 bar). Another experiment has been conducted at 47 bar, which shows features similar to that conducted at 24 bar, and is not detailed here.

92 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

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Figure 4.4: CO2 hydrate formation and growth at 30 bar and Tn 27 ◦C across a meniscus ∼ − between water (left) and liquid CO2 (right). Within less than 1 s (from a to b), the CO2 hydrate has nucleated on the meniscus and coated it with a thin polycrystalline crust. A CO2 hydrate halo then advances along the capillary wall: from b to c: 15 s, and from c to d: 54 s. Fibers growing from the meniscus towards the bulk of the water are apparent in (d).

93 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

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Figure 4.5: CO2 hydrate formation and growth at 10 bar at Tn 31 ◦C across a meniscus ∼ − between water and gaseous CO2. Within less than 1 second (from a to b), the CO2 hydrate has nucleated on the meniscus and covered it with a thin polycrystalline crust. The CO2 hydrate then propagates on both sides of the meniscus, as a halo spreading on glass on the CO2 side and as fast-growing fibers on the water side. Fiber velocity is estimated in the range of 200 µm/s. From b and c: 3/4 s: from c to d: 1/4 s.

94 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

Figure 4.6 shows snapshots of the two experiments. At room temperature where the CO2

is gaseous in both experiments, θ is observed to be slightly larger than 90 ◦, i.e., the glass substrate is intermediate-wet (Figure 6a). At 14 bar (Figure 4.6, left) θ remains in the

range of 90 ◦ (intermediate-wet substrate) all over the temperature descent; whereas at 24

bar (Figure 4.6, right), θ rises to 160 ◦ (CO2-wet substrate) when the CO2 condenses. ∼

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Figure 4.6: Snapshots from two experiments conducted at 14 bar (left) and 24 bar (right) in a silane-treated glass capillary. Left: at 14 bar, CO2 is gaseous from room temperature (a) down to Tn = 28.5 ◦C (b and c, taken 1 and 6 s following nucleation) and the substrate is − intermediate-wet (θ slightly larger than 90 ◦). Right: at 24 bar, CO2 condenses into a liquid at T 15 ◦C (d), and hydrate nucleation occurs at Tn = 26 ◦C (d and e, taken 1 and 6 s ∼ − − following nucleation). A breath figure of water droplets (BF) appears at T 15 ◦C on glass on ∼ − the CO2 side of the meniscus (e), which disappears starting from the meniscus as soon the CO2 hydrate is present on the meniscus.

In the experiment conducted at 14 bar (Figure 4.6, left), CO2 hydrate nucleation

occurs on the water – CO2 meniscus at Tn = 28.5 ◦C (> 30 ◦C, the CO2 condensation − − 95 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES temperature at 14 bar). Images 4.6, b and c are taken 1 s (b) and 6 s (c) following CO2 hydrate nucleation. Similarly to what is observed in water-wet (untreated) capillaries (see above), hydrate fibers grow very rapidly from the meniscus deep into the bulk of the water phase (fiber growth velocity > 300 µm/s). No hydrate halo is seen advancing over the glass substrate.

In the experiment conducted at p = 24 bar (Figure 4.6, right), the CO2, initially

(at room temperature) gaseous, condenses on lowering T, at -15 ◦C, where the contact angle jumps to 160 ◦, indicating a CO2-wet substrate. CO2 hydrate nucleation occurs at ∼ Tn 26 ◦C, slightly higher (by 2.5 K) than at 14 bar, a trend also observed with water- ∼ − ∼ wet (untreated) capillaries. These values for Tn are slightly higher than their counterparts in untreated glass capillaries, a point further discussed in the last section of this chapter.

A hydrate halo is seen advancing at Tn from the contact line of the meniscus over glass, on the water side of the meniscus (Figure 4.6, e and f), at an initial velocity of 25 µm/s. ∼ The experiment conducted at 47 bar exhibits similar features, with a nucleation temperature

Tn 22 ◦C, which is 4 K higher than the temperature Tn observed with the untreated ∼ − ∼ capillary (see Section 4.4).

In summary, and similarly to what has been observed in the previous study with 8 cyclopentane as the guest phase (see Chapter 3), substrate wettability orients CO2 hydrate growth over the substrate, once the hydrate has nucleated and grown as a crust on the water – guest meniscus and reached the contact line with the substrate. The hydrate continues to grow from this contact line as a halo over the substrate on the guest side if the substrate is water-wet, and on the water side if it is guest-wet; over an intermediate-wet substrate there is no halo. The first stages of hydrate nucleation and growth, namely the initial nucleation and growth of a polycrystalline hydrate crust on the meniscus, from which hydrate fibers quickly expand into bulk water, are not influenced by substrate wettability, except perhaps the slightly higher value Tn when the substrate is CO2-wet – indicating that nucleation might occur on the contact line, as further discussed in next section.

Comparison with previous results and discussion. The observations reported above are worth being compared with those in previous microthermometric studies of fluid in- clusions9,10 as well as in experiments conducted in large cells equipped with see-through 25 windows. The hydrate freezing temperatures in the range of -30 ◦C that we observe are similar to those observed in natural CO2-bearing aqueous fluid inclusions by Collins (1979),

96 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES who detects CO2 hydrate freezing at similar temperatures when the interfaces between the aqueous and the CO2 phases become jagged and irregular - conversely, the melting of the

CO2 hydrate is detected on raising the temperature when there is a sudden smoothing of these rough-textured interface. The initial radial texture, centered about the CO2 bub- ble and the crystals (that) grow radially and into the aqueous liquid phase,10 correspond respectively to our polycrystalline crust at the water – CO2 interface and to the hydrate fibers, also referred to as tiny dendrites by Roedder (1963).9 At a much larger scale and observed behind see-through windows, hydrate formation at a water – CO2 interface starts with a hydrate film rapidly covering this interface, followed by numerous hydrate crystals growing in crowds from the film surface into the liquid water, exhibiting a haze-like appear- ance, with crystals having a feather-like or dendritic appearance at large supercoolings:25 we identify these objects to the hydrate fibers described previously. Observations of fibers or needles growing in bulk water perpendicularly to the water – guest interface previously covered with a hydrate crust are frequent for high supercooling conditions: see for instance the study on methane hydrate needles growing at a water – methane by Subramanian and Sloan (2002).26

While gas hydrate climbing above the water – gas interface on glass or sapphire win- dows is frequently observed in experiments conducted in conventional cells,27,28 systematic investigations of how gas hydrate propagates on a solid substrate are scarce.27 The term halo was dubbed by Beltran and Servio (2010) in their study of methane hydrate propagat- ing on glass from the contact line of a water droplet (itself previously covered with a hydrate crust) to that of the neighboring droplet,6 which then covers itself up with a hydrate crust – the bridge effect. The impact of substrate wettability has recently been examined by Beltran et al (2016),29 who did not observe any methane hydrate halo advancing under methane on non-water-wet substrates. In the study of cyclopentane hydrate growth in the same (open) glass capillaries (see Chapter 3),8 the growth of the hydrate halo over glass was shown to be fed by a liquid water layer sandwiched between glass and the halo. This layer conveyed the water molecules from the bulk water at the rear of the meniscus to the leading edge of the halo, where the hydrate is formed, and its thickness increased with increasing T (or decreasing supercooling); it became visible with the optical microscope only at low enough supercooling – the results presented in the end of this section show that it is also the case with the water – CO2 system. The experiments presented above also show that, at high supercooling, the CO2 hydrate halo was observed to thin down to

97 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES submicron thickness and abruptly slow down after travelling a few hundreds of µms over glass.

4.3.2 Raising T towards the CO2 hydrate dissociation temperature.

We now describe and discuss two noteworthy phenomena, which we observe when temper- ature is increased from Tn to above 0 ◦C: (i) displacement or breakage of the crust and halo, and (ii) fiber recession towards the meniscus of the hydrate fibers.

Movement and rupture of the hydrate crust and halo. On raising the temperature above Tn, we usually observe that the crust and the halo are dragged towards the water side of the meniscus, because of the thermal contraction of water heated in this temperature range. The sliding of the halo is further evidence of the presence of a lubricating layer of water between the halo and the glass. Sometimes, however, the halo fractures with a surprisingly break, one side following the crust and the other remaining stuck to the glass on the CO2 side. The bare glass in the gap is rapidly patched over (1–2 s) by growth of hydrate halo fed by the water layer already noticed above (Figure 4.7).

On rare occasions, the halo adheres so tightly to the glass that both it and the crust were immobile. The pressure drop in the water side on raising the temperature then caused the crust to rupture, allowing CO2 to rush into the water, forming a bulb that was covered rapidly by a crust of hydrate, figure 4.8. The drop in pressure is a thermodynamic effect, due to isochoric heating of the liquid water.

Recession of hydrate fibers towards the meniscus. When T is raised slowly towards the hydrate dissociation temperature Teq, the hydrate fibers at the rear of the meniscus appear denser and shrink towards the meniscus, as is illustrated in Figure 4.9.

This recession can be qualitatively understood26 by considering the temperature de- pendencies of the equilibrium CO2 concentrations in liquid water schematically depicted in

Figure 4.10. In the absence of hydrate, the CO2 concentration in liquid water (curve a in Figure 4.10) increases with decreasing T, including in the metastable region (T below

Teq, dotted part of curve a), whereas in the presence of hydrate the CO2 concentration in liquid water (curve b) increases with T; the two curves meet at the temperature and CO2 concentration corresponding to liquid water/hydrate/gas equilibrium.

98 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

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Figure 4.7: View of the glass capillary across the water – CO2 meniscus a few seconds after hydrate nucleation at Tn = 26.5 ◦C and p = 14 bar (a). Increasing T over Tn, here at a rate of − 20 K/min, the hydrate-capped meniscus and the halo are pulled (black arrows) towards the contracting water, generating fractures in the halo seen at the tip of the red arrows in (b). The fractures are rapidly healed, filled with a new halo fed by the water layer present between glass and the (old) halo.

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Figure 4.8: CO2 pocket rushing from the meniscus into water when T is increased from Tn = 34 ◦C (p = 12 bar) to -8 ◦C. −

99 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

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Figure 4.9: Hydrate fiber recession towards the meniscus when T is raised slowly to the equilibrium temperature. p = 30 bar and T = 5 ◦C (a) and 6.6 ◦C just below Teq (b). Elapsed time between (a) and (b): 45 seconds.

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Figure 4.10: Schematic diagram of the evolution of CO2 concentration in water near enough from the meniscus during isobaric hydrate formation/dissociation cycle (see text). The scales are arbitrary.

100 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

At the start of the experiment when T is decreased from Ti ( 15 – 20 ◦C) to Tn, ∼ the CO2 concentration in liquid water very near the meniscus first increases, from Ci to Cn

(path 1 2 along curve a), which is reached at Tn, the temperature of primary nucleation → (see the beginning of this section), and then drops at Tn from Cn to Cf (path 2 3) when → the hydrate fibers have been formed. A large part of the CO2 initially dissolved in water, namely that corresponding to the difference between Ci and Cn, is in fact enclathrated in the hydrate fibers. As Cn does not exceed 2 – 3 mol% for the pressure and temperatures of interest here, the volume fraction of these hydrate fibers (in which the molar fraction of CO2 is one order of magnitude larger) cannot exceed a few percent. Further from the meniscus, the CO2 concentration profile prior to hydrate formation (at Tn) depends on the previous history, i.e., on how long the system has been held at Ti prior to the experiment and how fast temperature has been decreased to Tn. If over a certain distance from the meniscus the local CO2 concentration in water is larger than Cf, then hydrate is expected to form and grow.

When this system is heated but T remains below Teq, the CO2 concentration in the water equilibrated with the hydrate present follows the path 3 4 eq (curve b), i.e., → → it increases: therefore, CO2 molecules have to be provided to the bulk water + hydrate system, which come from the dissolution of the tip of the fibers. It is important here to emphasize that the hydrate crust covering the meniscus is nearly impermeable and prevents any CO2 supply from the CO2-rich phase on the other side of the meniscus. The dissolution of the hydrate fibers at their extremities to provide increased CO2 molecules to the water coexisting with the remaining fibers is responsible for the observed recession of the fiber front (Figure 4.9).

Here, it is worth mentioning the observations of CO2-rich aqueous phase inclusions made 4 - 5 decades ago by Roedder (1963) and Collins (1979). Upon warming these authors observed the fibers or tiny dendrites transform into coarse, irregular, platy (platelike) crystals or,10 according to Roedder (1963), they become nebulous at first and increasingly visible, showing generally rounded shapes with a few obvious flat sides, which themselves transform on cooling again into rapidly growing cubo-octahedrons.9 The results presented in next subsection provide some illustrations of these changes.

101 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

4.3.3 CO2 hydrate formation and growth under moderate super- cooling conditions

In some experiments, the CO2 hydrate was brought to complete dissociation by heating slightly ( 1 K) above Teq, and then reformed immediately by lowering T a few degrees ∼ below Teq, exploiting the memory effect. Following a certain induction time (a few seconds, typically) at the latter temperature, the CO2 hydrate was observed to nucleate and then grow rapidly as a crust on the water – CO2 meniscus, and a hydrate halo then advanced from the contact line over glass : this sequence of events, which did not last longer than 1 – 2 s, is similar to that occurring for hydrate formation and growth under strong supercooling conditions and described above. It is illustrated in the first two images (a and b) in Figure

4.11, which correspond to, respectively, a water – CO2 meniscus just following complete hydrate dissociation at 30 bar, 9 ◦C ( Teq + 1 ◦C) (a), and the same system in which T ∼ has been dropped (at a rate of 20 K/min) to 1.5 ◦C, i.e. ∆T 6.5 K (b). In this example, ∼ a hydrate crystal with an apparent cubo-octahedron shape is observed to grow at 1.5 ◦C on the water side of the meniscus (image c, Figure 4.11), favored by a strong CO2 saturation.

4.3.4 CO2 hydrate formation and growth under low supercooling conditions: evidence for a new morphology and growth pro- cess.

In this subsection, low supercooling conditions for CO2 hydrate formation below 0.5 K are investigated. A novel CO2 hydrate morphology and growth process is discovered, consisting of a cylindrical hollow crystal advancing concentrically to the capillary, fed by a thick water layer between this crystal and the capillary inner wall.

The formation process requires that a hydrate crystal, e.g., that resulting from the incomplete dissociation at T > Teq of a hydrate formed previously, be initially present in bulk water at some distance from the meniscus. As illustrated in Figure 4.12 (a and b) this hydrate crystal can be grown towards the meniscus by lowering T to slightly below Teq, in such a way that there is no hydrate formed on the meniscus and therefore no obstacle to CO2 transfer into bulk water. The diffusive flux in water of CO2 (arriving from the meniscus) feeds the growth of this hydrate crystal until it reaches the meniscus (Figure 4.12, b).

102 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

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Figure 4.11: CO2 hydrate formation and growth at a water – CO2 meniscus at moderate supercooling conditions (p = 30 bar, ∆T 6.5 K), in a capillary where the hydrate has been ∼ formed and dissociated shortly before. Here, the capillary inner diameter is 250 µm.

103 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

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Figure 4.12: CO2 hollow crystal (HC) forming on the water – CO2 meniscus at low supercooling conditions at p = 24 bar and T = 4.9 ◦C (∆T = 0.4 K). First (a and b), there is a hydrate crystal in water (CW) growing slowly towards the meniscus until it touches it (elapsed time from a to b: 112 s). Then (c and d) a hydrate filament (HF) grows rapidly between the meniscus and the hydrate crystal (CW) from the meniscus (elapsed times from b to c: 14 s; from c to d: 6 s). At some point (e and f) the hydrate grows from the filament end along the meniscus itself and evolves into a hollow cylindrical crystal (see Figure 4.13). Elapsed times from d to e: 2s; from e to f: 4 s.

104 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

When the hydrate crystal reaches the meniscus, a thin hydrate filament, with thickness of a few µms, appears at the point of contact and rapidly extends between the meniscus and the hydrate crystal, which thus appears to be repelled away from the meniscus (Figure 4.12, c and d). The filament grows from its end on the meniscus and, at some point, continues its growth along the meniscus itself (Figure 4.12, e and f), which deforms and adopts a conical shape, and ultimately evolves into a cylindrical hollow crystal concentric to the capillary (Figure 4.13).

This cylindrical hollow crystal grows along the capillary wall, fed at its edge by the

CO2 present and the water arriving through a thick water layer sandwiched between this crystal and the inner wall of the capillary (Figure 4.13). This water layer is itself drawn ahead of this crystal by the water-wet character of the capillary evidenced by the small contact angle (in water) at the triple line (water – CO2 – glass). The hollow crystal is seen to move back towards the water phase. This is because the water migrates from the rear of the meniscus to the edge of the hollow hydrate crystal.

Figure 4.13 displays snapshots of two experiments conducted at p = 22 bar and dif- ferent temperatures T and (low) supercoolings ∆T. In the first experiment (images a and b) T and ∆T are equal to 4.6 ◦C and 0.2 K, respectively; the thickness of the water ∼ layer is 20 µm, and the hollow crystal grows along the capillary at a rate 4.1 µm/s. ∼ ∼ In the second experiment (images c and d), the temperature T and the supercooling ∆T are first, i.e., at the beginning of the experiment (image c), equal to 4.7 ◦C and 0.1 K; ∼ the thickness of the water layer is 30 µm, and the crystal grows at a rate 0.7 µm/s; ∼ ∼ at some moment in this experiment, T is slightly decreased to 4.6 ◦C (∆T 0.2 K), and ∼ the diameter and growth rate of the hollow crystal are observed to progressively increase to values similar to those observed in the first experiment.

Clearly, the growth rate of the hollow hydrate crystal formed at low supercooling and the thickness of its accompanying water layer are very sensitive to the supercooling ∆T: the hollow crystal advances faster and the water layer is thinner when supercooling increases. These trends are similar to those observed for hydrate halos growing on glass,8 which however differs strongly from the hollow hydrate crystal of interest here in that it is polycrystalline. The growth mechanism of the cylindrical hollow crystal is likely to be similar to that of hydrate halos on glass and polycrystalline crusts at the interface between a water and guest phases.8 In short, the growth of the hollow crystal at its leading edge is

105 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

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Figure 4.13: Experiments of hollow hydrate crystal growth in a capillary at 22 bar and low supercooling. The temperature in the first experiment (images a and b) is 4.6 ◦C (∆T = 0.2 K). The temperature in the second experiment is 4.7 ◦C (∆T = 0.1 K) at the beginning (image c) and then (image d) is decreased to 4.6 ◦C (∆T = 0.2 K). See text. The black arrows indicate water arriving from the rear of the meniscus to the edge of the hollow crystal, and white arrows show the growth direction of the hollow crystal. The picture at the bottom shows a schematic cross-sectional view and a representation of the leading (and growing) edge of the hollow hydrate crystal.

106 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES ensured by the entrained water layer, which wets the glass substrate (see Figure 4.13) and therefore forms an interface with the CO2 phase; this water becomes saturated with CO2, and there is a flux of CO2 molecules in water towards the edge of the crystal (where CO2 concentration in water is lower, see Figure 4.10). It is assumed here that the CO2 hydrate is predominantly formed in the (CO2-saturated) water phase.

A Raman mapping has been carried out along a segment from the center to the inner wall of the capillary in the region of the hollow cylindrical crystal (see Figures 4.14 a and b). In this experiment, p = 22 bar and T = 4.3 ◦C (0.4 K of supercooling). To spatially map the various phases in the capillary, Raman signatures of each phase have been selected: 1 the CO2 stretching mode in the gas state at 1390 cm− the one corresponding to CO2 1 encapsulated in the hydrate at 1384 cm− , the water O–H stretching broad profile centered 1 at ca. 3300 cm− (see subsection Phase assignement by Raman spectroscopy) and the 1 characteristic silica band centered at ca. 500 cm− . Each point of the curves presented in figure 4.14c is then obtained by considering the intensities (integrated area of the peak) of the 4 characteristic bands normalized to the total intensity. The lines are guides to the eyes obtained by fitting Sigmoidal (for CO2 gas and silica) and Pseudo-Voigt functions (for encapsulated CO2 and water). Such intensity profiles yield to access the spatial distribution of the different phases along a radial axis within the capillary (figure 4.14c).

By analyzing the relative intensities of figure (4.14c), it is observed in the center of the capillary (for x/R varying from 0 to 0.4) that gaseous CO2 signature is present and that no Raman signature of CO2 hydrate is observed. In the region x/R from 0.5 to 1 (i.e. close to the inner wall), the existence of CO2 stretching signature together with that of

O–H stretching indicates the occurrence of CO2 hydrate and water phase. Moreover, one can observe a shift between the intensity maxima for the O–H stretching profile and that of the encapsulated CO2 profile: the maxima are indeed observed at x/R = 0.95 and x/R

= 0.82, respectively. In other words, the H2O maximum intensity is observed between the hydrate phase and the capillary wall (identified with the help of the increase of the silica profile at x/R 1). Thus, such observations clearly indicate (i) the hydrate exhibit a hollow ∼ shape and (ii) a depletion of CO2 at the inner capillary wall, so that a water phase exists between the hollow hydrate and the capillary wall.

107 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

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Figure 4.14: Raman mapping along a segment from the center to the inner wall of the capillary at 22 bar and 4.3 ◦C (0.4 K of supercooling). (a) and (b) show the images by reflection microscopy of the hollow hydrate with 10x and 50x zoom respectively. The lines correspond to the best fit of the different intensity ratios.

108 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

4.4 CO2 hydrate nucleation near the metastability limit

In this section, we report and discuss a series of measurements of CO2 hydrate pri- mary nucleation temperatures (called Tn) carried out under various conditions of cooling rate, pressure and substrate wettability. We argue that these measurements provide the

first experimental indication of the CO2 hydrate metastable limit of nucleation (in short: metastable limit) in the pT plane. This limit, a line in the pT plane, delineates the re- gion in which the hydrate form spontaneously from the region where liquid water remains metastable (supercooled) in presence of the guest phase. To the best of our knowledge, the only evidence for such limit in gas hydrate systems comes from molecular dynamic simulations.30

The measurements have consisted in cooling the capillary at a constant rate down to the nucleation temperature Tn, detected visually from the abrupt change in the meniscus’ aspect (as described in the beginning of previous section). For given conditions of pressure and cooling rate, the measurements were repeated several (up to 20) times in order to have meaningful statistics - it is reminded here that nucleation is a stochastic process. Our experimental setup and procedure allow such experiments to be carried out in a limited amount of time, by running consecutive cooling and heating sequences and noting for each cooling sequence the temperature Tn. The duration of the heating sequence at room temperature was long enough (a few tens of minutes) to dissociate the CO2 hydrate and eliminate any memory effect: two consecutive experiments could thus be considered as independent.

As a rule, the spread in the values of Tn observed for given pressure and cooling rate conditions was observed to be rather small, in the order of 1 – 2 K, as depicted in figures 4.15 and 4.16, thus witnessing the quasi-deterministic character of nucleation expected under strong supercooling conditions (here ∆T slightly larger than 30 K). These observed strong supercoolings are in line with the values observed in fluid inclusions (see section 4.1) and are primarily due to the small fluid volumes involved. Chilling more rapidly the sample lowers the nucleation temperatures: an example is provided by the experimental results gathered in Figure 4.15, which shows that at P = 24 bar the Tn’s are lower by 1.5 K ∼ when the cooling rate dT/dt is increased from 1 to 20 K/min. All nucleation temperatures reported elsewhere in this chapter have been obtained with a cooling rate of 20 K/min.

109 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

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Figure 4.15: FN, the fraction of cooling cycles in which CO2 hydrate nucleation has occurred, as a function of supercooling ∆T = Teq Tn, where Teq = 5.5 is the equilibrium temperature for − CO2 hydrate and Tn is the nucleation temperature for three different cooling rates at p = 24 bar.

Figure 4.16 below gathers the measurements of Tn obtained in a large range of pressure from 6 to 100 bar. Each data point (cross) in this Figure is the average of several (up to

20) values of Tn’s, which are represented in the form of histograms (number of experiments

N vs. interval of Tn): for simplicity, only four histograms are displayed.

Interestingly, the p vs.. Tn curve exhibits a trend similar to that of the equilibrium

between the liquid water, hydrate and CO2-rich phases: a rapid increase of Tn with p when

the CO2 is gaseous at nucleation, and then a slower increase when CO2 is liquid, where

the change in behaviors occurs at 26 ◦C and 20 bar, corresponding to the transition ∼ − between gaseous and liquid CO2. The change in the three-phase equilibrium line occurs at

the quadruple point Q2 (with coordinates 10 ◦C and 44 bar see Figure 4.16).

In these experiments, the small volumes and high cooling rates ensure that strong supercoolings are reached. From Figure 4.16, the maximum supercoolings (reached at

nucleation) are equal to Teq Tn 32 34 K. This is similar to what occurs with liquid − ∼ − − water under low to moderate pressures: when dispersed in the form of droplets or present

in fluid inclusions and chilled rapidly, water remains liquid down to 40 ◦C (or even slightly − below) where it forms ice Ih.31 The latter temperature is considered to be an approximation

of the temperature of homogeneous nucleation of ice. Likewise, in our system where the CO2

hydrate nucleates at the water – CO2 interface, the measured Tn’s are an approximation

110 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

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Figure 4.16: Nucleation temperatures of CO2 hydrate at the water – CO2 interface in a glass capillary. Cooling rate: 20 K/min. The crosses are the values averaged over several identical measurements, with nucleation temperatures represented as histograms: for clarity, only four histograms are represented, each corresponding to a given pressure. An enlarged view of the histogram corresponding to P = 24 bar is presented. The lines on the right-hand side are the three-phase Lw – H – V (liquid water – hydrate – CO2-rich vapor) and Lw –H–Lc (liquid water – hydrate – CO2-rich liquid) equilibrium lines, and Q2 is the upper quadruple point of the Lw – H–V–Lcc equilibrium

of the temperature of surface nucleation for the hydrate, which is referred to above as the metastable limit.

These results on CO2 hydrate nucleation temperatures have all been obtained in untreated (hence, water-wet) glass capillaries. A few nucleation temperatures (reported above in section 4.3.1) have been determined in silane-treated capillaries, for pressures p =

14, 24 and 47 bar, with values of Tn respectively equal to -28.5, -26 and -22 ◦C. The first of these values is very similar to that observed in an untreated glass capillary, whereas the

two others are higher (by 2 – 4 ◦C) than their counterparts in untreated glass capillaries.

The first value (Tn = 28.5 ◦C) have been obtained under conditions that CO2 is gaseous − and the glass substrate is intermediate-wet at hydrate nucleation, and the two others under

conditions that CO2 is liquid and the glass substrate is CO2-wet at nucleation (see above, section 4.3.1). It thus appears that the presence of guest-wet or (guest-philic) promotes hydrate nucleation, which very likely takes place on the contact line, consistent with recent observations, particularly by Nguyen et al.32

111 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES 4.5 Conclusion

The results presented in this chapter have all been obtained with the same experimental system: a glass capillary, sealed at one end and loaded with a liquid water (liquid volumes in the range of a few microliters) and the other end connected to a pressure pump filled with CO2 gas, acting as a high-pressure optical cell and equipped with a fine control of temperature and pressure. The two phases are separated by a meniscus. This system has proven to be very versatile and efficient in obtaining precise information as to how the CO2 hydrate nucleates on the waterCO2 meniscus and then grows on both sides of the meniscus, in a manner that depends on supercooling and substrate wettability.

CO2 hydrate primary nucleation in glass capillaries chilled from the ambient is de- tected easily from the observation of the water – CO2 meniscus, which at the nucleation temperature Tn abruptly changes aspect. Ice formation is usually not observed unless the temperature is decreased below Tn. Owing to the very small samples and the high cooling rates achievable, the observed Tn’s are much lower - by more than 30 K - than the three- phase (liquid water – hydrate – CO2-rich phase) equilibrium values. Because of these large supercoolings, the values of Tn obtained from experiments conducted under identical con- ditions (of pressure, cooling rate, etc.) fall in a narrow interval. This suggests that these nucleation temperatures are close to the metastable limit below which the CO2 hydrate forms spontaneously. To the best of our knowledge, this is the first experimental investi- gation of this limit, which turns out to be parallel to the three-phase equilibrium line. The optical setup does not allow to determine where nucleation takes place on the meniscus, even though the lower observed Tn’s suggests that at least with CO2-wet glass nucleation takes place on the contact line.

Following primary nucleation, i.e., under strong supercooling conditions (∆T > 30 K), the meniscus covers itself up with a polycrystalline hydrate crust almost instantaneously (within less than a second), and then hydrate growth proceeds on the water side of the meniscus as fibers rapidly growing from the crust. This crust continues its growth at some distance beyond the contact line in the form of a ”halo”advancing over the glass substrate, on the CO2 side of the meniscus if the glass is untreated or water-wet, on the water side if the glass is CO2-wet (silane-treated glass, CO2 liquid), and there is no halo if the substrate is intermediate-wet (silane-treated glass, CO2 is gaseous). The growth of this halo is fed by a

112 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES layer of the wetting phase (water or liquid CO2) present between the glass wall and the halo itself. Hydrate growth has also been investigated under intermediate and low supercoolings, which are attained by exploiting the memory effect, i.e., forming the hydrate shortly after it has been melted at a temperature slightly above the equilibrium temperature. Under moderate supercooling (∆T a few K), macroscopic hydrate monocrystals are observed ∼ to grow on the water side of the meniscus. Under low supercooling (∆T < 0.5 K), a novel hydrate morphology has been obtained, consisting of a hollow crystal starting from the meniscus and then growing as a hollow cylinder advancing parallel to the glass wall, with a thick water layer feeding the growth.

113 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES 4.6 R´ef´erences

[1] E. A. Smelik and H. E. King,“Crystal-growth studies of natural gas clathrate hydrates using a pressurized optical cell,” American Mineralogist, vol. 82, no. 1-2, pp. 88–98, 1997. 83

[2] M. L. Martinez de Banos, N. Hobeika, P. Bouriat, D. Broseta, E. Enciso, F. Clement, and R. Brown, “How do gas hydrates spread on a substrate?,” Crystal Growth and Design, vol. 16, no. 8, pp. 4360–4373, 2016. 83

[3] A. D. Daniel Broseta, Livio Ruffine, Gas Hydrates 1: Fundamentals, Characterization and Modeling. Great Britain and USA: ISTE Wiley, 2017. 83

[4] J. R. DuQuesnay, M. C. D. Posada, and J. G. Beltran, “Novel gas hydrate reactor design: 3-in-1 assessment of phase equilibria, morphology and kinetics,” Fluid Phase Equilibria, vol. 413, pp. 148 – 157, 2016. Special Issue: Gas Hydrates and Semi- clathrate Hydrates. 83

[5] V. Thieu, S. Subramanian, S. O. Colgate, and E. D. Sloan, “High-pressure optical cell for hydrate measurements using raman spectroscopy,” Annals of the New York Academy of Sciences, vol. 912, no. 1, pp. 983–992, 2000.

[6] J. G. Beltr´anand P. Servio, “Morphological investigations of methanehydrate films formed on a glass surface,”Crystal Growth & Design, vol. 10, no. 10, pp. 4339–4347, 2010. 83, 97

[7] E. Roedder, Fluid inclusions, vol. 12. Reston, Virginia, USA: Mineralogical Society of America 1984. 83 ” [8] A. Touil, D. Broseta, N. Hobeika, and R. Brown,“Roles of wettability and supercooling in the spreading of cyclopentane hydrate over a substrate,”Langmuir, vol. 33, no. 41, pp. 10965–10977, 2017. PMID: 28910532. 83, 84, 85, 92, 96, 97, 105

[9] E. Roedder,“Studies of fluid inclusions; [part] 2, freezing data and their interpretation,” Economic Geology, vol. 58, no. 2, p. 167, 1963. 84, 96, 97, 101

[10] P. L. F. Collins, “Gas hydrates in CO2-bearing fluid inclusions and the use of freezing data for estimation of salinity,” Economic Geology, vol. 74, no. 6, p. 1435, 1979. 84, 96, 97, 101

114 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

[11] L. W. Diamond, “Salinity of multivolatile fluid inclusions determined from clathrate hydrate stability,” Geochimica et Cosmochimica Acta, vol. 58, no. 1, pp. 19 – 41, 1994.

[12] P. Murphy and S. Roberts, “Melting and nucleation behaviour of clathrates in multi- volatile fluid inclusions: evidence of thermodynamic disequilibrium,”Chemical Geology, vol. 135, no. 1, pp. 1 – 20, 1997.

[13] A. Fall, B. Tattitch, and R. J. Bodnar,“Combined microthermometric and raman spec-

troscopic technique to determine the salinity of H2OCO2NaCl fluid inclusions based on clathrate melting,” Geochimica et Cosmochimica Acta, vol. 75, no. 4, pp. 951 – 964, 2011. 84

[14] R. S. F. E. R. Amos Bein, S. D. Hovorka, “Fluid inclusions in bedded permian halite, palo duro basin, texas: Evidence for modification of seawater in evaporite brine-pools and subsequent early diagenesis,”Journal of Sedimentary Petrology, vol. 61, pp. 1–14, 1991. 84, 92

[15] S. Marre and K. F. Jensen, “Synthesis of micro and nanostructures in microfluidic systems,”Chemical Society Reviews, vol. 39, no. 3, p. 1183, 2010. 84

[16] S. Marre, Y. Roig, and C. Aymonier, “Supercritical microfluidics: Opportunities in flow-through chemistry and materials science,” The Journal of Supercritical Fluids, vol. 66, pp. 251 – 264, 2012. Special Edition on the Occasion of Gerd Brunner’s 70th Birthday. 84

[17] I.-M. Chou,“Optical cells with fused silica windows for the study of geological fluids,” Raman spectroscopy applied to Earth sciences and cultural heritage, no. January 2012, pp. 227–247, 2012. 84

[18] N. Hobeika, P. Bouriat, A. Touil, D. Broseta, R. Brown, and J. Dubessy,“Help from a hindrance: Using astigmatism in round capillaries to study contact angles and wetting layers,”Langmuir, pp. 5179–5187, 2017. 84, 85, 92

[19] H. Watanabe and H. Kato, “Thermal conductivity and thermal diffusivity of twenty- nine liquids: alkenes, cyclic (alkanes, alkenes, alkadienes, aromatics), and deuterated hydrocarbons,”Journal of Chemical & Engineering Data, vol. 49, no. 4, pp. 809–825, 2004. 85

115 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

[20] S. R. Davies, E. D. Sloan, A. K. Sum, and C. A. Koh,“In situ studies of the mass trans- fer mechanism across a methane hydrate film using high-resolution confocal raman spectroscopy,” The Journal of Physical Chemistry C, vol. 114, no. 2, pp. 1173–1180, 2010. 85

[21] A. D. Bertrand Chazallon, Jennifer A. Noble, Spectroscopy of Gas Hydrates: From Fundamental Aspects to Chemical Engineering, Geophysical and Astrophysical Ap- plications. In Gas Hydrates: Fundamentals, Characterization and Modeling, ch. 2, pp. 63–112. Great Britain and USA: ISTE Wiley, 2017. 89

[22] A. K. Sum, R. C. Burruss, and E. D. Sloan, “Measurement of clathrate hydrates via raman spectroscopy,”The Journal of Physical Chemistry B, vol. 101, no. 38, pp. 7371– 7377, 1997. 89

[23] P. Prasad, K. S. Prasad, and N. Thakur, “Laser raman spectroscopy of thf clathrate hydrate in the temperature range 90300k,” Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, vol. 68, no. 4, pp. 1096 – 1100, 2007. Seventh International Conference on Raman Spectroscopy Applied to the Earth and Planetary Sciences. 90

[24] A. Giannasi, M. Celli, L. Ulivi, and M. Zoppi, “Low temperature raman spectra of hydrogen in simple and binary clathrate hydrates,” The Journal of Chemical Physics, vol. 129, no. 8, p. 084705, 2008. 90

[25] R. Ohmura, W. Shimada, T. Uchida, Y. H. Mori, S. Takeya, H. M. Jiro Nagao, T. Ebinuma, and H. Narita,“Clathrate hydrate crystal growth in liquid water saturated with a hydrate-forming substance: variations in crystal morphology,” Philosophical Magazine, vol. 84, no. 1, pp. 1 – 16, 2004. 96, 97

[26] S. Subramanian and E. Sloan,“Solubility effects on growth and dissolution of methane hydrate needles,”Proceedings of the International Conference on Gas Hydrates, 2002. 97, 98

[27] O. Fandi˜noand L. Ruffine, “Methane hydrate nucleation and growth from the bulk phase: Further insights into their mechanisms,”Fuel, vol. 117, Part A, pp. 442 – 449, 2014. 97

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[28] M. Ricaurte, C. Dicharry, D. Broseta, X. Renaud, and J.-P. Torr´e,“CO2 removal from

a CO2CH4 gas mixture by clathrate hydrate formation using thf and sds as water- soluble hydrate promoters,” Industrial & Engineering Chemistry Research, vol. 52, no. 2, pp. 899–910, 2013. 97

[29] “Methane hydrate propagation on surfaces of varying wettability,” Journal of Natural Gas Science and Engineering, vol. 35, pp. 1535 – 1543, 2016. 97

[30] F. Jim´enez-Angeles´ and A. Firoozabadi, “Enhanced hydrate nucleation near the limit of stability,” The Journal of Physical Chemistry C, vol. 119, no. 16, pp. 8798–8804, 2015. 109

[31] F. Caupin, “Escaping the no man’s land: Recent experiments on metastable liquid water,”Journal of Non-Crystalline Solids, vol. 407, pp. 441 – 448, 2015. 7th IDMRCS: Relaxation in Complex Systems. 110

[32] N. N. Nguyen, A. V. Nguyen, K. M. Steel, L. X. Dang, and M. Galib, “Interfacial gas enrichment at hydrophobic surfaces and the origin of promotion of gas hydrate forma- tion by hydrophobic solid particles,” The Journal of Physical Chemistry C, vol. 121, no. 7, pp. 3830–3840, 2017. 111

117 CHAPTER 4. CO2 HYDRATE FORMATION AND GROWTH IN GLASS CAPILLARIES

118 Chapter 5

Gas hydrate phase diagrams

Contents Abstract ...... 120 5.1 Methods of determining hydrate equilibria ...... 121 5.1.1 Abrupt change in the slope of the temperature or pressure . . . . . 124 5.1.2 Electrobalance method ...... 126 5.1.3 Differential Scanning Calorimetry (DSC) ...... 127 5.1.4 Quartz Crystal Microbalance (QCM) ...... 127 5.1.5 Visual observation ...... 128 5.2 Materials and methods ...... 129 5.2.1 Materials ...... 129 5.2.2 Experimental procedure ...... 129 5.3 Results and discussion ...... 132 5.3.1 Simple hydrate dissociation above the ice melting point ...... 133

5.3.2 Metastable extension of Lw – H – V below 0 ◦C ...... 137 5.3.3 Enthalpy of dissociation and the quadruple points ...... 141

5.3.4 Synergy effect in the formation of CO2 + cyclopentane system . . . 147 5.4 Conclusion ...... 151 5.5 Références ...... 152

119 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

Abstract

Knowledge of the stability domain of gas hydrates represents the most important set of hydrate properties1,2 for a number of applications of practical interest (i.e., flow assur- ance,3,4 gas storage5 and transportation of energy-carrier gases6,7 or greenhouse gases,8,9 gas-mixture separation,10–13 exploitation of future energy sources,14,15 seawater desalina- tion16–18, and secondary refrigeration19,20).

In this chapter, We will remind briefly a set of methods widely used in the literature, giving their advantages and limitations. Our aim is not to seek the best method, but to show the points that distinguish one method from the others. We will then present the proposed method based on the use of glass capillaries as pressure and temperature-controlled optical cells. Finally, we will give the phase diagrams of the studied systems, starting with the three-phase water liquid (Lw) + simple hydrate (H) + guest-rich vapor (V) equilibrium pressure-temperature conditions at temperatures above the ice melting temperature (0 ◦C) in the systems of water and each of the following guests: nitrogen (VN2 ), methane (VCH4 ) and carbon dioxide (VCO2 ). The three-phase water liquid (Lw) – hydrate (H) – CO2- rich liquid (LCO2 ) equilibrium pressure-temperature is also presented. The effect of a help gas on hydrate equilibrium is illustrated by the system cyclopentane + carbon dioxide.

The measurements were also performed for the supercooled water liquid (Lw∗ ) – hydrate (H) – guest-rich vapor (V) three-phase equilibrium conditions at temperatures below the ice melting point (0 ◦C). The pressure ranges of the present measurements are (10.5 to 300) bar in the water + nitrogen system, (10.4 to 280) bar in the water + methane system, (1.7 to 684.5) bar in the water + carbon dioxide system, and (1 to 50) bar in the water

+ carbon dioxide + cyclopentane system. We report in addition the gas (N2 an CO2) effect on the ice melting point and the lower quadruple points (Q1) and upper quadruple point (Q2) of the water + carbon dioxide system. The enthalpy of the dissociation of

CO2,N2 and CH4 simple hydrates into water and guest-rich vapor are determined using the Clausius-Clapeyron equation. The measured data will be compared with the corresponding data reported in the literature.

120 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

5.1 Methods of determining hydrate equilibria

A phase diagram is a graphical representation, generally in two or three dimensions, delimiting the domains of the stability of one, two or three phases under chosen variables. Common types of variables are used; pressure (p), temperature (T), concentrations, volume or density and phase amounts. In this study, we present pT phase diagrams. The conditions of pressure and temperature determine what are the phases (gas, liquid, solid) formed by the water and guest molecules. Different phase diagrams exist, depending on the number of compounds making up the system. The phase diagram of H2O is a starting point for the characterization of phase behavior in the systems forming clathrate hydrate (H). In the usual ranges of pressure and temperature, pure water which is a basic compound of hydrate

(host) is in the form of liquid water (Lw) or ice (I). The compound which is susceptible of being trapped in the hydrate (guest) such as CO2 may be in gaseous (V), supercritical

(SC) or liquid state (Lc). The increase of the number of components to two or three results in an increase in the complexity of the phase behavior. Figure 5.1 illustrates a typical phase diagram showing the phases formed from water and a single type of guest molecules, which themselves exhibit a liquid-vapor phase transition. For a 2-component system (water + guest), the phase rule says the three-phase coexistence are defined by lines in the pT coordinates, which delineate regions of two-phase coexistence (Figure 5.1). Two three- phase coexistence lines intersect at quadruple points, denoted Q1 (lower quadruple point) and Q2 (upper quadruple point) corresponding to the coexistence of four different phases (see their exact definition below). If the temperature and/or the pressure are changed so as to traverse a line of three-phase coexistence, a phase change will occur, where one of the two coexisting phases is replaced by another phase. In other words, a phase disappears and another phase appears when crossing this coexistence line. The dotted line is the line of coexistence between ice, liquid water and vapor (Lw - I – V): this line is not vertical as there is an effect of pressure (or dissolved gas) on the ice melting temperature (Figure 5.1).

The lower quadruple point (Q1) corresponds to the coexistence between ice (I), liquid water (Lw), guest-rich vapor (V), and hydrate (H). It is usually located very close to the triple point of pure water, where liquid water, ice and water vapor coexist. In the case of a guest with a liquid/vapor transition in the region of interest (such as CO2,C2H6,C3H8 or

H2S), there is in addition another quadruple point (Q2) corresponding to the coexistence

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Figure 5.1: pT phase equilibria of a water + guest binary system, in which the guest component has a liquid/vapor transition in the region of interest (at high enough p and T) and there is therefore an upper quadruple point Q2 (see text). Lw, water-rich liquid; I, ice; H, gas hydrate; V, guest-rich vapor; Lc, guest-rich liquid.

between liquid water, guest-rich liquid (Lc), guest-rich vapor, and hydrate, as illustrated in Figure 5.1. To go further in the understanding of equilibrium diagrams, the reader may refer to the remarkable synthesis by Mooijer in his thesis.21

The phase diagram can be either determined with experimental methods or predicted by theoretical models. In order to validate the theoretical models and be able to predict physical reality, we need thermodynamic data that must be carefully obtained with well- designed devices and methods. The determination of the dissociation temperature (or pressure) of the hydrates in the presence of an aqueous phase has been widely studied in the literature. It is reminded here that the thermodynamic (equilibrium) values are obtained in practice by letting one of the phases (here the hydrate) slowly vanish (hence the equivalence between dissociation and equilibrium conditions), whereas the formation of the hydrate phase usually requires conditions far from the equilibrium – the fluid system in the absence of the hydrate remains metastable.

At the beginning of the discovery of gas hydrates, researchers began to study either with highly soluble gases in water and/or under moderate pressure conditions where hy- drate can form in a blown glass apparatus. Then, numerous experimental techniques have

122 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS been developed to measure the properties of hydrates. In the majority of studies hydrate formation/dissociation is carried out in a closed cell under static conditions; that is to say without recirculation of a fluid phase. Use of the laser scattering, x-ray computed tomog- raphy, and electron microscopy tools to investigate the hydrate at mesoscopic scale and Raman, nuclear magnetic resonance spectroscopy, x-ray, and neutron diffraction tools at microscopic level, marked a remarkable advance. Conversely, the experimental devices used actually to measure the macroscopic properties such as phase equilibrium properties, are based on the same principle as that used by Deaton and Frost (1946) in their experimental setups.1 Generally, to build an experimental apparatus, it takes a period of several months (or even years) and, due to long metastable periods to trigger the formation of hydrates, an equilibrium pressure-temperature point requires one or two days of experimental effort. In order to better dissolve the guest in water and accelerate the formation and growth of gas hydrate, several ways are used, for example the mechanical, magnetic or ultrasonic agitator, rotation or tilting of the cell, injection of the guest directly into the water by the bottom of the cell, use of stainless steel balls to provide surface renewal and form more hydrate, addition to the aqueous phase of ice22 or chemicals called kinetic promoters, etc.

In order to obtain the equilibrium diagrams of gas hydrates, researchers apply pro- tocols based on the direct or indirect observation of the hydrate phase. A direct proof of existence or absence of the hydrate phase is the observation with eye, using optical devices, of the different phases (water and guest) contained in the experimental cell. The indirect method is based on the variation of a physical quantity such as pressure, temperature, vol- ume, heat, mass, resonance frequency, etc. The phase diagram study (direct or indirect) can be performed in a closed system, following an isochoric, isobaric or isothermal process, or in an open system, following an isobaric or isothermal process. By convention, a point (tem- perature and pressure) of the equilibrium diagram corresponds to the disappearance of the last hydrate crystal. This convention gives rise on the one hand to practical difficulties and, on the other, to ambiguities in the definition of equilibrium. Here, and as already pointed out above, the expressions ’hydrate dissociation diagram’ and ’hydrate equilibrium diagram’ are both considered to have the same meaning: limit of hydrate stability region. Stepwise heating and maintaining the system at constant temperature for a sufficient time generates more reliable experimental data.23 Moreover, the accuracy of the hydrate equilibrium points is found to be highly dependent on the heating rate during hydrate dissociation.23,24

123 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

5.1.1 Abrupt change in the slope of the temperature or pressure

This method is the most usual technique of determination of the dissociation diagram of gas hydrates. It consists in varying temperature (or pressure) and measuring pressure (or temperature) in a cell (reactor)25 where the hydrate may be present together with the aque- ous phase and the guest-rich phase.25 The cell is usually instrumented with temperature and pressure sensors, and these two parameters (T and p) are monitored. The physical quantity indicating the formation/dissociation of the gas hydrate is a sudden change in pressure or temperature during a cooling/heating or compression[1]/decompression[2] process.

In the example illustrated in Figure 5.2, the formation or dissociation of gas hydrate is seen through and abrupt change in pressure when temperature is decreased or increased in an isochoric cell[3]. The plot in Figure 5.2 represents a typical path in the temperature and pressure coordinates: temperature is lowered from the point P0 and the pressure decreases slowly until the conditions of hydrate formation (point P1) are reached. The formation stage is accompanied by a strong pressure drop due to the consumption of the gas, and sometimes an increase in temperature caused by the exothermicity of the hydrate formation.

At point P2 the temperature is slowly increased. Hydrate dissociation, gradually releasing the gas, causes a rapid increase in pressure at point P3, where it is assumed that all of the hydrate has dissociated. An abrupt variation of the slope then marks the end of the release of trapped gas. P3 is considered as a hydrate equilibrium point.

This method requires heavy equipment and long experimental times to ensure that equilibrium in a sample of a few tenths of centiliters is reached. The measurements can be made in static mode, in the form of a succession of isothermal stages, or in dynamic mode, according to a programmed temperature ramp (as illustrated in Figure 5.2. In this case, the heating rate must be very low (< 1 ◦C per hour) to ensure that the dissociation takes place under conditions very close to equilibrium. This method can be applied to opaque media, such as emulsions. Estimated uncertainty of the dissociation temperatures obtained using this method is ± 0.5 ◦C.

The study of hydrate stability below the ice melting point (which deponds on the pres- sure and dissolved gas) is important for example in oil/gas exploration in Arctic conditions

[1]decrease the volume using a piston or add gas in the cell [2]increase the volume using a piston or cause a gas leak [3]The hydrate formation and dissociation occur in a closed system

124 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

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Figure 5.2: Pressure and temperature changes during a hydrate formation/dissociation experiment by the isochoric presses (see text).

or in astrophysical research. To get the stability domain of hydrate below the ice point, ice powders are used instead of water (or aqueous phase) to form hydrate. After a few days, the surface of the ice (in contact with the gas) converts into a hydrate. Hydrate formation can be easily detected by a decrease in pressure. After hydrate formation, temperature is then incrementally increased in steps of some fractions of degrees. The hydrate dissociates at a certain temperature value, thereby is increasing the pressure. The point at which the pT data plots sharply change is considered to be the point at which all the hydrate crystals dissociate and, hence, is the three-phase equilibrium point.26

Another experiment consists in bubbling gas through water above 0 ◦C, to form a foam in a high-pressure cell. Before the cell is cooled below the ice point, free water was evacuated, then the temperature is lowered and a honeycomb mass of hydrate is formed.

The same protocol as that of LW – H – V (for temperatures above 0 ◦C) is used to measure the dissociation pressure.27 This procedure can be used to study the equilibria of simple hydrate, but the double hydrate dissociation may occur over a range of pressures, because the composition may be unevenly distributed over the sample.1

Instead of varying temperature, we can also keep it constant and change pressure by removal or addition of gas in the experimental cell. In one example of experiments conducted at temperatures below the ice melting point,28 the equilibrium pressure at a given

125 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

temperature is approached by a series of gas removals: a pressure drop indicates hydrate formation and an increase in pressure indicates hydrate dissociation (Figure 5.3). This process is repeated in successive approximations until the equilibrium pressure is reached, as shown on the right in Figure 5.3.

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Figure 5.3: The decrease and increase in pressure are monitored and indicate respectively the formation and dissociation of gas hydrate under isothermal process. The gas is rapidly admitted into or vented from the system. This process is repeated in successive approximations until the gap (difference between the hydrate formation and dissociation pressures) reaches 1 – 2 % of the absolute pressure.28

5.1.2 Electrobalance method

Hydrate formation/dissociation is detected from the mass change using a balance.29 First, the water is frozen and put in contact with a water-saturated gas phase at the desired pressure. The hydrate is formed from water molecules contained in the gas phase and its mass is added to that of the ice. After hydrate formation, the temperature is slowly increased (maintaining constant pressure by fluid withdrawal) until a weight loss is observed. The temperature at which this weight loss occurred is taken as the dissociation temperature.

The accuracy is estimated to be equal to 0.3 ◦C. This method requires a large gas volume with a high water content.

126 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

5.1.3 Differential Scanning Calorimetry (DSC)

At the beginning, DSC was used to determine the phase equilibrium data of solid/solid or solid/liquid in various fields: organic and inorganic chemistry, metallurgy, ceramics and pharmaceuticals.30 Then, it was used to determine the thermodynamic properties of model gas hydrates (temperature and enthalpy of dissociation) such as trichlorofluoromethane31 or tetrahydrofuran,1 which form at atmospheric pressure. Today, this technique is practically applied to all hydrates under low and high pressures.32

DSC detects transformations that involve heat flux, such as hydrate formation or dissociation. Unlike other techniques, measurement of the temperature of the sample is indirect. It consists in continuously measuring the flow of heat exchanged between the reactor containing the hydrate and other phases and a thermostat during a predefined tem- perature program. To eliminate the instabilities not caused by the transformation studied, this signal is subtracted from that obtained from a measurement carried out simultaneously on a reference cell. Only a few tens of µL of volume of the sample are necessary to make the measurements.

Hydrate crystallization in DSC experiments always requires a certain supercooling (commonly called subcooling) in order to compensate the absence of agitation. To increase the hydrate quantity in the cell, several cycles of formation and melting of ice and hydrate are realized before doing the measurement of dissociation point. The hydrate forms during ice melting. The main limitation of this method remains the absence of agitation. The use of this method becomes problematic when the dissociation temperature of the hydrate is close to the ice melting temperature.

5.1.4 Quartz Crystal Microbalance (QCM)

This method is based on the oscillation of a thin disk of quartz at a particular resonant frequency when an electric current is passed across two electrodes. This system (a thin disk sandwiched between two electrodes) is placed in a high-pressure cell containing water and gas and equipped with a pressure transducer and a thermocouple. The resonant frequency will be changed if any hydrate attaches to the surface of the disk. The QCM is extremely sensitive and measures small changes in mass: 1 ng mass change gives a 1 Hz frequency change.33 The measurement requires only a few tens of minutes because the volume of

127 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS the sample (one drop of water) is much smaller than in the three previous methods. If the hydrate does not adhere to the surface of the quartz crystal, then the dissociation of hydrates cannot be detected.

5.1.5 Visual observation

Visual observation remains the only direct evidence of the presence of hydrate phase provided that the crystals are sufficiently large. In this method, the hydrate crystals are formed within a transparent equilibrium cell, usually in synthetic sapphire or quartz. The formation of the hydrates in the cell is observed by eye or a camera.34–39. An optical microscope is often used.

The visual method allows both the study of the kinetics of formation and growth, morphologies of different hydrate structures, the effect of the substrate in contact with the hydrate (confinement, wettability, etc) and the determination of hydrate stability limit. Another advantage is to be able to study the hydrate at different scales depending on the optical instrument used (cf. Chapters 3 and 4).

Similarities between hydrate and ice make measurement of the conditions of gas hydrate dissociation in the presence of ice practically impossible. In the following, we expose a method based on visual observation of gas hydrate using a glass capillary as a high-pressure cell. The glass capillaries were used in the middle of the last century by C. L. Hosler, and C. R. Hosler (1955) in their studies on the effect of the radius of the capillary on the freezing point of water.40 The reasons that led us to use capillaries for hydrate study are detailed in Chapters 3 and 4.

128 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

5.2 Materials and methods

5.2.1 Materials

The experimental scheme is detailed in Chapter 4 devoted to the study of the mech- anisms of formation and growth of CO2 hydrate.

The gases used in this work, carbon dioxide, methane and nitrogen (purity 99.995 mol%) were provided by Air Liquid with a certified purity of 99.995 mol%. Pure water (resistivity of 18.2 MΩ·cm) produced by a laboratory water-purification system from Purelab. Cy- clopentane with more than 98% purity, was purchased from Sigma-Aldrich.

5.2.2 Experimental procedure

The experiments are conducted at constant pressure under a varying temperature. They all start by forming the hydrate for the first time (primary nucleation) on the menis- cus between the water and guest phases and then raising the temperature until the hydrate disappears (first hydrate dissociation). The features associated with these first two steps have been described and discussed in Chapter 4. Then the dissociation temperature Teq is obtained by consecutive sequences of hydrate dissociation and reformation, taking advan- tage of the memory effect (see Figure 5.4). Each sequence of dissociation and reformation consists in first raising temperature until the complete dissociation of the hydrate crystals to a value T1 which is the first approximation of equilibrium temperature. The dissocia- tion sequence lasts as long as some hydrate crystal is present at or near the water – guest meniscus.

T1 = Teq + ∆T1 (5.1)

where the deviation from equilibrium ∆T1 depends on the heating rate, the size of the hydrate crystals formed, its morphology and its position in the capillary (in bulk water or as a halo on the inner wall of the capillary). Then, the temperature is then lowered rapidly until hydrate is reformed again by virtue of the memory effect (which itself depends on 41 ∆T1 and on the waiting time at this temperature). In this formation step, the hydrate is reformed under a supercooling much less than in the case of the first formation (see Figure 5.4). Then, in a subsequent sequence of dissociation/formation, the temperature is increased to a value slightly lower than (e.g., one degree below) T1 with a lower heating

129 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

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Figure 5.4: Typical temperature sequence to determine the gas hydrate dissociation condition at temperatures above than the lower quadruple point Q1.

rate (e.g., 1 ◦C/min). If the hydrate does not melt, the temperature is then increased in

steps of 0.2 ◦C. The system is left at constant temperature in each step for a duration that depends on the dissociation kinetics. If there is no change in hydrate texture, the system is heated to a higher temperature. The last step corresponds to the disappearance of the

last crystal of hydrate. In this way, a temperature (T2) closer to equilibrium (∆T2 < ∆T1) is obtained,

T2 = Teq + ∆T2 (5.2)

By repeating this process with a slower heating rate, the interval between the disso-

ciation and reformation temperature decreases, until it reaches about 0.2 ◦C thus providing

a value for the equilibrium temperature to within ±0.2 ◦C. This deviation is considered as the measurements uncertainty.

To check the accuracy of our result, the system is kept at the determined temperature and the pressure is increased to reform hydrate, then the system is slowly brought back to the dissociation pressure. If the hydrate crystals is completely decomposed, this means that the determined temperature is the good value.

Approaching hydrate equilibrium, large hydrate crystals are observed to grow at very slow growth rates at the expense of smaller hydrate crystals. We interpret this phenomenon as an Ostwald ripening effect. The hydrate halo is often observed to melt at a slightly lower

130 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

temperature than bulk crystals, which could be explained by Gibbs-Thomson effect. The time required for such a measurement is in the order of one hour.

As emphasized in Chapter 4, the formation of ice must be avoided, in such a way that only one meniscus is present during the experiment. In fact, ice formation induces difficulties. Ice traps gas in the form of gas inclusions. When the ice melts, the entrapped gas is released and forms bubbles, with diameters sometimes equal to the inner diameter of the capillary; therefore, several water – gas interfaces (meniscus) are generated. Then, the hydrate grows on these menisci and forms crusts which adhere to the capillary inner wall (see Figure 5.5). These systems (water – hydrate – gas) are not in mechanical equilibrium. When heated, the hydrate decomposes at different temperatures depending on local pressure.

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Figure 5.5: A schematic representation of the formation of hydrate crusts on water – gas menisci.

Once a point of equilibrium pT is obtained, the pressure is increased and the hydrate

is reformed by memory effect, and the new Teq is obtained more rapidly. Thus, a complete phase diagram can be obtained in a day.

Quartz capillaries, used in the present work, resist to pressures up to 1000 bar. The metastability effect of water that is related to the capillary size allowed us to explore

temperatures below 0 ◦C (see below, section 5.3.2): water remains supercooled liquid down

to very low temperature, -30 to -40 ◦C in some cases.

131 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

5.3 Results and discussion

The three-phase equilibrium in the binary systems containing water in contact with different gases (methane, nitrogen, and carbon dioxide) and in ternary system water – cyclopentane - carbon dioxide determined in the present work are listed in Tables 5.1.

Hydrate former Phases at equilibrium p range (bar) T range (◦C) Figure Table Lw∗ –H–V 1.7 – 12.0 -17.0 – -0.5 5.13 Lw –H–V 16.0 – 40.0 2.0 – 9.1 5.7 CO2 5.5 Lw –H–Lc 45.0 – 684.5 9.8 – 15.2 5.6 Lw –I–V 10.4 – 20.0 -0.8 – -1.4 5.17 Lw∗ –H–V 2.0 – 8.0 -9.8 – -2.9 5.15 CH4 5.6 Lw –H–V 30.5 – 280.0 0.7 – 22.0 5.10 Lw∗ –H–V 10.5 – 150.0 -27.0 – -1.1 5.14 N2 Lw –H–V 180.0 – 300.0 1.2 – 6.1 5.9 5.7 Lw –I–V 40.0 – 130.0 -0.7 – -1.5 5.18 CP + CO2 Lw – DH – LCP –V 1.5 – 50.0 10.5 – 150.0 5.21 5.8

Table 5.1: different three-phase equilibrium examined in the present study: Lw, water-rich liquid; I, ice; Lw∗ , supercooled water; V, guest-rich vapor; Lc, guest-rich liquid; LCP cyclopentane liquid; H, simple hydrate; DH, double hydrate.

The uncertainty in the determination of equilibrium temperature is estimated to be in the range of 0.2 ◦C. The pressure is measured by both a digital manometer and the high- pressure pump used in the constant-pressure mode. The pressure values up to 300 bar, reported in the present work, are those displayed in the digital manometer. The accuracy of this manometer is 0.1 % at ambient temperature. At pressure above 300 bar, the reported pressure is that displayed by the high-pressure pump. The variation of room temperature where the high-pressure pump is located induces small changes in gas pressure, to which the high-pressure pump (used in the constant-pressure mode) responds when pressure varies by ±0.3 bar around the target value.

132 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

5.3.1 Simple hydrate dissociation above the ice melting point

5.3.1.1 Carbon dioxide hydrate

Carbon dioxide is a water-soluble compound and together with water forms a clathrate

hydrate of structure I. For each chosen pressure, the dissociation temperature of CO2

hydrate along the three-phase coexistence (liquid water, hydrate, and CO2 vapor or liquid) is measured by means of the procedure described above and in Figure 5.4. The results are

plotted in Figures 5.6 and 5.7, corresponding respectively to the Lw –H–Lc and Lw –H – V equilibria, together with some of the results published in the literature.

Figure 5.6 displays the measured equilibrium data at pressures from 45 to 684.5 bar,

where CO2 is liquid in the temperature range of CO2 hydrate stability. The Lw –H–

Lc equilibrium data are plotted together with those obtained by using other methods and available in the literature. In their determination of hydrate dissociation point, Ohgaki and his coworkers (1993)42 used a high-pressure view cell where they varied gradually the temperature and the pressure drop or increase indicates hydrate formation or dissociation (see section 5.1.1 and Figure 5.2). The data reported by Takenouchi and Kennedy (1965)43 were obtained by varying the pressure instead of temperature in a stainless-steel autoclave (see section 5.1.1).

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Figure 5.6: water – CO2 hydrate – CO2-rich liquid three-phase equilibrium pT conditions in a carbon dioxide + water system. X, Takenouchi et al.43; , Ohgaki et al.42; , present study ⃝ ▲ (cf. table 5.5).

Figure 5.7 displays the measured equilibrium data corresponding to pressures below

45 bar, where CO2 is a vapor in the temperature range of CO2 hydrate stability. The Lw –

133 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

H – V equilibrium data are plotted together with literature data obtained by other methods.

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Figure 5.7: liquid water – CO2 hydrate – CO2 gas three-phase equilibrium pT conditions in a carbon dioxide + water system: X, Vlahakis et al.44; , Larson.45; , present study (cf. table ⃝ ▲ 5.5).

Judging from Figures 5.6 and 5.7, the agreement of the new data with the literature data is satisfactory.

5.3.1.2 Nitrogen hydrate

Nitrogen molecules together with water form a hydrate of structure II, where the 12 N2 molecules occupy the small cavities 5 . Similarly to what is observed with CO2 (see

Chapter 4), the N2 hydrate is usually formed first at the interface between water and N2

prior to ice for p > 100 bar when lowering the temperature to around -38 ◦C (see Figure 5.8). In a few experiments, we however formed ice rather than nitrogen hydrates directly from

supercooled water and N2 gas, presumably because of the very low solubility of nitrogen gas in water; in these cases, the temperature was increased until ice melting, and the melting of the ice promoted hydrate nucleation and growth.

The N2 hydrate equilibrium curve was determined experimentally from 1.2 ◦C and

180 bar to 6.1 ◦C for 300 bar. It is represented in Figure 5.9, together with the data by van Cleeff and Diepen46 and by Jhaveri and Robinson,47 who used an autoclave of stainless steel with two glass window and a method based on visual determination of hydrate dissociation points at constant temperature and variable pressure. The three sets of data are in good agreement. van Cleeff and Diepen46 measured equilibrium points for temperatures down to

134 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

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Figure 5.8: N2 hydrate formation on the water – N2 meniscus at 200 bar and -38.5 ◦C: the meniscus between water and N2-rich vapor (a) was covered within less than one second by a hydrate crust (b), and hydrate needles (or fibers) were observed to grow from the meniscus to bulk water (b).

-4 ◦C corresponding to metastable liquid water in equilibrium with N2 vapor and hydrate.

The pT equilibrium points of nitrogen hydrate determined by the method presented in this work agree very well with those determined by Van Cleeff and Diepen and by Jhaveri and Robinson.

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Figure 5.9: water liquid – N2 hydrate – N2 gas three-phase equilibrium pT conditions in a nitrogen + water system: X, van Cleeff et al.46; , Jhaveri et al.47; , present study (cf. table ⃝ ▲ 5.7).

5.3.1.3 Methane hydrate

The CH4 hydrate equilibrium curve was determined in the temperature and pressure

ranges of 0.7 – 22 ◦C and 30 – 280 bar, respectively. The data are plotted in Figure 5.10, together with the data provided by Adisasmito et al.48 and Mcleod et al.49. The measured data are presented in Table 5.6.[4]

[4] data determined jointly with Dyhia Atig, LFCR.

135 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

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Figure 5.10: water liquid – CH4 hydrate – CH4 gas three-phase equilibrium pT conditions in a methane + water system: X, Adisasmito et al.48; , Mcleod et al.49; , present study (cf. 5.6). ⃝ ▲

The kinetics of dissociation of methane hydrates is slower than that of CO2 hydrate.

This is due to the fact that its water solubility is lower than that of CO2 molecules.

I noticed that the memory effect is very weak. For each new equilibrium point, the complete protocol described in the procedure section 5.2.2 is applied.

The halo (see Chapter 3) of methane hydrate sometimes melts at a lower temper- ature than that of the hydrate in bulk water, which is considered to be the equilibrium temperature.

136 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

5.3.2 Metastable extension of Lw – H – V below 0 ◦C

Numerous researchers have experimentally observed that hydrates may remain stable for prolonged periods outside their stability region when the system is brought back to atmospheric pressure. This phenomenon is widely known as the self-preservation50 effect or the anomalous preservation50–52 of gas hydrates. One of the explanations for self- preservation effect is that the hydrate particles are covered by an ice layer. This layer prevents guest molecules diffusion from hydrate to the surrounding phase.53 Investigations via molecular dynamic simulation, coupling between the mass transfer resistance and heat transfer resistance, indicate that heat transfer facilitates the formation of the ice-like layer and hence inhibits the further dissociation of the hydrates.54 Despite many studies on the self-preservation effect,55–57 the mechanism of this phenomenon is still not fully understood. The ability to lower the equilibrium pressure of gas hydrates and extend their stability is desirable for gas storage and transportation applications.58,59

Melnikov and his coworkers showed in experiments conducted with water droplets 60 61 62 that, below the ice melting point, methane , propane and CO2 hydrate dissociate into supercooled water (Lw∗ ), and vapor. These visual observations were confirmed with NMR based measurements on dissociation of Freon-12 hydrate .63,64 Raman spectroscopy has revealed that ethane hydrate also decomposes into supercooled water and gas once the system pressure drops below equilibrium value for ice, hydrate, and free gas.65 Melnikov et al. determined the coexistence between supercooled (metastable) liquid water (Lw∗ ), C vapor and hydrate in a range of temperatures extending well below 0 ◦ : the L∗w –H–

V coexistence line determined by these authors is in fact an extension of the Lw –V–H coexistence line to these temperatures (see Figure 5.11).46

In this thesis, the extension of Lw – H – V to T below the lower quadruple point

Q1 has been determined for these three guest compounds: methane, carbon dioxide and nitrogen. The hydrate was first formed at high enough pressure by decreasing T to very high supercooling. We remind that the water remains a supercooled liquid even if T reaches

-35 ◦C. Then, the pressure is slowly dropped (1 bar/min) to a value for which we want to determine the equilibrium temperature (see Figure 5.12). To get a first approximation on the Teq, the temperature is increased to dissociate completely the first formed hydrate.

Then the dissociation temperature Teq is obtained by consecutive sequences of hydrate

137 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

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Figure 5.11: Metastable hydrate boundaries in the pT phase diagram for a H2O + gas system. Q1 is the lower quadruple point where liquid water, ice, hydrate and gas coexist at equilibrium.

dissociation and reformation, taking advantage of the memory effect as is described in

section 5.2.2. The same phenomena that are observed at temperatures above 0 ◦C are also encountered in the supercooled water + gas system. In particular, monocrystals formed at very small supercoolings are observed.

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Figure 5.12: Typical temperature sequence to determine the gas hydrate dissociation condition at temperatures below than the lower quadruple point Q1.

Figures 5.13, 5.14 and 5.15 show the metastable extentions of the three-phase diagram

(Lw – H – V) for the water + guest-rich phase (CO2,N2 and CH4 respectively) system

at temperatures below 0 ◦C. These determined data are also reported in Tables 5.5, 5.7

138 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

and 5.6 for different systems. Our data agree very well with those determined by Melnikov and his coworkers and van Cleeff and Diepen using the visual method. For the best of our knowledge, no data is reported in the literature for Nitrogen hydrate metastable extension

below -4 ◦C.

The dissociation of metastable hydrates into supercooled water and gas, shows in these systems a reversible character. If, after the completion of the hydrate melt into

supercooled water and gas, the temperature is decreased below Teq, the hydrate nucleate at low supercoolings on the meniscus and the halo is observed to grow from the meniscus into the gas phase as described in Chapter 4. Ice growth, which is very fast and occurs in bulk water, is not observed in these experiments. According to the thermodynamics, this growth is possible only if the chemical potential of water in the metastable hydrate is lower than that of supercooled water in the area bounded on the pT phase diagram by the ice- hydrate-gas (I – H – V) equilibrium line and the supercooled water-hydrate-gas metastable

equilibrium line (Lw∗ – H – V), cf. Figure 5.11. It is interesting to note that the presence of hydrate in the supercooled water did not lead to fast ice nucleation, whereas using thawed water promotes hydrate nucleation.

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Figure 5.13: Supercooled water – CO2 hydrate – CO2 gas three-phase equilibrium pT conditions in a carbon dioxide + water system: , Melnikov et al.62; , present study (cf. 5.5). ⃝ ▲

139 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

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Figure 5.14: Supercooled water – N2 hydrate – N2 gas three-phase equilibrium pT conditions in 46 a nitrogen + water system: X, van Cleeff and Diepen. ; ▲, present study (cf. 5.7).

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Figure 5.15: supercooled water – CH4 hydrate – CH4 gas three-phase equilibrium pT conditions 63 in a methane + water system: X, Melnikov et al. ; ▲, present study (cf. 5.6).

140 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

5.3.3 Enthalpy of dissociation and the quadruple points

5.3.3.1 Quadruple Points

In the present work, the lower quadruple, Q1, point was determined graphically. It corresponds to the intersection of the three-phase Lw – H – V including the metastable C extension down to temperatures well below 0 ◦ (Lw∗ – H – V discussed in previous subsec- tion) with the extrapolated liquid water – ice – vapor phase (Lw – I – V) line. This last three-phase line has been determined by observing the ice melting at low pressure.

Ice is birefringent. Birefringence is the optical property of a material having a refrac- tive index that depends on the polarization and propagation direction of light. Figure 5.16 illustrates the appearance and disappearance of light when the rays pass through the polar- ising filter and then through the ice. This property allows to accurately track the melting of ice.

Figure 5.16: The ice birefringence property at -1.5 ◦C and 6 bar of CO2. A polarising filter has been detected when the light pass through the polarising filter and then through the ice

At low pressure, the ice is formed prior to hydrate at temperatures around -20 ◦C.

Figures 5.17 and 5.18 show the effect of CO2 and N2 gas on ice melting point at different pressures. By increasing the pressure, the melting point of ice is shifted to low temperatures.

The effect of CO2 is slightly important than N2 gas. This is probably due to the fact that

CO2 is much more soluble (by more than one order of magnitude) in water than the N2.

The three-phase Lw –I–VCO2 and Lw –I–VN2 pT conditions data are respectively reported in table 5.5 and 5.7.

The lower quadruple point, Q1, is determined for CO2 (see figure 5.17) and N2 (5.18) hydrates and reported in table 5.2. In the literature, Sloan and Koh (2008) report a lower quadruple point values of (-0.1 ◦C, 12.56 bar) for CO2 and (-0.2 ◦C, 143 bar) and (-1.3 ◦C, 143.38 bar) for nitrogen.1

141 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

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142 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

Hydrate former Point T (◦C) p (bar) Q1 -1.6 10.6 CO2 Q2 10.0 44.2 N2 Q1 -1.5 140.9

Table 5.2: Lower quadruple point, Q1 of the CO2 and N2 hydrates determined graphically based on the intersection between Lw – I – V and Lw – H – V and upper quadruple point, Q2 of the

CO2 hydrate corresponds to the intersection between Lw –H–LCO2 and Lw –H–VCO2 lines

In addition to the lower quadruple point, Q1, the Lw + H + CO2 system presents an upper quadruple point Q2. In the present study, this point is determined graphically and it’s corresponds to the intersection of the extrapolated Lw –H–LCO2 line with the three-phase

Lw –H–VCO2 , see figure 5.17. The value of the upper quadruple point (Lw –H–LCO2

–VCO2 ) is reported in table 5.2. In the literature, several authors have determined this 66 quadruple point: Robinson and Mehta reported 10.1 ◦C and 44.68 bar, Mooijer-van den 67 1 Heuve and his coworkers find 10.12 ◦C and 44.8 bar and Sloan and Koh 9.85 ◦C and 44.99 bar.

Methane and nitrogen have no upper quadruple point, Q2. The pure component critical temperatures of methane and nitrogen (-82.6 ◦C and -147 ◦C, respectively) prevent any possible intersection of their vapor pressures with the three-phase Lw – H – V.

5.3.3.2 Enthalpy of hydrate dissociation

The pT data in Table 5.5, 5.7 and 5.6 correspond to CO2,N2 and CH4 hydrate, respectively, are plotted as ln(P) vs 103/T in Figure 5.19. As can be seen from Figure 5.19, the curves ln(P/Pa) vs 103/T/K exhibit a very good linear relation.

To a first-order approximation, the pT curves can be fitted by the equation ln(P) = a + b, where a and b are positive parameters reported in table 5.3. − T Hydrate former a b R2 CO2 8701.42 45.95 0.998 N2 6942.55 42.02 0.999 CH4 7468.8 42.166 0.998

Table 5.3: Best linear fit parameters of the data reported in figure 5.19, R2 the coefficient of determination

The enthalpy of gas hydrate dissociation can be determined from the univariant slope

143 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

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Figure 5.19: Semilogarithmic plot of the dissociation pressure versus the reciprocal temperature along three-phase equilibrium Lw – H – V for different hydrate former: ,N2; , CO2; X, CH4. ⃝ △

of the phase equilibrium line reported in table 5.3 and by using the Clausius-Clapeyron equation.

dlnP ∆Hd = (5.3) d(1/T) − zR

where z is compressibility factor and R is gas constant. This equation is valid only if

heat of formation, ∆Hd, compressibility factor, and stoichiometry ratios of water to guest (or occupancy) are relatively constant over the range of temperature considered.

The dissociation enthalpies calculated by equation 5.3 for CO2,N2 and CH4 hydrates

are listed in Table 5.4. As the compressibility factor of CO2 changes significantly in the temperature range examined in this work, the enthalpy of hydrate dissociation is calculated

using the compressibility factor corresponding to lower and upper quadruple point (Q1 and

Q2).

The deviation of the experimental data reported in table 5.5 to 5.7 from the values

obtained using the Clausius-Clapeyron equation 5.3 (Tcalc) is calculated using the following expression:

144 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

Hydrate former Point z ∆Hd (kJ/mol) ∆Hd∗ (kJ/mol) Q1 0.924 66.5 63.4 CO2 Q2 0.690 49.6 62.7 N2 Q1 0.997 57.5 46.8 CH4 T0 0.935 58.1 52.0

Table 5.4: Enthalpies of dissociation of simple hydrate and quadruple point, z is the

compressibility factor obtained from www.peacesoftware.de/einigewerte web site.∆Hd∗ 68 calculated using Kamath’s correlation (1984) , T0 = 0 ◦C

Texp Tcalc dev = − ·100 (5.4) Tcalc

Sloan and Koh1 presented a review of literature data for the enthalpy of hydrate dis- sociation obtained by different authors based on Differential Scanning Calorimetry method and Clausius-Clapeyron equation. It is noteworthy that in some cases, the authors did not express at which temperature ∆Hd was calculated and in others presented an average value of ∆Hd for a range of temperature. Even though there is wide variation in the results presented by different authors (57 to 73 kj/mol for CO2 hydrate, 52 to 58 kj/mol for CH4 hydrate and 46 to 66 kj/mol for N2 hydrate), it is observed that the average value is close to the values obtained in this study, showing the consistency of the presented results, in table 5.4, with those of other researchers.

145 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

Lw∗ –H–VCO2 Lw –H–LCO2 T (◦C) p (bar) dev (%) T (◦C) p (bar) -17.0 1.7 2.1 9.8 45.5 -15.0 2.2 4.6 9.9 50.0 -9.6 4.5 7.8 10.0 60.0 -8.0 5.0 1.7 10.3 75.5 -5.5 7.0 1.4 10.4 100.0 -3.8 8.0 5.5 11.0 151.0 -2.6 9.5 2.6 11.4 200.0 -2.0 10.0 4.5 12.0 251.8 -1.5 10.5 5.5 12.3 300.0 -0.5 12.0 3.9 12.9 352.4

Lw –H–VCO2 13.3 402.7 T (◦C) p (bar) dev (%) 13.6 453.0 2.0 16.0 3.9 14.0 503.4 3.0 18.0 3.6 14.3 553.7 3.8 20.2 1.1 14.6 604.0 4.7 22.0 2.7 14.9 654.3 4.9 23.1 0.1 15.2 684.5

5.3 24.0 0.7 Lw –I–VCO2 5.6 25.4 1.6 T (◦C) p (bar) 6.6 28.0 0.3 -1.4 8.0 7.0 30.0 2.8 -1.0 6.0 7.9 33.0 2.4 -0.9 4.0 8.1 35.0 6.3 -0.8 2.0 9.1 40.0 8.9

Table 5.5: Experimental dissociation pressures for CO2 hydrates formed from water – CO2 meniscus in glass capillary.

Lw –H–VCH4 Lw∗ –H–VCH4 T (◦C) p (bar) dev (%) T (◦C) p (bar) dev (%) 0.7 30.5 3.35 -9.8 10.4 4.51 6.7 51.0 3.67 -5.3 15.2 5.14 7.4 58.0 2.49 -2.9 20.0 2.55 9.5 70.4 2.09 12.5 90.6 0.45 16.3 150.0 16.94 22.0 280.0 32.65

Table 5.6: Experimental dissociation pressures for methane hydrates formed from water – CH4 gas meniscus in glass capillary.

146 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

Lw –H–VN2 Lw∗ –H–VN2 T (◦C) p (bar) dev (%) T (◦C) p (bar) dev (%) 1.2 180.0 0.5 -27.2 10.5 16.5 1.7 190.0 0.5 -23.7 15.0 12.0 2.2 200.5 0.5 -18.1 25.0 6.7 4.1 250.0 0.3 -11.6 50.0 2.3 6.1 300.0 0.0 -8.1 75.0 0.9

Lw –I–VN2 -4.6 100.0 0.0 T (◦C) p (bar) -2.8 125.0 0.31 -1.5 130.0 -1.1 150.0 0.5 -1.1 100.0 -0.9 70.0 -0.7 40.0

Table 5.7: Experimental dissociation pressure for N2 hydrates formed from water – nitrogen gas meniscus in glass capillary.

5.3.4 Synergy effect in the formation of CO2 + cyclopentane sys- tem

5.3.4.1 Double hydrate formation and growth

To reduce the equilibrium pressure of CO2 hydrates in gas separation processes, one approach is to reduce the crystallization temperature, but it increases the operating cost due to further cooling. Another option is to add a small quantity of thermodynamic promot- ers, for instance organic compounds such as tetrahydrofuran (THF), tetrabutylammonium bromide (TBAB), and cyclopentane (CP),69,70 that enlarge the hydrate stability domain.

CP is known to form sII hydrates with a dissociation point of ±7 ◦C at atmospheric pressure (cf. Chapter 3).71 CP can only occupy the large cavities of the sII structure and the small 72 gas molecules such as H2 and CO2 can be entrapped in the small cavities. These small molecules further stabilize the structure. They are called a help gas.

To study the water + CP + CO2 system, the capillary is first loaded with water and cyclopentane as described in Chapter 4, then sealed on the water side, and finally centrifuged to bring these two liquids on the sealed side of the capillary. The rest of the procedure follows that used when water is the only liquid. In the end, two menisci are present in the capillary: water – CP liquid and CP – CO2 (see Figure 5.20). The CP between these two menisci slows down the arrival of CO2 at the water – CP interface and therefore the approach to equilibrium. This distance between the two menisci should not exceed a few tens of microns. If this distance is too large, one way to reduce it is to vaporize

147 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

part of the CP by raising the temperature to 45 ◦C.

To form the CP + CO2 double hydrate, the same protocol as described in the pro- cedure 5.2.2 is adopted. At high enough pressure and by lowering the temperature well

below 0 ◦C, the hydrate nucleates on the water – CP meniscus without forming ice. As an

exemple, at 75 bar, hydrate nucleates at 24 ◦C. The morphology of this hydrate look ∼ − like those of the CO2 hydrate (see Chapter 4). A change in a texture of hydrate appears during the heating stage that lead to the textures of Figure 5.20.

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Figure 5.20: Snapshots showing CP+CO2 double hydrate growth from water – CP meniscus: formation of hydrate filaments in bulk water at 5 ◦C and 24 bar, (a); small hydrate crystals ejected from water – CP interface into bulk water at 10 ◦C and 75 bar, (b); hydrate tunnels (or pockets) of CP in the water wrapped by a thin layer of hydrate at 20 bar and 8 ◦C, (c)

The latter sII hydrates grow from the CP – water interface in the form of filaments (see Figure 5.20a and 5.20c). Tunnels (or pockets) of CP in the water wrapped by a thin layer of hydrate, is formed from the water – CP interface, this layer ”explodes”after a certain tunnel size of some tens of microns (Figure 5.20b). This phenomenon produces a lot of CP drops in the water. At high pressure, hydrate crystals are formed at the water – CP interface and are ejected into the water (Figure 5.20b).

Note that these experiments have been conducted at the same supercooling (), the change in crystal morphology and the increase of the velocity of ejection Is due to an increase in the concentration of CO2 on the water - CP interface. The presence of CO2

148 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS molecules on the interface reduce considerably (by half) the interfacial tension between water and CP.

After dissociation of all hydrate crystals, it was difficult to reform the hydrate again for small supercoolings. No memory effect was observed as in the case of simple hydrates of CP or CO2. A possible cause for this absence of memory effect is that the intermediary needed to form the sII CP + CO2 hydrate, namely the sI CO2 hydrate, cannot form because its dissociation temperature is approximately 10 ◦C below that of the CP + CO2 hydrate (see Figure 5.21). A Raman spectroscopy analysis is needed to shed some light on this structural transition from sI to sII.73

In the water + CO2 and water + CP binary systems, the simple hydrate forms a thin crust on the water – guest meniscus and then grows as a halo on the substrate in guest phase side. The conversion of gas and water into gas hydrate stops after a few minutes, which implies a small amount of hydrate formed. The same behavior was observed in the case of simple CP hydrate. Whereas, in the ternary system (water + CP + CO2), the hydrate crystals are formed on the water – CP interface, then ejected into the water phase, and no hydrate halo is seen growing on the inner wall of the capillary on the guest side as has been widely observed in simple hydrates of CP or CO2. The CO2 mass transfer through the CP liquid to the aqueous phase continues and thus the hydrate grows until one of the compounds (water, CO2 or CP) is exhausted. CO2 and CP act in synergy to form more and more hydrate, the conversion reaction of water + CP + CO2 to a double hydrate is continues as long as the three compounds are present. This synergy effect can be associated with the fact that the double hydrate formed from water + CP + CO2 has a much greater affinity for water than in the case of simple hydrates of CP or CO2. This wettability effect prevents forming a hydrate crust between the aqueous and guest phase which stops the conversion of CO2 into hydrate. Further work is needed to characterize the interfacial mechanisms that drive the ejection of the crystals from the water – CP interface when the pressure (or the CO2 content in the CP-rich phase) increases.

5.3.4.2 Double hydrate dissociation

The dissociation temperatures of the double hydrate of CP + CO2 are more difficult to determine with precision than those of simple hydrates presented above. This difficulty is mainly related to:

149 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

i) the size of hydrate crystals that does not exceed a few microns,

ii) the decomposition of hydrate crystals gives rise to an emulsion mixture (CP droplets

and CO2 bubbles) in water, these emulsions rise towards the upper part of the capillary and screen the view of the hydrate crystals,

iii) the progressive melting of hydrate which begins 2 to 3 ◦C below the temperature of disappearance of the last crystal.

iv) and absence of memory effect.

The measurement uncertainty, which is related to the repeatability, is estimated at

±0.5 ◦C.

Figure 5.21 presentes the line of four-phase coexistence (Lw –H–LCP –VCO2 ) of

water + CO2 + CP system. The present results are compared with two examples from the literature where dissociation temperatures were determined experimentally by DSC (Zhang and Lee 2009)74 or isochoric method (Mohammadi and Richon 2009)75.

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Figure 5.21: Four-phase (Lw –H–LCP –VCO2 ) equilibrium pressure-temperature conditions: X, Zhang and Lee74; , Mohammadi and Richon75; , present work (cf. table 5.8). Three-phase ⃝ ▲ (Lw –H–VCO2 ) equilibrium pressure-temperature conditions: □, present work (cf. 5.5).

The dissociation temperature of double CP + CO2 hydrate is significantly higher than

that of CO2 hydrate with a difference of more than 10 ◦C for a given pressure. In other

150 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS words, the stability pressure of the hydrate is considerably reduced. As an example, when

T is 9.5 ◦C, the hydrate equilibrium pressure is 2 bar for CO2 + CP hydrate (see Table 5.8, while the hydrate equilibrium pressure is 40 bar for simple CO2 (see 5.5. Figure 5.21 also shows that the equilibrium data in this work is accord with that from the literature.

The dissociation temperatures of CP + CO2 double hydrate are listed in Table 5.8.

T ( ◦C) p (bar 9.5 2 15.5 12 16.5 15 17.5 18 18.2 24 19.2 30 20.0 50

Table 5.8: Dissociation Temperatures of CP + CO2 double hydrate at Different Pressures

5.4 Conclusion

A new procedure has been proposed to determine the dissociation temperatures of some gas hydrates by means of video-microscopy using glass capillaries as high-pressure and temperature-controlled optical cells. The dissociation temperature Teq is obtained at a given pressure by consecutive sequences of hydrate dissociation and reformation, taking advantage of the memory effect. A large temperature and pressure range, including the metastable extension of the three-phase (water – hydrate – guest) coexistence line down to temperatures well below 0 ◦C are investigated for CO2 (form -17.0 to 15.2 ◦C and 1.7 to 684.5 bar), CH4 (from -9.8 to 22.0 ◦C and 10.4 to 280.0 bar) and N2 (from -27.2 to

6.1 ◦C and 10.5 to 300.0 bar) hydrates. The effect of gas (CO2 and N2) and pressure on the ice melting point is investigated in order to determine the lower quadruple point (water – ice – hydrate – vapour) for water + gas system. The upper quadruple point (water – hydrate – CO2 vapour – liquid CO2) for water + CO2 system is also determined. Finally, the mechanisms by which CO2 and cyclopentane synergistically act to form a structure II hydrate are discussed and the four-phase (water – hydrate – cyclopentane – CO2 vapour) pressure-temperature conditions are also determined for pressures up to 50 bar.

151 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

5.5 R´ef´erences

[1] E. D. Sloan and C. A. Koh, Clathrate Hydrates of Natural Gases. Boca Raton, Florida: CRC Press, 2008. 120, 123, 125, 127, 141, 143, 145

[2] E. D. Sloan Jr, “Fundamental principles and applications of natural gas hydrates,” Nature, vol. 426, pp. 353–359, 2003. 120

[3] C. A. Koh,“Towards a fundamental understanding of natural gas hydrates,”Chemical Society Reviews, vol. 31, no. 3, pp. 157–167, 2002. 120

[4] M. A. Kelland, “History of the development of low dosage hydrate inhibitors,” Energy and Fuels, vol. 20, no. 3, pp. 825–847, 2006. 120

[5] I. Kim, M. Nole, S. Jang, S. Ko, H. Daigle, G. A. Pope, and C. Huh, “Highly porous

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[7] H. P. Veluswamy, R. Kumar, and P. Linga, “Hydrogen storage in clathrate hydrates: Current state of the art and future directions,” Applied Energy, vol. 122, pp. 112 – 132, 2014. 120

[8] S. Takeya, S. Muromachi, T. Maekawa, Y. Yamamoto, H. Mimachi, T. Kinoshita, T. Murayama, H. Umeda, D.-H. Ahn, Y. Iwasaki, H. Hashimoto, T. Yamaguchi, K. Okaya, and S. Matsuo, “Design of ecological co2 enrichment system for green- house production using tbab + co2 semi-clathrate hydrate,” Energies, vol. 10, no. 7, 2017. 120

[9] K. Z. House, D. P. Schrag, C. F. Harvey, and K. S. Lackner,“Permanent carbon dioxide storage in deep-sea sediments,” Proceedings of the National Academy of Sciences, vol. 103, no. 33, pp. 12291–12295, 2006. 120

[10] V. R. Avula, P. Gupta, R. L. Gardas, and J. S. Sangwai, “Thermodynamic modeling of phase equilibrium of carbon dioxide clathrate hydrate in aqueous solutions of pro-

152 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

moters and inhibitors suitable for gas separation,” Asia-Pacific Journal of Chemical Engineering, vol. 12, no. 5, pp. 709–722, 2017. 120

[11] A. Eslamimanesh, A. H. Mohammadi, D. Richon, P. Naidoo, and D. Ramjugernath, “Application of gas hydrate formation in separation processes: A review of experimental studies,”Journal of Chemical Thermodynamics, vol. 46, pp. 62–71, 2012.

[12] N. Dabrowski, C. Windmeier, and L. R. Oellrich, “Purification of natural gases with

high CO2 content using gas hydrates,”Energy & Fuels, vol. 23, no. 11, pp. 5603–5610, 2009.

[13] A. Adeyemo, R. Kumar, P. Linga, J. Ripmeester, and P. Englezos,“Capture of carbon dioxide from flue or fuel gas mixtures by clathrate crystallization in a silica gel column,” International Journal of Greenhouse Gas Control, vol. 4, no. 3, pp. 478–485, 2010. 120

[14] M. R. Walsh, S. H. Hancock, S. J. Wilson, S. L. Patil, G. J. Moridis, R. Boswell, T. S. Collett, C. A. Koh, and E. D. Sloan,“Preliminary report on the commercial viability of gas production from natural gas hydrates,”Energy Economics, vol. 31, no. 5, pp. 815 – 823, 2009. 120

[15] Y. K. Makogon, I. M. andE.D. Kozlovskaya, and V. Bozhelvolnov, “Secondary nu- cleation in the formation of methane crystal hydrate,” Russian Journal of Physical Chemistry A, vol. 81, pp. 1645–1649, 2007. 120

[16] H. Fakharian, H. Ganji, and A. Naderifar,“Saline produced water treatment using gas hydrates,” Journal of Environmental Chemical Engineering, vol. 5, no. 5, pp. 4269– 4273, 2017. 120

[17] K. C. Kang, P. Linga, K. nam Park, S. J. Choi, and J. D. Lee,“Seawater desalination by gas hydrate process and removal characteristics of dissolved ions (na+, k+, mg2+, ca2+, b3+, cl-, so42-),”Desalination, vol. 353, pp. 84–90, 2014.

[18] D. Corak, T. Barth, S. Høiland, T. Skodvin, R. Larsen, and T. Skjetne, “Effect of subcooling and amount of hydrate former on formation of cyclopentane hydrates in brine,”Desalination, vol. 278, no. 1, pp. 268 – 274, 2011. 120

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[19] M. D. C. Martinez Valentin-Gamazo, Study of CO2 clathrate hydrate slurries in the presence of additives for secondary refrigeration applications. Theses, Ecole´ Nationale Sup´erieuredes Mines de Paris, Apr. 2009. 120

[20] H. Zhou and C. I. Ferreira, “Purdue e-pubs investigation of hydrate growth rate on the interface between liquid and solid film investigation of hydrate growth rate on the interface between liquid and solid film,”2016. 120

[21] M. Mooijer-Van den Heuvel, Phase Behaviour and Structural Aspects of Ternary Clathrate Hydrate Systems – The Role of Additives. Theses, Universiteit Delft, 2004. 122

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[43] S. Takenouchi and G. C. Kennedy, “Dissociation pressures of the phase co2 + h2o,” The Journal of Geology, vol. 73, no. 2, pp. 383–390, 1965. VIII, 133

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[49] H. O. M. Jr. and J. M. Campbell, “Natural gas hydrates at pressures to 10,000 psia,” vol. 13, 1961. IX, 135, 136

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[51] L. A. Stern, S. Circone, S. H. Kirby, and W. B. Durham, “Anomalous preservation of pure methane hydrate at 1 atm,”The Journal of Physical Chemistry B, vol. 105, no. 9, pp. 1756–1762, 2001.

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[53] V. A. Vlasov, “Diffusion model of gas hydrate dissociation into ice and gas: Simula- tion of the self-preservation effect,” International Journal of Heat and Mass Transfer, vol. 102, pp. 631–636, 2016. 137

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158 CHAPTER 5. GAS HYDRATE PHASE DIAGRAMS

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160 Chapter 6

Conclusion and outlook

Conclusion and outlook

In this thesis, some important non-equilibrium and equilibrium properties of gas hydrates have been experimentally investigated by means of glass microcapillaries used as pressure- and temperature-controlled optical cells. These properties include the nucleation and growth, the interaction with solid substrates of gas hydrates, as well as the phase equi- librium (i.e., dissociation) conditions of a few pure and mixed hydrates. Insights into the governing mechanisms have been obtained from the visualization down to the sub-micron scale of the relevant phenomena, such as the creeping of a thin hydrate halo on a sub- strate or the hydrate formation processes at and across the water/guest interface. Because of the very small fluid volumes involved, the nucleation and growth of gas hydrates have been observed over an unprecedented range of supercooling conditions, similarly to what is known and has been observed for decades in gas-bearing aqueous fluid inclusions. Lastly, glass capillaries can be viewed as model (cylindrical) pores in a quartzitic sandstone, and therefore this study offers insights into the properties of gas hydrate-bearing sediments.

Hereafter we summarize the experimental results obtained in this thesis and raise a few questions and draw perspectives that need to be addressed, possibly by using the same experimental approach; in some cases, preliminary tests have been carried out, which are briefly reported. Italic characters are used below for expressing the unanswered or open questions, the preliminary results and perspectives.

The first part of this thesis (Chapter 3) consisted in experiments conducted in open capillaries (at ambient pressure) with water and cyclopentane (CP), which form a hydrate

161 CHAPTER 6. CONCLUSION AND OUTLOOK on the water – CP meniscus when the water is first frozen and then melted. This hydrate was dissociated by heating to slightly above 7 ◦C. Shortly after dissociation, by virtue of the memory effect, a second formation was triggered at the water – CP meniscus by lowering

T to a few degrees below 7 ◦C. Once the meniscus was covered with a polycrystalline hydrate crust, a thin hydrate layer (halo) was seen to spread along the inner wall of the capillary, fed both by the (non-wetting) fluid in place and an accompanying wetting fluid layer. The velocity and direction of spreading of the hydrate halo over the substrate and hydrate morphology are controlled by supercooling and by substrate wettability. The results are summarized as follows:

Effect of wettability on hydrate halo growth direction: On water-wet glass, the hydrate ’halo’ and an underlying water layer spread along the inner wall of capillary on the CP side of the meniscus. Symmetrically, on CP-wet glass, a halo and an underlying CP layer grow on the water side of the interface. No halo is observed on intermediate wet glass. When the hydrate halo reaches one of the two menisci between the liquid (water or CP) and its vapor, it continues to grow in vapor phase.

Effect of supercooling on hydrate halo morphology: The thickness of the hy- drate halo and its underlying wetting fluid strongly depend on supercooling. At low su- percooling, the halo morphology is rough and composed of large monocrystals that leave considerable space for the wetting fluid between the halo and glass. At high supercooling the halo is smooth and grows very close to the glass wall: the halo and its underlying wetting fluid are too thin to be visible. However, with the proper capillary dimensions, their presence causes a bright cusp on the inner wall, so that their presence and lateral advance along the glass can be precisely monitored by transmission microscopy.

Effect of supercooling on growth velocity: The halo lateral velocity, which is steady in the early stages of halo growth, strongly increases with supercooling ∆T, in a manner similar to what is observed for gas hydrate crusts growing at water-guest interfaces. It varies as ∆T2.7. A simple mass balance model of halo growth in a round capillary has been developed, which relates the consumed water and CP and the thicknesses of the halo and its underlying wetting fluid to the halo velocity. For the strongest supercoolings, and past some distance, the halo abruptly decelerates and its front position can be reconciled within a very simple approach adapted from the Lucas-Washburn model (see Appendix A). A clear understanding of why and for what conditions this sudden change occurs has still

162 CHAPTER 6. CONCLUSION AND OUTLOOK to be reached.

The following related topics have been addressed and/or deserve to be further inves- tigated:

• The effect of the substrate curvature on hydrate halo growth could be investigated by using round capillaries with different diameters; preliminary results using three differ- ent capillary diameters indicate that the halo growth rate decreases with increasing curvature (or with decreasing capillary diameter).

• Square and rectangle capillaries have the advantage of providing distortion-free im- ages. The wetting fluid advances more rapidly along the four corners of these capillar- ies, and the water-guest meniscus is indeed far from being spherical: the hydrate halo is observed to grow first longitudinally along the corners and then perpendicularly.

• Cavitation in the water zone, with bubbles of vapor, was occasionally observed in some experiments with the capillary sealed on the water side, which signaled a strong pressure drop in the water compartment.

• A better insight into hydrate crystal morphologies and the inhibiting or promoting mechanisms of surfactants or other additives could be provided by the proposed setup and procedure used in combination with higher-resolution microscopy.

The second part of this thesis (Chapter 4) was concerned with some natural gas hydrates (CO2, CH4 and N2 hydrates) formed under a high enough pressure. Sealed glass capillaries, filled with an aqueous phase and then connected to a gas reservoir, act as a high-pressure optical cell and constitute the main modification in the experimental setup used in the first part. The results are summarized as follows:

Nucleation temperatures: In repeated experiments conducted under the same pres- sure and cooling rate, these hydrates nucleate on the liquid water – guest meniscus in a narrow temperature interval and under an extremely high supercooling. This means that the hydrate nucleation temperature is not so stochastic and the metastability limit of water + gas system is approached. Moreover, this temperature increases with pressure and with silane-treated capillaries and slightly decreases with higher cooling rate.

163 CHAPTER 6. CONCLUSION AND OUTLOOK

Hydrate growth: Within less than one second, the water – guest meniscus is covered with a polycrystalline crust and the hydrate then propagates, as a thin polycrystalline crust, or halo, along the capillary wall. Similar to cyclopentane hydrate, the same effects of supercooling and wettability on the halo growth mechanism (velocity, morphology and the thickness of underlying fluid-wet phase) are observed. In addition to the halo, we observed a rapid growing fibers or dendrites in bulk water that recede towards the meniscus when T is raised slowly to the equilibrium temperature.

A novel morphology is observed at very low supercooling (less than 0.5 ◦C): the CO2 hydrate grows from the meniscus as a cylindrical hollow mono-crystal, which is

filled with the CO2 gas and surrounded by a thick water layer that wets the capillary wall. This morphology is assessed by a Raman mapping.

Some important fundamental questions are raised as to gas hydrate nucleation be- havior, which deserve to be further investigated:

• Why does hydrate nucleate prior to ice at temperature well below 0 ◦C? It is known that due to the expansion of the liquid water during its freezing the pressure lowers the freezing point. The dissolved gas plays a role in inhibiting the formation of ice. The driving force of hydrate nucleation is the degree of supercooling resulting in increase in guest solubility (supersaturation).

• The hydrate does not nucleate ice; however, the presence of ice crystals promotes hydrate formation.

• The dependence of hydrate hollow diameter on small changes in supercooling is observed but not explained in this work. More experiments are needed to establish a model that can be used to understand how the temperature and contact angle at the front of the underlying water act on the size of hollow crystal.

• The crust and the halo are dragged towards the water side of the meniscus when the temperature is increased after hydrate nucleation. This is due to the thermal contraction of water heated in this temperature range. Sometimes, however, the halo fractures, which provides information as to the adhesion (glass-hydrate) and cohesion (hydrate-hydrate) forces: this point is further developed in the ongoing PhD thesis of Dyhia Atig.

164 CHAPTER 6. CONCLUSION AND OUTLOOK

In the final part (Chapter 5), a procedure based on the use of capillaries is proposed to determine the dissociation temperatures of presented gas hydrates. The dissociation temperature is obtained at a given pressure by consecutive sequences of hydrate dissociation and reformation, taking advantage of the memory effect. Large temperature and pressure ranges, including the metastable extension of the three-phase (water – hydrate – guest) coexistence line down to temperatures well below 0 ◦C, are investigated. When the pressure is increased, the ice melting point is shifted slightly to lower temperatures. The quadruple points of water + CO2 and water + N2 system are determined. In addition to these simple gas hydrates, the mixed CO2 + CP hydrate system is investigated: the equilibrium four- phase (water – hydrate – CP – CO2 vapor) pressure-temperature conditions are determined, and the mechanisms by which CO2 and cyclopentane synergistically act to form a structure II hydrate are elucidated.

• These mechanisms are very likely governed by the wetting behavior of the hydrate at the interface between the water-rich and CP-rich phases: this hydrate is increasingly

wet by the water-rich phase when the pressure or CO2 content in the two phases increases.

• The accurate prediction of gas hydrate formation conditions is vital to industrial applications. Equilibrium data are widely available for conditions above the quadruple

point Q1, but are difficult to obtain at low temperatures and pressures especially the

metastable extension of Lw – H – V line. In the present study, pressure-temperature conditions have been determined for larger range but limited to a few components. Moreover, compositions in different phases of the systems cannot be obtained with the present method. A thermodynamic modeling combining the model of van der Waals and Platteeuw to incorporate the hydrate phase and an equation of state (EoS) that takes into account the properties of supercooled water could overcome these limitations and respond to industrial needs.

Conclusion et perspectives

Durant ma th`ese,je me suis int´eress´e`ades propri´et´esd’´equilibre et hors-´equilibre des hydrates de gaz dun point de vue exp´erimentaleau moyen de micro-capillaires en quartz utilis´escomme cellules optiques `ahaute-pression. Ces propri´et´escomprennent la cin´etique

165 CHAPTER 6. CONCLUSION AND OUTLOOK de formation et de la croissance, l’interaction des hydrates de gaz avec des substrats solides, ainsi que les conditions d’´equilibre de phase (c’est-`a-dire,de dissociation) de quelques hy- drates simples et mixtes. Jai mis en avant lutilit´edutiliser la microscopie optique (et la spectroscopie Raman) pour lobservation de r´eactionset processus de transformation de phases `atravers des micro-capillaires de mouillabilit´ebien d´efinie. Cette approche nouvelle permet de mieux comprendre les m´ecanismesqui gouvernent les comportements des hy- drates de gaz en milieu naturel (s´edimentaire)`ades ´echellesmicroniques, jusqu`apr´esent peu explor´es.Ces r´eacteursminiatures d´eriv´esde la micro-fluidique pr´esententune inertie thermique tr`esfaible, ce qui permet de consid´erablementacc´el´ererles r´eactions(temps d´equilibre) par rapport aux m´ethodes classiques. En raison des tr`espetits volumes de fluide impliqu´es,la nucl´eationet la croissance des hydrates de gaz ont ´et´eobserv´eeset ´etudi´ees dans une tr`eslarge gamme de conditions de sous-refroidissement, comparable `ace qui est connu et observ´edepuis des d´ecenniesdans les inclusions fluides.

Ci-apr`essont r´esum´esles r´esultatsexp´erimentauxobtenus ainsi que (en caract`eres italiques) les questions et perspectives qui peuvent ˆetreabord´espar la mˆemeapproche exp´erimentale; dans certains cas, des tests pr´eliminairesont ´et´eeffectu´es.Une partie des travaux pr´esent´esdans ce manuscrit de th`ese(chapitre 3 et Annexe B) a d´ej`adonn´elieu `a 2 publications dans la revue Langmuir en 2017.

Dans la premi`erepartie (chapitre 3) sont abord´esles rˆolesde la mouillabilit´eet du sous-refroidissement dans le m´ecanismede croissance de lhydrate de cyclopentane (CP) au voisinage du m´enisqueeau – CP dans un capillaire, aussitˆotapr`esavoir form´ela glace et lavoir fait fondre. Lint´erˆetde lhydrate de CP est quil se forme `apression atmosph´erique, ce qui facilite sa manipulation. En chauffant l´eg`erementau-dessus de 7 ◦C, cet hydrate se dissocie. En refroidissant le syst`emepeu de temps apr`esla dissociation, en vertu de l’effet de m´emoire,lhydrate de CP se reforme `ades petits sous-refroidissements. Une fois le m´enisquerecouvert d’une croˆuted’hydrate polycristalline, un halo dhydrate (film mince polycristalline) se propage le long de la paroi interne du capillaire, aliment´epar une couche liquide (eau ou CP, selon la mouillabilit´edu substrat) entre le halo dhydrates et la surface int´erieurdu verre. Un r´esultatnotable est que la vitesse, la direction de propagation et la morphologie de ce halo sont contrˆol´eespar le sous-refroidissement et la mouillabilit´edu substrat. Les r´esultatssont r´esum´escomme suit :

Effet de la mouillabilit´esur la direction de croissance du halo d’hydrate : Sur

166 CHAPTER 6. CONCLUSION AND OUTLOOK un substrat mouill´epar leau, l’hydrate ´nhaloz˙ et une couche d’eau sous-jacente se propagent le long de la paroi interne du capillaire du cˆot´eCP du m´enisque.Sym´etriquement,sur un verre mouill´epar le CP (capillaires silanis´es),un halo et une couche de CP sous-jacente se d´eveloppe du cˆot´eeau du m´enisque. Lorsque le halo d’hydrate atteint l’un des deux m´enisquesentre le liquide (eau ou CP) et la vapeur, il continue `acroˆıtre en phase vapeur. Aucun halo n’est observ´esur le verre de mouillabilit´einterm´ediaire.

Effet du sous-refroidissement sur la morphologie du halo dhydrate : L’´epaisseur du halo d’hydrate et de la couche de liquide sous-jacent d´ependent fortement du sous- refroidissement. A` faible sous-refroidissement, la morphologie du halo est rugueuse et compos´eede grands monocristaux qui laissent un espace consid´erablepour le fluide mouil- lant entre le halo et le verre. A` des sous-refroidissements ´elev´es,le halo est lisse et compos´e de petits cristaux dhydrate. Il pousse tr`espr`esde la paroi de verre: le halo et son fluide sous-jacent sont trop fins pour ˆetrevisibles. Cependant, avec des dimensions de capillaires appropri´ees,leur pr´esenceest d´etect´eepar une ligne brillante (r´eflexion totale) sur la paroi interne du capillaire, mˆemesi leur ´epaisseurest bien inf´erieureau micron. Il sagit l`adune exploitation des propri´et´esde r´efraction(d´ecritesdans lannexe B) permettant la mise en ´evidencede films tr`esminces.

Effet du sous-refroidissement sur la vitesse de croissance : La vitesse lat´erale de propagation du halo, qui est constante aux premiers stades, augmente fortement avec le sous-refroidissement ∆T, d’une mani`eresimilaire `ace qui est observ´epour les croˆutes d’hydrates de gaz qui poussent aux interfaces eau – gaz. Cette vitesse varie comme ∆T2.7. Un mod`elede bilan de masse, reliant les quantit´esconsomm´eesd’eau et de CP et les ´epaisseursdu halo et son fluide sous-jacent `ala vitesse de croissance du halo, a ´et´e d´evelopp´e.Pour les sur-refroidissements les plus forts, et au-del`ad’une certaine distance, le halo d´ec´el`erebrusquement et sa position frontale ob´eit`aune loi de Lucas-Washburn (voir l’annexe A). Une bonne compr´ehensiondes raisons pour lesquelles et `aquelles conditions ce changement soudain se produit doit encore ˆetreobtenus.

Les sujets connexes suivants ont ´et´etrait´eset/ou m´eritentd’ˆetreapprofondis :

• L’effet de la courbure du substrat sur la croissance du halo d’hydrate pourrait ˆetre ´etudi´een utilisant des capillaires ronds de diff´erentsdiam`etres;des r´esultatspr´elim- inaires utilisant trois capillaires de diam`etresdiff´erentsindiquent que la vitesse de

167 CHAPTER 6. CONCLUSION AND OUTLOOK

croissance du halo diminue avec l’augmentation de la courbure du substrat.

• Les capillaires carr´eset rectangulaires ont l’avantage de fournir des images sans dis- torsion optique. Le liquide mouillant avance plus rapidement aux quatre coins de ces capillaires, et le m´enisqueeau – CP est en effet loin d’ˆetresph´erique: le halo dhydrate croˆıt d’abord longitudinalement le long des coins, puis perpendiculairement.

• Le ph´enom`enede cavitation dans leau a ´et´eoccasionnellement observ´edans certaines exp´eriencesen utilisant des capillaire scell´esdu cˆot´eeau, t´emoindune forte chute de pression dans le compartiment aqueux. Cette baisse de pression est provoqu´eepar la croissance du halo dhydrate.

Lhydrate de CP est souvent pr´esent´ecomme un analogue des hydrates de gaz na- turel et les capillaires comme des mod`elesde pores siliceux. Le CP ´etantliquide, il peut pr´esenterun comportement diff´erentde celui des hydrates de gaz en ce qui concerne les processus de formation, dadh´esionaux s´ediments(microm´ecanique)ou de dissociation. N´eanmoins,compte tenu de la facilit´edutilisation de ce compos´e`apression atmosph´erique et `abasse temp´eraturepour former des hydrates, le choix parait raisonnable pour une pre- mi`ereapproche. Par ailleurs, la justification du choix de capillaires cylindriques pour mimer le syst`emer´eel(porosit´edu milieu s´edimentairenaturel) est abord´eedun point de vue pra- tique (facilit´ede lajustement de la mouillabilit´e,bonne conductivit´ethermique, propri´et´es optiques pour la d´etectionde halo mince (annexe B).

La deuxi`emepartie de cette th`ese(chapitre 4) porte sur certains hydrates de gaz naturel (hydrates de CO2, de CH4 et de N2) form´essous une pression suffisamment ´elev´ee. Les capillaires en verre doivent ˆetrescell´es,le cˆot´egaz du m´enisque´etantreli´e`aun r´eservoir de gaz : cela constitue la principale modification dans la configuration exp´erimentaleutilis´ee dans la premi`erepartie.

En raison des tr`espetits volumes deau introduits dans les capillaires, leau reste liquide `ades tr`esbasses temp´eratures.Contrairement `ace qui est observ´edans la premi`erepartie, lhydrate de gaz nucl´eeen premier sans avoir besoin de le former `apartir de la glace. Les r´esultatssont r´esum´escomme suit :

Les temp´eraturesde nucl´eation: Dans des exp´eriencesr´ep´et´ees,r´ealis´eessous une mˆemepression et mˆemevitesse de refroidissement, ces hydrates nucl´eentsur le m´enisque

168 CHAPTER 6. CONCLUSION AND OUTLOOK eau – gaz dans un intervalle de temp´eraturetr`es´etroitet sous un sous-refroidissement extrˆemement´elev´e.Cela signifie que la temp´eraturede nucl´eationdes hydrates n’est pas si stochastique et que la limite de m´etastabilit´edu syst`emeeau + gaz est approch´ee.De plus, cette temp´eratureaugmente avec la pression et avec lhydrophobie du substrat, et diminue l´eg`erementquand la vitesse de refroidissement croit.

La croissance des hydrates de gaz : En moins d’une seconde, le m´enisqueeau – gaz est recouvert d’une croˆutepolycristalline, puis l’hydrate se propage, sous la forme d’un halo tr`esmince, le long de la paroi interne du capillaire. De mani`eresimilaire `a l’hydrate de cyclopentane, ´etudi´edans a premi`erepartie, on observe les mˆemeseffets de sous-refroidissement et de mouillabilit´esur le m´ecanismede croissance du halo (vitesse, morphologie et ´epaisseurde la phase fluide-mouillant sous-jacente). En plus du halo, des fibres ou dendrites croissant rapidement du cˆot´eeau sont observ´es,qui se r´etractentvers le m´enisqueeau – gaz lorsque la temp´eratureest ´elev´eelentement jusqu’`ala temp´erature d’´equilibre.

Monocristal dhydrate creux : Si un cristal dhydrate est pr´esentdans leau au voisinage du m´enisqueeau-gaz, il croit lentement vers le m´enisquepour de faibles sous- refroidissements (moins de 0.5 ◦C au dessous de la temp´eratured´equilibre de lhydrate en question). Un hydrate se d´eveloppe alors vers le cˆot´egaz `apartir du m´enisquesous la forme d’un monocristal creux et cylindrique, rempli de gaz (CO2) et entour´ed’une ´epaissecouche d’eau qui mouille la paroi capillaire. Cette morphologie est ´evalu´eepar une cartographie Raman.

Quelques questions fondamentales importantes sont soulev´eesquant au comporte- ment de nucl´eationdes hydrates de gaz, qui m´eritentd’ˆetreapprofondies :

• Pourquoi lhydrate de gaz nucl´ee-t-ilavant la glace `ades temp´eraturesbien inf´erieures

`a0 ◦C ? Pour r´epondre `acette question, trois aspects peuvent ˆetreconsid´er´es: (i) La pression a un effet sur le volume et en raison de l’expansion de l’eau liquide pendant sa cong´elation,l’augmentation de la contrainte de pression abaisse le point de cong´elation.(ii) La force motrice de la nucl´eationdes hydrates est li´eeau degr´ede sous-refroidissement. Quand ce dernier augmente, il entraˆıne une augmentation de la solubilit´ede gaz dans leau (sursaturation), ce qui facilite la formation des nucl´eides

dhydrate. (iii) lhydrate de type sI (comme lhydrate de CO2) et sII (comme lhydrate

169 CHAPTER 6. CONCLUSION AND OUTLOOK

de N2) ont une structure cubique, tandis que la glace a une structure hexagonale. Cette derni`eredemande plus d´energiepour ˆetrenucl´e´ee.

• Une fa¸contr`espratique pour acc´el´ererla formation des hydrates de gaz est dajouter des petits cristaux de glace dans leau. La pr´esencede ces cristaux induisent la formation d’hydrates, tandis que lexistence des hydrates dans leau surfondue (mˆeme

`ades temp´eratureinf´erieures`a-30 ◦C) ne provoque pas une cong´elationde leau liquide.

• La d´ependance du diam`etrede cristal dhydrate creux `ade petits changements dans le sous-refroidissement est observ´eemais nest pas expliqu´eedans ce travail. Plus d’exp´eriencessont n´ecessairespour ´etablirun mod`elepermettant de comprendre comment la temp´eratureet l’angle de contact `al’avant de la couche l’eau sous- jacente agissent sur la taille du cristal creux.

• Apr`esavoir form´eun halo dhydrate le long du capillaire, la croˆute`alinterface et le halo sont entraˆın´esvers le cˆot´eeau du m´enisquelorsque la temp´eratureest augment´ee. Cela est dˆu`al’augmentation de la densit´e( 0.975 to 1 g/cc) dans cette plage de ∼ temp´erature.Parfois, le halo se fracture et une partie reste coll´ee`ala paroi interne du capillaire. Une ´etudeapprofondie sur ce m´ecanismepeut fournir des informations sur les forces d’adh´esion(substrat-hydrate) et de coh´esion(hydrate-hydrate). Ce point est d´evelopp´edans le travail de th`eseen cours de Dyhia Atig.

Dans la derni`erepartie (chapitre 5), une proc´edurebas´eesur l’utilisation des capillaires est propos´eepour d´eterminerles temp´eraturesde dissociation des hydrates de gaz. La temp´eraturede dissociation est obtenue `apression constante par des s´equencescons´ecutives de dissociation et de reformation des hydrates, tout en profitant de l’effet m´emoire. Les grandes plages de temp´eratureet de pression, y compris l’extension m´etastablede la ligne de coexistence tri-phasique (eau – hydrate – gaz) jusqu’`ades temp´eraturesbien inf´erieures

`a0 ◦C, sont ´etudi´ees.Les effets de la pression et du gaz sur la temp´eraturede fonte de la glace sont ´egalementexamin´es: Lorsque la pression augmente, le point de fusion de la glace est l´eg`erementd´ecal´evers les basses temp´eratures.Les points quadruples de syst`emeeau + gaz ont ´et´ed´etermin´esen utilisant les diff´erentescourbes d´equilibre d´etermin´eesdans ce pr´esenttravail. Un hydrate mixte de CO2 + CP a ´et´e´etudi´een utilisant la mˆemeapproche : les conditions pression-temp´eratured’´equilibre quadri-phasique (eau – hydrate – CP –

170 CHAPTER 6. CONCLUSION AND OUTLOOK

CO2 gaz) ont ´et´ed´etermin´ees,et les m´ecanismespar lesquels le CO2 et le cyclopentane agissent en synergie pour former un hydrate de structure II sont ´elucid´es.

• Le m´ecanismequi gouverne la synergie est probablement li´eau mouillage de l’hydrate

par leau `al’interface entre les deux phases, eau et CP, riches en en CO2 : cet hydrate

est de plus en plus mouill´epar leau riche en CO2 lorsque la pression ou la solubilit´e

de CO2 dans les deux phases augmentent.

• La pr´edictionpr´ecisedes conditions de formation des hydrates de gaz est essentielle pour les applications industrielles. Les donn´eesd’´equilibre sont largement disponibles

pour les conditions au-dessus du point quadruple Q1, mais sont difficiles `aobtenir `a basses temp´eratureset pressions particuli`erementl’extension m´etastablede la ligne

Lw – H – V. Dans la pr´esente´etude,les conditions pression-temp´eratureont ´et´e d´etermin´eespour une gamme plus large mais limit´ees`aquelques types hydrate. De plus, les compositions ne peuvent pas ˆetreobtenues avec la pr´esentem´ethode. Une mod´elisationthermodynamique combinant le mod`elede van der Waals et Platteeuw pour incorporer la phase hydrate et une ´equationd’´etat(EoS) qui prend en compte les propri´et´esde l’eau surfondue pourrait surmonter ces limitations et r´epondre aux besoins industriels.

171 CHAPTER 6. CONCLUSION AND OUTLOOK

172 Appendix A

Model of cyclopentane hydrate halo growth in a round capillary

Figure A.1 shows longitudinal and transverse cross-sections of a model of the propagating halo. While still moving in the guest (CP) phase, the hydrate halo and its underlying water layer form two concentric cylinders against the inner wall of the capillary. Both are thin compared to the radius of the capillary, R. As a first approximation, the thicknesses of the

hydrate and the water layer, eh and ew are taken to be constant. By virtue of the thinness of

the layers compared to the tube cross-section, the halo velocity, Vh, may be taken to be be

the constant and much larger than the velocities of the water – vapor meniscus, Vwv, and

of the CP – vapor meniscus, VCPv. When the halo has overrun the CP – vapor meniscus,

there is an additional thin-walled cylinder for liquid CP, with thickness eCP (Figure A.1b); velocities are then noted with superscript ”’ ”.

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Figure A.1: Physical picture of the hydrate halo growing along a glass capillary wall. (a) Growth in the CP phase ; (b) under the CP vapor, after the halo has overrun the CP – vapor meniscus.

With the above notation, we next consider mass balance, to first order in all the ei/R where i = w,h,CP. Consider first the halo propagating in the liquid CP. The withdrawal 2 of the water – vapor meniscus, at a mass rate πR Vwvρw, must match the water being

i APPENDIX A. MODEL OF CYCLOPENTANE HYDRATE HALO GROWTH IN A ROUND CAPILLARY incorporated into the hydrate halo, at a mass rate 2πRehVhρw,h, and into the underlying water layer, at a mass rate 2πRewVhρw:

2 (A.1) πR Vwvρw = 2πR(ewρw + ehρw,h)Vh or, equivalently,

Vwv ew ρw,h eh = + (A.2) 2Vh R ρw R

3 In the above two equations, ρw 1 g/cm is the density of liquid water and ρw h ≈ , ≈ 0.785 g/cm3 the density of water in the CP hydrate. A similar equation relates the advance 2 of the CP – vapor meniscus, with a CP mass rate πR VCPvρCP, to the rate of displacement of liquid CP by the advancing halo and its underlying water layer, 2πR(eh+ew)VhρCP, and to the mass rate of CP incorporated into the hydrate halo, 2πRehVhρCP,h (to be subtracted), i.e.

VCPv ew + eh ρCP,h eh = , (A.3) 2Vh R − ρCP R or VCPv ew ρCP,h eh = + (1 ) , (A.4) 2Vh R − ρCP R

1 3 3 where ρCP 0.765 g/cm and ρCP h 0.182 g/cm are the densities of CP as a liquid and ≈ , ≈ in the hydrate phase. Equation A.3 provides bounds for the total thickness of the films, a lower bound deduced from the equation as it stands, and an upper bound derived by subtracting ρCP,h ew from the right and side and rearanging terms: ρCP R

RVCPv 1 RVCPv < ew + eh < , (A.5) 2Vh 1 ρCP,h 2Vh ( − ρCP ) or simply RVCPv ew + eh , (A.6) ≈ 2Vh

ρ 1 since 1 CP,h − 1.31. ( − ρCP ) ≈ Using for example’s sake the values for experiment 3 in table 3.2 (cf. Chapter 2) the thickness ew + eh = 12 µm would appear at first sight underestimated compared to the

ii APPENDIX A. MODEL OF CYCLOPENTANE HYDRATE HALO GROWTH IN A ROUND CAPILLARY corresponding micrograph in figure 3.4 (cf. Chapter 2), where the water layer has an apparent thickness of 10–20 µm. However, it must be remembered that refraction by the cylindrical interfaces distorts the image of the contents of the capillary, creating an effective variable zoom that increases with distance from the capillary axis. Numerical simulations like those in ref.2 show that a 10 µm sleeve of hydrate or water film has an apparent thickness of 25 µm.

All the coefficients of ew and eh in equations A.2 and A.3 are known or measured, so the system could in principle be used to determine ew and eh individually. In practice the system is poorly determined because the coefficients of eh/R on the right-hand sides, respectively ρw h/ρw 0.785 and 1 ρCP h/ρCP 1 0.18/0.765 0.762, are nearly equal. , ≈ − , ≈ − ≈ Therefore, ew and eh cannot be determined independently.

Rearranging the previous two equations, one obtains

ew VCPv αVwv = − (A.7) R 2(1 α)Vh − and

eh Vwv VCPv = − , (A.8) R 2βVh where both left hand sides must be positive and the coefficients are

α = ρw(1 ρCP h/ρCP)/ρw h 0.97 and β = ρw h/ρw + ρCP h/ρCP 1 0.023. − , , ≈ , , − ≈ Hence,

αVwv < VCPv < Vwv , (A.9) i.e. the velocities of the two menisci are expected to be comparable, in agreement with experiment.

Velocity VCPv is maximum and equal to Vwv when all bulk water consumption is for the advancing water layer (which then has the maximum possible thickness, the halo having vanishing thickness), and VCPv is minimum and equal to 0.97Vwv when all bulk water goes into the hydrate halo (which has the maximum possible thickness, the water layer has vanishing thickness). With the data of experiment 3 as an example, i.e. a value

iii APPENDIX A. MODEL OF CYCLOPENTANE HYDRATE HALO GROWTH IN A ROUND CAPILLARY

Vwv/Vh = 0.42/1.86 = 0.23 (see table 3.2 of Chapter 2), these two maximum thicknesses are equal to 11 and 29 µm, respectively. The true thicknesses are below those values, but their determination would require being able to determine a difference of less than 3% between the two meniscus velocities, which is indeed not feasible experimentally.

When the halo has overrun the CP – vapor meniscus and is advancing in the vapor phase (Figure A.1b, there is additional layer, that of liquid CP covering the halo, with

′ thickness eCP. The velocity of the CP – vapor meniscus, VCPv, is related to eCP eh as follows:

′ V eCP ρCP,h eh − CPv = + (A.10) ′ R ρ R 2Vh CP

Interestingly, the addition of equations A.3 and A.10 leads to a simple relation between

+ + ′ the total thickness ew eh eCP and velocities VCPv and VCPv:

′ VCPv V ew + eh + eCP CPv = (A.11) 2V − ′ R h 2Vh

From the velocity data reported in Table 3.2, this sum represents a fraction 5 – ≈ 12 % of the capillary radius R for supercoolings ∆T 5 – 6 K. As already pointed out ≈ and apparent in figure 3.4 (cf. Chapter 2, larger values are observed for lower supercooling (higher temperature) primarily due to the thicker water layer, whereas smaller fractions are expected for higher supercooling or longer lengths of halo. It is important to emphasize here that the above description holds only in the initial stages of halo propagation, when steady lateral velocities are observed. This regime is rather extended for low or moderate supercooling (T above 0 ◦C) but rather limited for higher supercooling, as discussed in subsection 3.3.2 of Chapter 2.

iv APPENDIX A. MODEL OF CYCLOPENTANE HYDRATE HALO GROWTH IN A ROUND CAPILLARY A.1 R´ef´erences

[1] K. Harris, P. Newitt, and L. A. Woolf, “Temperature and density dependence of the viscosity of cyclopentane,”J. Chem. Eng. Data, vol. 49, pp. 138–142, 2004.

[2] N. Hobeika, P. Bouriat, A. Touil, D. Broseta, R. Brown, and J. Dubessy,“Help from a hindrance: Using astigmatism in round capillaries to study contact angles and wetting layers,”Langmuir, pp. 5179–5187, 2017.

v APPENDIX A. MODEL OF CYCLOPENTANE HYDRATE HALO GROWTH IN A ROUND CAPILLARY

vi Appendix B

Using astigmatism in round capillaries to study wetting layers

Abstract

Round glass capillaries are a basic tool in soft-matter science, but often are shunned due to the astigmatism they introduce in micrographs. Here, we show how refraction in a capillary can be a help instead of a hindrance to obtain precise and sensitive information on two important interfacial properties: the contact angle of two immiscible fluids and the presence of thin films on the capillary wall.

Understanding optical cusps due to refraction allows direct mesurement of the inner diameter of a capillary at the meniscus, which with the height of the meniscus cap, deter- mines the contact angle. The meniscus can thus be measured without intrusive additives to enhance visibility, such as dyes or calibrated particles, in uniform, curved or even tapered capillaries or under demanding conditions not accessible by conventional methods, such as small volumes (µlitres), high temperatures or high pressures.

We further elicit the conditions for strong internal reflection on the inner capillary wall, involving the wall and fluid refractive indices and the wall thickness, and show how to choose the capillary section to detect thin (sub-micron) layers on the wall by the contribution of total internal reflection to the cusps.

As examples, we report: (i) CO2-water or -brine contact angles at glass interfaces, measured at temperatures and pressures up to 200 ◦C and 600 bar, revealing an effect apparently so far unreported: The decrease in the water-wet character of glass, due to

vii APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS dissolved salts in brine, is strongly reduced at high temperatures, where contact angles converge toward the values in pure water; (ii) A tenuous gas hydrate layer growing from the water-guest contact line on glass, invisible in transmission microscopy but prominent in the cusps due to total internal reflection.

B.1 Introduction

The observation of fluids and other objects in thin transparent capillary tubes under the transmission microscope is becoming a common practice in many laboratories, driven by the current trend towards using smaller volumes in fluid characterization and other applications. It is facilitated by the availability of glass and plastic capillaries at low cost, of cooling or heating stages and of pumps allowing precise control of the temperature and pressure over wide ranges under the optical microscope1. In addition, the wettability of standard borosilicate or fused silica glass capillaries can be controlled to a large extent by surface treatment such as silanization.

However, astigmatism, the optical distortions and aberrations induced by the presence of the cylindrical container are usually disregarded or inadequately corrected; or the difficulty is (we note only partially) solved at the expense of convenience, by immersing the capillary in a liquid with similar refractive index2, or by substituting vessels with optically flat walls. It appears that the only attempts to describe these refraction effects, decades ago3,4 and in a rather limited context, have been largely overlooked. The present paper aims to show the rich potential of capillary observations by harnessing rather than avoiding refraction.

We focus here on situations where the capillary contains one or two fluids. In the latter case, these two fluids are separated by a meniscus, which intersects the inner wall with a certain contact angle, θ, characterising the wettability of the wall with respect to the two fluids, see figure B.1 . Similar to the mercury thermometer, the glass appears thinner than reality, or the bore is overestimated when examined under the microscope. Hence the apparent contact angle differs from the true angle. Furthermore, the inner wall commonly appears as a more or less bright streak, a cusp, depending on refractive indices and capillary dimensions. This paper presents the analysis needed to exploit these features, with experimental illustrations. Section B.2.1 is a reminder of how the true internal

viii APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

Figure B.1: Sketch diametral section through a spherical cap meniscus in a (locally) cylindrical glass capillary with internal and external radii Ri and Re. Equation (B.1) relates the contact angle, θ, to the cap height, h, from pole, P, to base, BB′, and the radius at the cap base, Ri. diameter relates to the contact angle. Section B.2.2 shows how to identify the apparent internal diameter from the cusps and how correct it for refraction. Section B.2.3 discusses the brightness of the cusp, and how it may be used to reveal thin films or layers creeping out of the meniscus on the inner wall. One known example is salt creeping from the meniscus between a supersaturated brine and air or oil5–7.

After discussing experimental details in section B.3, we provide illustrations in section

B.4. We examine the CO2-water or brine interfaces with glass, under conditions of high temperatures and pressures or strong brines relevant to CO2 geological storage, section B.4.1.

Section B.4.2 is an example of how the presence or absence of a cusp reveals thin layers creeping over the substrate, in this case tenuous gas hydrate ’halos’.

B.2 Refraction in a glass capillary

B.2.1 Contact angles by measuring a meniscus

Figure 1 shows an equatorial or diametral section through a cylindrical capillary containing a wetting and a non-wetting fluid. The capillary is mounted on a transmission microscope, with the capillary axis perpendicular to and passing through the optical axis. K¨ohler illumi- nation is assumed, with the condenser aperture stop closed as far as possible, to illuminate

ix APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS the sample with a nearly parallel beam of light, focused into the equatorial plane. The image is in general deformed by refraction of light by both the inner and the outer capillary walls. Thus, a bubble or drop in the capillary does not appear spherical8, and the apparent inner diameter of the capillary differs from the true diameter. The contact angle, θ, cannot simply be measured off micrographs of the wedge of the wetting fluid at the contact line.

However, provided that the inner diameter of the capillary, 2Ri, is less than the capillary length9,10, (σ/g∆ρ)1/2 , where σ is the interfacial tension, ∆ρ the density difference be- tween the two fluids, and g the acceleration due to gravity), the meniscus is a spherical cap with a base radius Ri, equal to that of the capillary tube at the position of the contact line. From simple geometry (derivation in the supplementary information, SI), the contact angle is then given by

R2 h2 tanθ = i − , (B.1) 2Rih determined by the height of the cap, h, from pole to base ( P and B-B’, in figure B.1) and the radius Ri.

The pole and the base generally are not simultaneously in focus. However there is no axial aberration, so provided the capillarity is carefully levelled, there is no difficulty measuring h as the difference of the abscissae of the pole and the base of the cap. Similarly, the outer diameter of the capillary, 2Re, can be measured in air by focusing on the equatorial plane.

But astigmatism due to the curved intefaces makes the bore, 2Ri, harder to determine. The simple solution is immersion in an index matching fluid improves the situation by suppressing refraction at the outer surface2. Even then, some refraction persists at the inner surface, distorting images of the contents, except for the exceptional case that the index of the contents matches that of the glass. Further, this method is not always available nor even suitable. For example, immersion oils may not be compatible with measurements over the range of temperatures available to temperature controlled stages, due either to congealing or to frying. Another method is to photograph calibrated beads in the capillary8. However, these tricks do not apply when measurements are to be made ”on the fly”in capillaries with unknown or varying inner diameter, at an unpredetermined position of the meniscus, e.g. when the meniscus creeps along the capillary axis. Direct optical determination of the inner diameter would therefore be useful.

x APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

Figure B.2: Transmission micrographs of the same meniscus (between pure water, left, and CO2, right, at 500bar, 40 ◦C) with the focus on the pole P (a), and on the base BB’ (b). The prominent cusps on the outer (OC) and inner walls (IC), are due to rays such as those shown in the transverse sections (c), which come into focus in order, on focusing towards the objective, starting beyond the capillary. The capillary inner and outer diameters are here 200 and 330µm. Scale bar in (b): 100µm.

B.2.2 Using a cusp to determine the true internal diameter

The difficulty above is that refraction produces longitudinal shadows and bright regions (cusps, see e.g. figure B.2), that bewilderingly widen and narrow as the focus is swept over the thickness of the capillary tube, making it hard to decide what to measure, at which depth of focus and how to correct for refraction.

Now cusps in general signal an extremum in the angular deviation of a bundle of rays impinging on a refracting object, in practice usually a minimum deviation. Rainbows are the most familiar example11. We now describe how to identify a particular cusp, that furthermore presents a maximum separation from the capillary axis at a particular depth of focus in the capillary. The double extremum condition favours accurate estimation of an apparent internal diameter 2Ra, only weakly sensitive to errors in focusing.

We first performed Monte Carlo ray tracing simulations to understand the observed sequence of cusps. The conclusions are as follows (for more details, see the SI). When the focus is swept through the capillary, starting on the side opposite the objective, two cusps are particularly prominent. The first, outer cusp, OC in figure B.2, appears brightest and sharpest when the focus reaches the equatorial plane of the capillary, thus providing the

xi APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS outer diameter 2Re. It is formed by reflection off the outside of the capillary wall. Note that at this point, the axis of the capillary and in particular the top of the meniscus, are out of focus, due to refraction.

Attention should next be focused on the inner cusp, IC in figure B.2. This cusp is formed by rays that do not enter the capillary cavity, but are reflected off the inner surface. With the condenser carefully adjusted to focus K¨ohler illumination into the equatorial plane of the capillary, cusp IC is sharpest at a focus somewhat within the focus for cusp OC.

Cusp IC may be weakened by refraction of light into the capillary cavity, depending on the refractive index of the fluid or material lying against the wall. Nonetheless the high dynamic range of even cheap digital cameras makes jumps in the brightness of cusp IC a sensitive probe of inhomogeneities of the solids or fluids in contact with the capillary wall.

At the other extreme, total internal reflection (TIR) makes cusp IC very bright at places where the refractive index of the fluid or material lying against the capillary wall, nf, is low enough compared to that of the glass, ng. The precise conditions are derived and discussed below. Dimming of cusp IC under nominal conditions of TIR, due to tunneling losses through the film in contact with the glass, make this cusp very sensitive to the thickness of wetting films or some other material extending on the capillary wall into the other fluid, see section B.2.3. Examples will be given in section B.4.2.

Cusp IC broadens or narrows and moves perpendicular to the capillary axis as the focus is adjusted. This effect is due to some rays grazing into and out of the capillary cavity. Because the fluids on each side of the meniscus generally have different refractive indices, the cusps do not in general line up to the left and right of the meniscus. But at a particular focus, both sides align, as rays are refracted into the capillary wall, reflected on its inner face, and refracted out of the outer surface either totally, i.e. without entering the cavity (see figures B.2(b) and B.3), or partially. At this special position, cusp IC arises from rays propagating solely in the capillary wall. The position, but not the brightness, is therefore independent of the contents of the capillary at the point of observation. The cusp is also sharpest and brightest and at a maximum distance from the capillary axis: this distance is the apparent radius, Ra. Together with the corresponding cusp on the other side of the capillary, cusp IC determines an apparent inner capillary diameter 2Ra.

Under the adjustments described above, rays giving rise to cusp IC in practice are

xii APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

Figure B.3: Schematic illustration of the formation of an image of the inside capillary wall by reflection, corresponding to cusp IC when ie + ϕ = π/2, i.e. vanishing, hence minimum deviation, and a ray entering and exiting the capillary parallel to the optical axis, at a distance Ra off it.

xiii APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS reflected off the inner capillary surface at points close to its diametral plane. Figure B.3 shows a ray reflected exactly off the equator at point P on the inner surface. It is incident from the top, in the plane perpendicular to the capillary axis, at a point Q defined by the hour angle ϕ (determined in the SI). Let ie and re be the angles of incidence and refraction at the outer surface, and ii and ri those at the inner surface. In order to determine the relation between the true and the apparent inner diameters, we consider the particular rays that enter and exit the capillary parallel to the optical axis, i.e. such that ϕ + ie = π/2, see figure B.3. They therefore correspond to a minimum (because vanishing) deviation and are at the heart of the cusp IC. See the SI for a proof that a there is always a ray satisfying these constraints.

The cusp will be bright provided indeed the conditions for significant reflection on the inner surface of the capillary are met, rather than loss by refraction into the capillary cavity, see below. For the moment, the incoming ray is first refracted at the outer surface at point Q, then reflected at the inner wall at point P in the diametral plane, and finally refracted again at point Q’ on the other side of the outer surface. Q’ and Q are symmetrical with respect to the diametral plane. The apparent radius Ra is the distance between the outgoing ray and the optical axis, or half the distance between the cusps IC on both sides of the capillary.

We may now derive the relation between the apparent and the true radii. Applying Snell’s second law of refraction at the outer capillary wall,

ng sinre = n0 sinie , (B.2) where we assume for generality that the capillary is immersed in a medium of refractive index n0. Usually, n0 = 1 for a capillary in air.

The law of sines in triangle OPQ reads

sinre/Ri = sin(π (re + ϕ))/Re = sin(re + ϕ)/Re , (B.3) − whence sinre sinre Ri/Re = = . (B.4) sin(re + ϕ) sinre cosϕ + cosre sinϕ 2 1/2 Now, in triangle ODQ, cosϕ = Ra/Re (and sinϕ = [1 (Ra/Re) ] ). − Equation (B.2) also reads

sinre = n0 sinie/ng . (B.5)

xiv APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

Furthermore, from the condition ϕ + ie = π/2 in eqn. (B.3), sinie = sin π/2 ϕ = − cosϕ. Thus, we have ( )

n0 Ra sinre = n0 sinie/ng = n0 cosϕ/ng = , (B.6) ng Re

2 from which one derives cosre (expressed as 1 sinr )and a little algebra leads to the final − e relation: √ Ra/Re Ri/Re = , (B.7) n 1 R2/R2 1 R2/n2R2 + R2/R2 − a e − a e a e √ √ where for generality n = ng/n0.

Equation B.7 shows that the inner radius Ri, needed in eqn. (B.1) to determine the contact angle θ, can be directly inferred from the measured quantities Re, the capillary outer radius, and Ra , the apparent radius of the cusp, or half of the distance between the two cusps IC. As expected, the fluid in the capillary has no impact on the value of Ra, though some impact on the brightness of cusp IC is expected, as we soon shall see. This result was derived a quarter of a century ago4, in a very limited context, but remained unnoticed. Ongoing progress in capillary manufacture, capillary pullers, cameras and microscopes, as well as in accessories for use of microcapillaries at controlled temperature and pressure, make the method generally attractive today. It allows in particular the simple and precise determination of volumes in microcapillaries, provided there is a symmetry of revolution around the capillary axis.

The ratios Ri/Re and Ra/Re are central in the discussion below. We call them the true and the apparent aspect ratios of the capillary. The ratio Ri/Re 0 (resp. 1) characterises → thick (resp. thin) walled vessels. Using eqn. (B.7), figure B.4 shows the true vs. the apparent aspect ratio for the typical value ng = 1.46 (fused silica glass). The cavity appears enlarged (Ra > Ri), particularly for thin-walled capillaries. Note also the very small error introduced by an uncertainty δng = ±0.02 in ng. The relative error is by numerical inspection

δRi/Ri < δng/2ng for realistic capillary aspect ratios Ri/Re.

Equation (B.7) and this all-optical method for determining the capillary inner diameter

Ri and dependent quantities such as the contact angle, are particularly attractive for home- made capillaries, e.g. drawn capillaries. The method requires neither dyes12 nor calibrated beads8, which may be intrusive in some experiments. Recall for example that many dyes are ionic and may be surface-active.

xv APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

Figure B.4: Relation between the apparent (Ra) and the true internal radius (Ri) of a capillary, from eqn. (B.7), for three values of ng: 1.44,1.46 & 1.48 (arrow). The inset, showing a water-CO2 meniscus (150bar, 25 ◦C), illustrates the apparent wall thinning for a capillary with internal and external diameters 300 and 400µm (tie-line in main figure), scale bar 100µm. The cusps IC (white arrows) render the apparent inner wall readily visible on the CO2 side of the meniscus, despite the presence of water droplets formed on the glass on the right during an earlier stage of the experiment. The cusps are not visible on the water side for reasons explained in section B.2.3.

xvi APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

B.2.3 Taking advantage of total internal reflection (tir)

Case 1: Single fluid lying against the inner wall Up to now, we showed that the cusp IC is due to reflection off the inner wall, back into the glass, but did not consider its brightness. As shown in the SI, the cusp must always be present. Furthermore, according to the Fresnel relations13, the intensity of the reflection at general angle of incidence increases with the contrast in the refractive index between the glass and the fluid, ng nf , where ng and nf are the indices of the glass and the fluid in ¯ − ¯ ¯ ¯ the vessel. But by far the most common case, e.g. aqueous media, even strong brines, is nf < ng, opening the possibility for TIR at the inner wall and a particularly brilliant cusp.

Quite generally, TIR occurs when the angle of incidence i exceeds the critical angle, ic defined by:

ng sinic = nf sinπ/2 = nf , (B.8)

Under the conditions of TIR, light cannot propagate into the fluid, except in the form of an evanescent or tunneling field, with intensity decaying away from the interface with a characteristic length scale, the penetration depth, d, dependent on the angle of incidence, 13 i, and the critical angle, ic, as :

λ λ d = = , (B.9) 2 2 1/2 2 2 1/2 4πnf sin i/sin ic 1 4πng sin i (nf/ng) [ − ] [ − ] where λ is the wavelength. The penetration depth is appreciable only for i ic. ∼

We next derive a surpisingly simple relation between the capillary section and the limit refractive index for TIR, nfl. It will be noticed that for cusp IC, the angle of incidence at the inner wall is i = ii = ϕ+re (see figure B.3), where, as shown in the SI, the cusp condition completely predetermines both ϕ and re as functions of the index of the glass and the aspect ratio of the capillary. Therefore, setting ic = ϕ + re in eqn. (B.8), the cusp will be particularly bright due to TIR, for fluids with indices up to a limit, nfl, defined by

nf n = ng sin(ϕ + re). (B.10) ≤ fl xvii APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

Thus, by eqn. B.3,

nfl = sin ϕ + re ng Re n( 0 ) = sinie (by eqn. (B.2)), Ri ng Re n0 = sin(π/2 ϕ) (see figure B.3), Ri ng − Re n0 = cosϕ . (B.11) Ri ng

Observing that cosϕ = Ra/Re (cf. figure B.3) , we have the final simple relation between nfl and the true and apparent aspect ratios:

n Ra Ra/Re fl = = . (B.12) ng nRi n(Ri/Re)

In the next paragraph, we make use of the fact that it is largely possible to tune the aspect ratio of the capillary to a particular value of nfl. This choice requires expressing nfl as a function of the true aspect ratio. One route is to solve for Ra in a cubic equation easily obtained from eq. (B.7). An alternative used here, again with a cubic equation, is to determine ϕ and re appearing in eq. (B.10), as functions of ng and Ri/Re, see the SI.

Thus, nfl is an intrinsic property of the capillary, determined (via ϕ and re) by Ri/Re and the refractive index ng (strictly n = ng/n0). Figure B.5 shows nfl/ng thus determined as a function of the true aspect ratio, for silica capillaries in air.

The penetration depth, d, can then be rewritten as follows

λ d = , (B.13) 2 2 1/2 4πng (n /ng) (nf/ng) [ fl − ]

or, for fluid indices nf slightly below the critical value, nfl,

λ d , (B.14) 1/2 1/2 ∼ 4π(2n ) (n nf) fl fl −

Fluids with refractive index nf > nfl give rise to a partial reflection determined by the

Fresnel relations. The reflection decays very fast with incresing nf, see section 2 in the SI, which shows the reflectivity calculated as a function of nf for the two capillaries used in this study.

xviii APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

Figure B.5: How to tune the capillary dimensions to exhibit a fluid by total internal reflection (TIR). The curve shows the limit refractive index of the fluid for TIR on the inner wall, nfl (plotted as nfl/ng), as a function of Ri/Re, for a silica capillary (ng = 1.46) in air. The vertical tie-lines show capillaries used here, with aspect ratios Ri/Re = 100/165 0.61 and 150µm/200µm ∼ = 0.75. Fluids with indices nf below the curve give rise to a brilliant cusp IC, by TIR; those above the line do not (e.g. figure B.4), see the text.

Figure B.5 highlights the sensitivity of the intensity of the cusp to the aspect ratio and the refractive indices. The limit refractive indices for the silica capillaries used here

(ng = 1.46), with aspect ratios 100µm/165µm and 150µm/200µm, are for example n 1.36 fl ∼ and 1.26. TIR occurs (bright inner cusp IC), if the material in contact with the inner ∼ wall has a refractive index below this limit index, nf < nfl: this is for instance the case for water (nf =1.33) and supercritical CO2 (nf =1.24) in a capillary with radii 100 and 165

µm (see Figure B.2), and with supercritical CO2 but not water in a capillary with radii 150 and 300 µm (see Figure B.4). On the other hand, in a 200/330µm capillary, figure B.6 (and incidentally in the Monte Carlo simulation in figure 4 of the SI), the cusp is bright for both water and CO2, as expected from figure B.5.

For the same reasons, many oils, with a refractive index nf 1.4, are expected to give ∼ weak or very weak cusps in both the capillaries used here. Anticipating, cyclopentane in

figure B.9 (nCP = 1.41),is an example.

Case 2: Detection of a wetting layer along the capillary wall Consider now what happens when extraneous matter intrudes between a core fluid and the capillary wall. As we now show, the wide range of aspect ratios of commercial capillaries means that one can often be chosen to detect a solid or liquid intrusion, by arranging that

xix APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS nintrusion < nfl < ncore fluid. The preceding discussion on indices also applies to the intruding material, whose leading edge will always be visible as a discontinuity in the brightness of the cusp. The jump in intensity is particularly spectacular when only one of the fluids meets the condition for TIR and is thicker than the tunneling length, see section B.2.3.

Consider for instance an oil, with typical refractive index nf=1.4, that is displaced by water or hydrate (both with refractive indices in the range of 1.33-1.35) forming a layer on the capillary wall: a bright inner cusp is expected from this replacement if the capillary has diameters 200 and 330 µm, but only a faint or invisible cusp is expected in a capillary with diameters 300 and 400 µm. The example given in section B.4.2 below, shows how sensitive this method can be, provided the capillary dimensions are appropriately chosen. In this example co-crystallization of the two fluids occurs on the capillary wall: water and an immiscible hydrate–former, here a light oil, readily give rise to a thin ’halo’ of hydrate propagating over the hydrophilic substrate, on the guest side of the meniscus14–16. Salt or salt hydrate films are other candidates for this effect5–7.

B.3 Experimental materials and methods

Materials: We used 10cm fused silica capillary tubes (clear fused quartz, VitrotubesTM).

The fluids were compressed CO2 (Linde, purity 4.5) and deionised water (resistivity > 18MΩcm, PureLab Classic from ELGA Labwater). Dry cyclohexane (99.9%) and the dichloro-dimethyl-silane (DCDMS) were purchased from Aldrich for hydrophobizing the glass. Absolute ethanol (analytical grade) and lithium chloride, LiCl were also supplied by Aldrich.

Methods: Some capillaries were rendered mildly hydrophobic by silane-treating the 17 2 glass with a procedure adapted from Dickson et al. A solution of 10− M DCDMS in dry cyclohexane was introduced by capillary rise into the capillary tube and left for one hour under inert N2 atmosphere. Unreacted silane was removed by washing the capillaries several times with pure dry cyclohexane. Finally they were washed in absolute ethanol and dried at 110 ◦C for 30min. According to Dickson et al. the proportion of unreacted silanol (SiOH) groups on the surface of the silane-treated glass is about 12%, making the glass ’intermediate-wet or mildly hydrophobic as assessed by the contact angle measured at atmospheric pressure, 98 ± 2◦. The treated glass became CO2-wet when the pressure was

xx APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS increased, with contact angles in water approaching 160◦ with dense (liquid) CO2.

Instrumentation and procedure: We loaded the tubes by capillary rise of the aqueous phase and flame-sealed one end with a microtorch (Prodont Holliger). Centrifugation (5000 rpm for about 1/2h) drove the aqueous phase to the sealed end of the capillary. The meniscus was typically located about 10–20mm from the closed end.

Capllaries were photographed with a Ueye SE1240 camera on an Olympus B50 upright microscope equipped with a CAP500 temperature-controlled stage (Linkam), which provides temperature control to within 0.1-0.2 ◦C. The capillaries were set in the 1mm x 0.6mm rectangular channel of the silver block of the stage. The stage allows recentering the capillary when the meniscus responds to changing pressure (the aqueous phase is slightly compressible) or temperature (here a bigger effect). The open end of the capillary was glued with cyanoacrylate glue into a stainless steel tube (OD = 1/16, ID = 500µm), connected via a three-way valve to an ISCO piston pump (65DM) filled with CO2, allowing pressure control up to 700bar. Prior to carrying out the measurements, the system was purged 3–4 times at a pressure in the range 30-40bar.

The microscope operated in transmission mode with K¨ohler illumination and a x10 long working distance objective. Care was taken to set the capillary axis on, and perpendic- ular to the optical axis, so that the height of the meniscus could be accurately determined from micrographs focused successively on the pole and the contact line.

Contact angle isotherms were measured as follows, between 22 and 205 ◦C, over a pressure interval extending up to 600bar: Pressure was increased by steps to the maximum value, and then decreased stepwise back to the minimum pressure, usually 50bar; then T was changed (usually increased) to the next isotherm. Photographs of the meniscus were taken after waiting a few minutes at each step to equilibrate the system.

We emphasize that static contact angles can take any value between two limits: the advancing and receding angles18. Such hysteresis relates to various factors such as the existence of pinning defects on the substrate, or the adsorption on the substrate of compounds from the displaced fluid. Compression induces a contraction, very limited in the case of water because of its very low compressibility. The contact angles recorded when increasing pressure along an isotherm should thus be close to the water-receding, or

CO2-advancing limit, and vice versa while releasing the pressure. Likewise, measurements

xxi APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS along an isobar while increasing the temperature correspond to water-advancing angles.

We did not notice any significant difference between the contact angles obtained upon increasing and releasing the pressure, except in the measurements carried out with a strong brine as the aqueous phase (8M LiCl). Possible reasons are discussed below. Unless otherwise specified, the contact angles displayed in the graphs below are recorded at increasing pressure. It should further be borne in mind that silica surfaces display variable types and density of hydroxyl groups (silanols), depending on the underlying structure (crystalline or amorphous) and substrate preparation or history, with an impact on wettability and contact angles19.

Error bars shown below (±2◦) were deduced from random perturbation of the experi- mental data based on the estimated 4-pixel error on all measurements. An extension of the analysis carried out by Cheong et al.12 shows that the error on the contact angle, ∆θ, is related to that on the height ∆h, and that on the inner radius, ∆Ri, as follows: ∂θ ∂θ δθ = ¯ ¯∆h + ¯ ¯∆R ¯ h¯ ¯ R ¯ i ¯∂ ¯ ¯∂ i ¯ ¯1 + sin¯ θ ¯ ¯ ∆Ri = ∆h + cosθ (B.15) Ri Ri 12 Cheong et al. neglected errors in Ri. Eqn. (B.15) shows that for low contact angles 10% error in Ri contributes 6◦ error in θ, underlining the importance of an accurate determination of the capillary inner diameter.

B.4 Experimental illustrations

B.4.1 CO2-water and CO2-brine contact angles at high tempera- ture or pressure

Contact angles of pure water and CO2 on hydrophilic and mildly hydrophobic glass

We start with the results obtained with the mildly hydrophobic (silane-treated) glass at room temperature (22 ◦C), because they can be compared readily to those of Dickson et al.17, obtained by means of the conventional sessile drop technique. The micrographs in figure B.6 show the strong pressure dependence of substrate wettability: it is intermediate- wet at low pressure, with contact angle slightly above 90◦, and becomes CO2-wet at high

xxii APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

Figure B.6: Micrographs of the water-CO2 meniscus (water on the left) in a silane-treated capillary at increasing pressures at room temperature (22 ◦C). Scale bar: 100µm (in the first vignette).

xxiii APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

Figure B.7: Pressure dependence of the contact angle of water-CO2 in (a) a hydrophobic, 17 silane-treated capillary at 22 ◦C (filled and open data from ref. and this work, respectively) and (b) a hydrophilic, untreated capillary at different temperatures: 40 ◦C (circles), 100 ◦C (triangles), 150 ◦C (squares), 205 ◦C (diamonds). Error bars are shown only for the latter isotherm.

pressure (or CO2 density). Figure B.7 shows the contact angles extracted by the method of sections B.2.1 and B.2.2, together with those measured by Dickson et al.17. The two sets of results are in very good agreement: contact angles increase to about 160◦ under

CO2 at 200bar, with a surge near the vapour pressure of CO2 at the temperature of the experiment, 60bar at T=22 ◦C. Figure B.7(b) shows the pure water-CO2 contact angles ∼ measured in the untreated (bare) capillaries along four isotherms from 40 to 205 ◦C, for a pressure range extending from 50 to 600bar. The angles are low, in the range of 5 to 9◦, and show negligible pressure dependence. The figure also shows a marginal increase of the contact angle with increasing temperature, consistent with the analysis of literature results presented in ref.20.

xxiv APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

Figure B.8: Pressure dependence of a 8M LiCl brine-CO2 contact angle on untreated glass at : ∼ 40 ◦C ( ), 100 ◦C ( ), 150 ◦C ( ), 205 ◦C ( ). Full symbols correspond to water-advancing ⃝ △ □ ⋄ angles (see text).

Contact angles of a strong brine and CO2 on glass

The strong brine is an 8M solution of LiCl, chosen because it is highly soluble in water. Figure B.8 displays the contact angles measured along the same isotherms as above and for a similar range of pressure (cf. figure B.7(b)). The data are somewhat more dispersed and hysteresis is larger than for pure water, possibly because contact line pinning was occasionally observed, an effect most likely due to small salt crystallites observed on the capillary wall. They arise by evaporation occurring in the repeated CO2 injections and purges at the beginning of the experiment. Some authors have pointed out the difficulty of measuring these angles, specially the receding angle21.

The relatively high angles observed at low pressure, 50–100bar, are likely to be ad- vancing angles, as they are obtained after heating from the previous isotherm, which induces expansion of the brine. Compression, on the other hand, induces contraction and retreat of the contact line. This effect was noticeable only if the pressure was significantly increased, because the compressibility of water, specially brine, is extremely small.

Comparing figures B.7(b) and B.8 shows that, at least for the lowest temperature investigated, 40 ◦C, contact angles are significantly higher, 25◦, when the aqueous phase ∼ xxv APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS is an 8M LiCl brine than when it is pure water, 6◦. This trend is in line with what has ∼ been observed with other brines (mainly NaCl brines, but CaCl2 and MgCl2 brines as well), by conventional drop methods, for temperatures not exceeding 80 ◦C and in a narrower pressure range, 150 bar20,22–25. Higher contact angles with brine than with water are also ≤ observed at ambient temperature and pressure, i.e. in the absence of a gas, so that the brine is in equilibrium with its vapour. For example, Sghaier et al.26 observed a significant increase of the contact angle of nearly-saturated NaCl brines at 20 ◦C, in the range 10–35◦, depending on the glass substrate, consistent with our observations with a concentrated LiCl brine on silica at 40 ◦C in a wide range of CO2 pressures (figure B.8).

These authors accounted qualitatively for this variation by considering the salt-induced increase of the denominator,γlv, (the water surface tension) in the Young equation:

cosθ = (γsv γsl)/γlv , (B.16) − where γsv and γsl are the substrate-vapour and substrate-liquid water interfacial tensions (IFT’s). A similar argument has been invoked by Espinoza and Santamarina23 and by Jung and Wan25 to account for the effects of pressure and brine salinity on θ.

Of the three interfacial tensions involved in eqn. (B.16), only the brine-CO2 IFT, γlv, can be measured and is well characterized as a function of brine salinity and CO2 pressure. These two parameters act independently27, i.e.

+ (B.17) γlv(p,salinity) = γW,CO2 (p) δ(salinity), where γW,CO (p) is the pure water-CO2 IFT, which decreases from 70mN/m at 40 ◦C 2 ∼ at low pressure to a plateau of 25mN/m when p exceeds 100–150bar22. The pressure- ∼ independent increase in tension due to dissolved salts, δ, is 13mN/m for a 8M LiCl brine ∼ 28 at 40 ◦C .

Now, the Young equation can be used to relate the contact angle θ to that under reference conditions, e.g. low pressure p and/or pure water, (subscript 0):

(γsv γsl) γlv0 cosθ = cosθ0 − (B.18) (γsv γsl)0 γlv −

The dependence of γsv γsl with pressure and brine salinity is poorly known. However, − γsv decreases with increasing pressure, since CO2 adsorbs on silica, and is not influenced by brine salinity. Furthermore, we observe experimentally that cosθ remains approximately

xxvi APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS constant when pressure increases above 100bar. Therefore, γsv γsl must decrease in ∼ − such a way that it balances the decrease of γlv. We also observe that, at T=40 ◦C, θ increases from θ0 5◦ to θ 25◦ when salinity increases from 0 to 8M LiCl, which is ∼ ∼ roughly consistent with cosθ cosθ0γlv0/γlv cosθ0 ×70/(70+13), meaning that γsv γsl ∼ ∼ − is barely influenced by the presence of salt.

The present data suggest however that the full story is more complicated, as we now show. Figure B.8 also shows that as the temperature is raised above 100 ◦C, the presence of dissolved salt (8M LiCl) diminishes the contact angle θ, which for the highest

T investigated (150 and 205 ◦C) comes close to the values observed with pure water at similar T and P (see Figure B.7(b)). To our knowledge this is the first observation of this effect. This behaviour might be rationalized by the fact that increased thermal agitation at high temperature possibly annihilates the disturbance of the water hydrogen bond network by dissolved ionic species, with an effect on γsl and γlv. Molecular dynamics simulations similar to those in ref.19 might be used to test this conjecture.

B.4.2 Thin layers revealed by the capillary inner cusp

As pointed out in section B.2.3, thin liquid or solid films intruding along the inner capillary wall give rise to a discontinuity in the brightness of cusp IC. The jump may be particularly pronounced if the aspect ratio is chosen such that the conditions for total internal reflection are met by the intruding fluid or layer on the wall, but not by the bulk fluid in the cavity.

Only if the index of the latter fluid is close to the critical value, nfl, will the cusp be significant on the bulk fluid side of the meniscus, see figure 3 in the SI.

As an illustration, consider a water-cyclopentane interface in presence of a glass substrate. Under appropriate conditions29, a layer of cyclopentane hydrate can be induced to grow over the water-oil or ice-oil interface, here the meniscus. When the interface is completely covered, a tenuous layer of hydrate, called a ’halo’14, extends over the glass substrate, here the capillary wall. Viewed growing over a flat substrate, the halo is hardly visible in standard transmission microscopy, but requires more complicated methods such as phase contrast or fluorescence microscopy15.

In figure B.9(a), the lateral extension of total internal reflection in the cusps IC coincides with the halo, which is readily visible. The jump in brightness is conspicuous

xxvii APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS because the refractive index of cyclopentane, 1.41, is higher than the critical index for total internal reflection in this particular capillary (Ri/Re = 100/165, ng = 1.46, nfl = 1.361 cf. the 30 left tie-line in figure B.5), while that of the hydrate, nh = 1.35 , is below it. Hence the progress of the growing halo is highlighted by a bright cusp creeping over the much dimmer one on the oil-filled side of the meniscus. Furthermore, the intensity of the reflection in figure B.9(a) drops sharply at the halo tip, which is therefore blunt. Note that the halo is manifest all over the glass in transmission images.

Later, figure B.9(b-c), the halo edge is so thin that it is not detectable directly in transmission images. It is nonetheless revealed by the cusps IC. Moreoever, the progressive dimming of the cusp towards the direction of growth shows that the thickness tapers towards the front. The vanishing of the cusp corresponds to a thickness comparable to the penetration length d in eqn. (B.9). Using the refractive indices of the glass (1.46) and the hydrate (1.35), we estimate d 140nm, in good agreement with an earlier estimate of the ∼ thickness of the halo front, deduced from a combination of techniques including confocal reflectance15.

The results derived in section B.2.3 and illustrated here are not only anecdotal. Even without the effect of total internal reflection, the sensitivity and high dynamic range of modern digital cameras make it easy to detect the jump or even subtle variations in the brightness of the cusp. Furthermore, for aqueous media, the aspect ratio of the capillary can in general be chosen in advance to fulfill the TIR switching condition. For example, the aspect ratios of the current standard silica capillaries from VitrotubeTM are in the interval

0.588 Ri/Re 0.8, or 1.17 n 1.37. This range of refractive indices covers strong ≤ ≤ ≤ fl ≤ brines and dense (supercritical or liquid) CO2.

xxviii APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

Figure B.9: Using the contrast of cusp IC to highlight growth of thin films: (a) Growth of a thin but visible film of polycristalline cyclopentane hydrate, initiated at the water-cyclopentane meniscus on the left at 4 ◦C; (b-c) Views 60 and 102s later (capilllary recentred). Although the − halo is tenuous to the point of invisibility in the transmission image, the cusps IC clearly show up its progression to the right and thickening. Scale bar in (a): 200µm.

xxix APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS B.5 Conclusion and outlook

Studies of contact angles and wetting by capillary rise have a venerable history, stretching back at least as far as the work of Jurin31,32. Lately, instruments such as contact-angle goniometers have superseded the capillary, which largely has been relegated to the elemen- tary classroom. Today, however, both the modest glass capillary2, and more sophisticated versions such as pulled pipettes33,34 are commonly used in investigation of fundamental aspects of wetting phenomena and flow transpmort in porous media. Indeed, the capillary is the simplest example of a microfluidic device and a pore model. Even modest research microscopes and digital cameras provide high resolution images of round capillaries that can be used to measure contact angles to a high degree of accuracy, provided one understands the distorsion introduced by the curved surfaces. Our aim here was to provide and illustrate the necessary perspective. The central point is to understand the conditions of formation of the cusp due to reflection of light off the inner capillary wall.

Variations of the brightness of the cusp parallel to the capillary axis are explained here and turned to advantage to highlight thin liquid or solid films growing or disappearing on the inner glass wall. The variation is spectacular when the capillary aspect ratio is chosen so that only one of the media in contact with the glass fulfills the conditions for total internal reflection. This condition is readily met thanks to the wide range of capillary aspect ratios available commercially. The method is just as well applicable to capillaries with variable diameter, and can be extended to higher pressures and temperatures as pumps and heating plates operating in these ranges are becoming commercially available.

As an illustration, the wettability of silica at the water- or brine-CO2 interface is of practical importance for geological storage of CO2. Our measurements in bare or silane- treated glass capillaries range from 20 to 200 ◦C, at pressures up to 600bar and salinity ∼ up to 8M LiCl, representative of conditions encountered in geological storage of CO2. They confirm confirm and extend the range of earlier data: A strong effect of CO2 pressure or density on contact angle is observed with silane- treated glass, but not with bare glass. Increasing the temperature slightly increases contact angles on glass. We observed a new ef- fect in hot brine: Salinity does increase contact angles on glass, but this effect is attenuated at high temperatures (T > 100 ◦C), where glass thus remains strongly water-wet.

In conclusion, understanding and exploiting refraction in capillaries is for several rea-

xxx APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS sons appealing to study wetting and to determine contact angles from the geometry of a capillary meniscus: ease of use and availability of the equipment; need for insignificant amounts of the fluids; adaptability to demanding conditions such as high pressures or ex- treme temperatures. A further advantage of the present method is that it does not require additives to enhance meniscus visibility, that might perturb the contact angle. Here, both the fluids were transparent, but it suffices that just the wetting fluid should be clear.

xxxi APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS B.6 R´ef´erences

[1] I.-M. Chou and Z. Pan, Fused Silica Capillary Reactor and Its Application, ch. 6. Dordrecht: Springer, 2014.

[2] M. Heshmati and M. Piri, “Experimental investigation of dynamic contact angle and capillary rise in tubes with circular and noncircular cross sections,” Langmuir, vol. 30, no. 47, pp. 14151–14162, 2014. PMID: 25323811.

[3] L. M. Coucoulas, R. A. Dawe, and E. G. Mahers, “The refraction correction for the spinning drop interfacial tensiometer,”Journal of Colloid and Interface Science, vol. 93, no. 1, pp. 281 – 284, 1983.

[4] E. Q. Chen, C. F. Lam, and A. Periasamy, “Effect of refraction on optical micro- scopic measurement of internal blood-vessel diameter and its correction,” Journal of Microscopy, vol. 164, no. 3, pp. 239–245, 1991.

[5] N. Shahidzadeh-Bonn, S. Rafa¨ı, D. Bonn, and G. Wegdam,“Salt crystallization during evaporation: Impact of interfacial properties,” Langmuir, vol. 24, no. 16, pp. 8599– 8605, 2008. PMID: 18652495.

[6] M. Bouzid, L. Mercury, A. Lassin, and J.-M. Matray, “Salt precipitation and trapped liquid cavitation in micrometric capillary tubes,” Journal of Colloid and Interface Sci- ence, vol. 360, no. 2, pp. 768 – 776, 2011.

[7] A. Naillon, P. Duru, M. Marcoux, and M. Prat, “Evaporation with sodium chloride crystallization in a capillary tube,” Journal of Crystal Growth, vol. 422, pp. 52 – 61, 2015.

[8] Z. Liu, K. Muldrew, R. G. Wan, and J. A. W. Elliott,“Measurement of freezing point depression of water in glass capillaries and the associated ice front shape,”Phys. Rev. E, vol. 67, p. 061602, Jun 2003.

[9] P. G. de Gennes, F. Brochard-Wyart, and D. Qu´er´e, Capillarity and Wetting Phenom- ena. Berlin: Springer, 2003.

[10] H. Y. Erbil, Surface Chemistry of Solid and Liquid Interfaces. Oxford: Blackwell, 2006.

xxxii APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

[11] M. Minnaert, Light and color in the outdoors. New York: Springer, 5th edition ed., 1993.

[12] B. H.-P. Cheong, T. W. Ng, Y. Yu, and O. W. Liew,“Using the meniscus in a capillary for small volume contact angle measurement in biochemical applications,” Langmuir, vol. 27, no. 19, pp. 11925–11929, 2011. PMID: 21859131.

[13] J. D. Jackson, Classical Electrodynamics, Third Edition. Hoboken, NJ: J. Wiley, 1999.

[14] J. G. Beltr´anand P. Servio, “Morphological investigations of methane-hydrate films formed on a glass surface,”Cryst. Growth Des., vol. 10, no. 10, pp. 4339–4347, 2010.

[15] M. L. Mart´ınez de Ba˜nos,N. Hobeika, P. Bouriat, D. Broseta, E. Enciso, F. Cl´ement, and R. Brown,“How do gas hydrates spread on a substrate?,”Crystal Growth & Design, vol. 16, no. 8, pp. 4360–4373, 2016.

[16] A. Touil, N. Hobeika, D. Broseta, and R. Brown 2017, in preparation.

[17] J. L. Dickson, G. Gupta, T. S. Horozov, B. P. Binks, and K. P. Johnston, “Wetting phenomena at the co2/water/glass interface,”Langmuir, vol. 22, no. 5, pp. 2161–2170, 2006. PMID: 16489803.

[18] O. Carrier and D. Bonn, Contact angles and the surface free energy of solids, ch. 2. Dordrecht, Holland: Elsevier, 2015.

[19] C. Chen, N. Zhang, W. Li, and Y. Song, “Water contact angle dependence with hydroxyl functional groups on silica surfaces under co2 sequestration conditions,” En- vironmental Science & Technology, vol. 49, no. 24, pp. 14680–14687, 2015. PMID: 26509282.

[20] D. Palamara, T. Neeman, A. Golab, and A. Sheppard, “A statistical analysis of the effects of pressure, temperature and salinity on contact angles in co2brinequartz sys- tems,”International Journal of Greenhouse Gas Control, vol. 42, pp. 516 – 524, 2015.

[21] E. Bormashenko,“Wetting of real solid surfaces: new glance on well-known problems,” Colloid and Polymer Science, vol. 291, no. 2, pp. 339–342, 2013.

[22] P. Chiquet, D. Broseta, and S. Thibeau,“Wettability alteration of caprock minerals by carbon dioxide,”Geofluids, vol. 7, no. 2, pp. 112–122, 2007.

xxxiii APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

[23] D. N. Espinoza and J. C. Santamarina,“Water-co2-mineral systems: Interfacial tension, contact angle, and diffusionimplications to co2 geological storage,” Water Resources Research, vol. 46, no. 7, pp. n/a–n/a, 2010. W07537.

[24] S. Saraji, M. Piri, and L. Goual, “The effects of {SO2} contamination, brine salinity, pressure, and temperature on dynamic contact angles and interfacial tension of super- critical co2/brine/quartz systems,” International Journal of Greenhouse Gas Control, vol. 28, pp. 147 – 155, 2014.

[25] J.-W. Jung and J. Wan, “Supercritical co2 and ionic strength effects on wettability of silica surfaces: Equilibrium contact angle measurements,” Energy & Fuels, vol. 26, no. 9, pp. 6053–6059, 2012.

[26] N. Sghaier, M. Prat, and S. B. Nasrallah,“On the influence of sodium chloride concen- tration on equilibrium contact angle,”Chemical Engineering Journal, vol. 122, no. 12, pp. 47 – 53, 2006.

[27] C. Duchateau and D. Broseta, “A simple method for determining brinegas interfacial tensions,”Advances in Water Resources, vol. 42, pp. 30 – 36, 2012.

[28] A. A. Abramzon and R. D. Gaukhberg, “Surface tensions of salt solutions,” Russ. J. Appl. Chem., vol. 66, p. 1139, 1993.

[29] C. J. Taylor, K. T. Miller, C. A. Koh, and E. Dendy Sloan Jr., “Macroscopic investi- gation of hydrate film growth at the hydrocarbon/water interface,” Chem. Eng. Sci., vol. 62, no. 23, pp. 6524 – 6533, 2007.

[30] E. D. Sloan and C. A. Koh, Clathrate Hydrates of Natural Gases. Boca Raton, Florida: CRC Press, 2008.

[31] J. Jurin, “An account of some experiments shown before the royal society; with an enquiry into the cause of the ascent and suspension of water in capillary tubes,”Phil. Trans., vol. 30, pp. 739–747, 1717-1719.

[32] C. W. Extrand,“Origins of wetting,”Langmuir, vol. 32, no. 31, pp. 7697–7706, 2016. PMID: 27459085.

xxxiv APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

[33] J.-B. Gorce, I. J. Hewitt, and D. Vella, “Capillary imbibition into converging tubes: Beating washburns law and the optimal imbibition of liquids,”Langmuir, vol. 32, no. 6, pp. 1560–1567, 2016. PMID: 26784118.

[34] A. Budaraju, J. Phirani, S. Kondaraju, and S. S. Bahga,“Capillary displacement of vis- cous liquids in geometries with axial variations,”Langmuir, vol. 32, no. 41, pp. 10513– 10521, 2016. PMID: 27653244.

xxxv APPENDIX B. USING ASTIGMATISM IN ROUND CAPILLARIES TO STUDY WETTING LAYERS

xxxvi Appendix C

N2 hydrate growth in glass capillary

X-ray data have shown that N2 forms type sII hydrates. Raman spectra acquisitions for water + N2 system at different locations in the capillary are performed as is described in with section 4.2.3 (cf. Chapter 4). Figure C.1 shows the Raman spectra of the N–N stretching vibration for nitrogen molecules both in cages of hydrates and in gas state. This experiment is conducted at 230 bar, in which the N2 hydrate has been formed at -38.5 ◦C, and then the temperature raised and stabilized at -10 ◦C. We can see from Figure C.1 that 1 Raman peak of N–N stretching vibration is observed for nitrogen hydrates at 2324 cm− , 1 while in the gas state, it is found at 2328 cm− . The published data for Raman shifts for N–N stretching vibration are quite different from each other.1–3 These differences, however, lie in the fact that the Raman shifts for N–N stretching vibration depends on the pressure and temperature of the system.

Figure C.2 shows snapshots of experiment where the capillary contains water in con- tact with nitrogen (N2) gas at 240 bar. A bubble of N2 gas in the water, located at 550 µm from the water – N2 meniscus, results from a previous hydrate dissociation. The system is cooled at a rate of 20 ◦C/min, the N2 hydrate first nucleates on the surface of the gas bubble at -38 ◦C.N2 hydrate needles then grow from the interface to bulk water. The needles that grow to the right will go more than twice as fast as those that go to the left.

This difference in growth rate is related to the concentration gradient of N2 which was established during the decent of temperature.

xxxvii APPENDIX C. N2 HYDRATE GROWTH IN GLASS CAPILLARY

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Figure C.1: Raman shifts showing the N–N stretching vibrations in the N2 hydrate and nitrogen gas at the same pressure and temperature (230 bar and -10 ◦C).

xxxviii APPENDIX C. N2 HYDRATE GROWTH IN GLASS CAPILLARY

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Figure C.2: N2 hydrate formation on N2 gas bubble at 240 bar and -38 ◦C: the water – N2 interface is covered in less than 14 of second by hydrate crust. Hydrate needles then grow from the interface to bulk water.

xxxix APPENDIX C. N2 HYDRATE GROWTH IN GLASS CAPILLARY

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Figure C.3: N2 hydrate formation and growth in bulk water at moderate supercooling conditions: (a), P = 15 bar, T = 15 ◦C, ∆T 6 ◦C; (b), P = 25 bar, T = 22 ◦C, ∆T 4 ◦C, in − ≈ − ≈ a capillary where the hydrate has been formed and dissociated shortly before.

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Figure C.4: N2 hydrate halo growth along the glass capillary wall in N2 gas phase from supercooled water – N2 gas meniscus at 50 bar and -15 ◦C (the subcooling ∆T 3.4 ◦C). This ≈ halo is fed by the underlying water. Elapsed time from (a) to (b) 7 s and from (b) to (c) 21 s

xl Appendix D

Raman shifts of CP in hydrate and liquid state

xli APPENDIX D. RAMAN SHIFTS OF CP IN HYDRATE AND LIQUID STATE

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Figure D.1: Raman shifts showing the cyclopentane stretching vibrations in the CP hydrate and liquid CP at ambient pressure and 5 ◦C.

xlii APPENDIX D. RAMAN SHIFTS OF CP IN HYDRATE AND LIQUID STATE

D.1 R´ef´erences

[1] Pauer, F., Kipfstuhl, J. & Kuhs, W. F. Raman spectroscopic and statistical studies on natural clathrates from the greenland ice core project ice core, and neutron diffraction studies on synthetic nitrogen clathrates. Journal of Geophysical Research: Oceans 102, 26519–26526 (1997). URL http://dx.doi.org/10.1029/97JC02352.

[2] Champagnon, B. et al. Nitrogen and oxygen guest molecules in clathrate hydrates: different sites revealed by raman spectroscopy. Journal of Raman Spectroscopy 28, 711–715 (1997). URL http://dx.doi.org/10.1002/(SICI)1097-4555(199709) 28:9<711::AID-JRS167>3.0.CO;2-S.

[3] ling Liu, C., long Lu, H. & guang Ye, Y. Raman spectroscopy of nitrogen clathrate hydrates. Chinese Journal of Chemical Physics 22, 353 (2009). URL http://stacks. iop.org/1674-0068/22/i=4/a=03.

xliii APPENDIX D. RAMAN SHIFTS OF CP IN HYDRATE AND LIQUID STATE

xliv Appendix E

Development of a homemade software

The electronic measuring devices used in the research lab, such as cameras, pumps, tem- perature or pressure sensors, are sometimes supplied with software to control them. These applications sometimes require paid licenses or their functions are limited and do not meet the needs of customers. I describe below software for collecting the data from three devices (camera, pump, temperature controller) that I used during my thesis work.

The initial idea was to create a simple and efficient interface to meet the needs of the research team I worked with during my PhD. The purpose of this software application is summarized as follows:

• In research laboratories, we usually work with different operation system (OS): Win- dows, Linux or macOS. So I had to find a way to create a multiplatform software application so that I can install it with any OS.

• In my experiments, phenomena such as hydrate dissociation in bulk water, or the growth of the hydrate halo on the substrate at low subcooling, take a long time, whereas hydrate nucleation and hydrate fiber growth are very fast phenomena. In order to facilitate post-processing of videos and to intelligently manage the space of our hard disk, it is more convenient to be able to change the acquisition frequency during video recording.

• My work is relies on visual observations of phase transformations in the sample at controlled temperatures and pressures. The processing of the image and the under- standing of the events that occur during these transformations will be simpler if we store together image, the time, the pressure and the temperature in the same film.

xlv APPENDIX E. DEVELOPMENT OF A HOMEMADE SOFTWARE

• Some devices are not equipped with an application to manage their functionalities like isco pumps

Qt Creator is an integrated development environment (IDE) that is part of the Qt Framework. It is therefore oriented for programming in C++. It integrates directly into the interface a debugger, a tool for creating graphical interfaces, code publication tools and Qt documentation. The source code editor allows autocompletion as well as syntax highlighting. Qt Creator uses the gcc compiler on Linux. It can use MinGW or the Visual Studio compiler (MSVC) under Windows and Clang under macOS. Under this last OS, we must first install XCode. For more information, I advise the reader to go to openClassrooms website[1].

To develop any application, we have to create a project that will contain different files. A ’.pro’ file specific to Qt is used to configure the project at compilation step. In a Qt project, at least, we need one file to start programming ’main.cpp’. To be able to communicate with an external device, I included in my project some additional files such as header ’.h’ and libraries ’.lib’ or ’.dll’ files specified for each device. I created a new class consisting of two files. One header file ’.h’ in which variables, subclasses, slots and signals are declared. The second file, ’.cpp’ contains the definition (implementation) of the various functions and methods declared in the header file.

In most GUI (Graphical User Interface) libraries, of which Qt is a part, all the elements of a window, such as buttons, checkboxes, images, are called widgets (or objects). The window is also considered as a widget. There are two ways to create a GUI under Qt Creator:

• The first method consists to create, using the command line, a window on which we insert objects with the command ’new’. This method is sometimes cumbersome when it is needed to specify some object properties and their method.

• Qt includes a tool called ’Qt Designer’, this tool is very convenient to designate an application with a simple click to add an object. A file resulting from the manipulation of Qt Designer, ’.ui’, will contain the graphical interface (XML type).

[1]https://openclassrooms.com/courses/programmez-avec-le-langage-c/ introduction-a-qt

xlvi APPENDIX E. DEVELOPMENT OF A HOMEMADE SOFTWARE

I present below (Figure E.1 and E.4) two applications used on two different experimen- tal setups. The representative diagrams of the user-computer-external device interactions of these two applications are presented in Figures E.2 and E.3.

The uEye cameras supplier, IDS (Image Development System), provides customers with an application that offers many functionalities. Unfortunately, this application does not offer the possibility to record long videos, and no way to superimpose information such as temperature and pressure into a video. This provider developed library files (uEye - tools.h, uEye.h, uEye api.lib, uEye tools.lib) to communicate with their cameras via other interfaces. OpenCV is another way that offers a complete set of libraries to handle any kind of camera.

In both applications presented in Figures E.1 and E.4, the computer receives a con- tinuous stream of images from a camera mounted on a microscope. These images are displayed directly on the computer screen with a frame rate of 20 frames per second (13).

When launching a new movie recording, using the ”Filmer” button (2), the number of images (7) and the time (6) are initialized to zero. The recording frequency of the images is initialized by the user. Changing this frequency at any time during the recording is possible by entering the desired time step value in the number editor and confirming with the ”ok” button (6). For reasons of file organization in the disk, the file name takes the form ”year.month.day hour.minute.second system”. For each experiment, the user must enter the name of the studied system, for example ”H2O + CO2 22 bar”. At each time step, the current image, which has just been captured by a camera, is stored as a new main image in a matrix variable [3; n: m]. Images containing information on the studied system, (temperature, pressure, time, etc.) are added by replacing a portion of the main image. The position of secondary images is located at the top center of the main image.

This main image contains both the image received from the camera and secondary images, is added to the movie being recorded. To stop recording, the ”Arrˆeter”button (3) allows to save the movie in ”.avi”format and free the space allocated in the RAM memory. The ”Quitter”button (4) allows to close connections with external devices, destruct pointers and timers and exit the application.

Temperature acquisition: Depending on the temperature sensor used, external files may be needed to communicate with the measuring instrument.

xlvii APPENDIX E. DEVELOPMENT OF A HOMEMADE SOFTWARE

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N◦ QObject Descreption 1 QLabel label displays information about the camera type and the system studied 2 QPushButton button to start video recording 3 QPushButton button to stop video recording and save the video in ”.avi”format 4 QPushButton button to close connection and exit the application 5 QLineEdit number editor to modify the time between two successive images 6 QPushButton button to transmit time step to the timer 7 QLabel label displays the number of images that have been added to the current movie 8 QLabel label displays the elapsed time of the experience 9 QCheckBox when is activated, the serial port of ISCO pump is open 10 QCheckBox when is activated, the LinkSys32 software is connected to the application 11 QLabel label displays the pressure measured by the ISCO pump 12 QLabel label displays the temperature of the studied sample 13 QScrollArea visualize, in real time, the sample with a frequency of 20 frame/s 14 QLineEdit text editor to write remarks 15 QCheckBox when is activated, the remarks are included in the recording video

Figure E.1: Graphical user interface of an application for video, temperature and pressure acquisition.

xlviii APPENDIX E. DEVELOPMENT OF A HOMEMADE SOFTWARE

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Figure E.2: Representative diagram of the input and output data linking different parts of the experimental setup described in Chapters 3 and 4

In the experimental configuration described in Chapters 3 and 4, I used a Linkam temperature controller. The software ’LinkSys32’ provided by the manufacturer allows us to manage this controller. To my knowledge, this company does not provide any library files to communicate with its instrument. This software does not produce an output file that can be used for post-processing. There are three ways to get the temperature measured by this instrument: to analyze the data transmitted via the serial port, to communicate with the manufacturer’s software ’linksys32’ using Windows APIs (Application Programming Interfaces) or QProcess (is Qt class), or programing a screenshot on a specific area where temperature is displayed in linksys32 window. In this work, I opted for the last option.

If the checkbox ”Temp´erature”(10) is activated, the screenshot is done continuously on specific locations of LinkSyd32 window (software that communicates with the tempera- ture control device) 10 times per second. Three informations are captured: the temperature, the cooling or heating rate and the target temperature. These images are added to the main image depending on the frame rate of the recording movie. The instantaneous value of the temperature is also displayed in a label (12) in the window of Figure E.1.

The high-pressure pump ’Isco D Series’ can be remotely controlled by a computer through a RS-232-C serial interface. Writing programs for serial control requires sub- stantial knowledge of the software language used, so ’Isco’ does not provide support for developing our own programs. It provides the syntax and responses for serial commands. All data transfers to the instrument are in a frame format. The frame format for data transfers from the network controller is as follows: ”destination\acknowledgement\message source\length\message\checksum\[CR]”. I will not detail here the meaning of each term,

xlix APPENDIX E. DEVELOPMENT OF A HOMEMADE SOFTWARE

but the reader wishing to develop an application to communicate and control these pumps, these project are available[2] to provide him an example with commented code.

If the checkbox ”Pression” (9) is activated, a message ”PRESS” is sent to the high- pressure pump every second, then the computer receives the pressure value. This value is displayed in a label (11). During movie recording, this value is transformed into an image so that it is superimposed on the main image.

This application offers the possibility to write remarks directly in the video being recorded to facilitate post-processing. Just write the text in the text editor (14) and activate the checkbox (15). This text is transformed into an image and then integrated into the video. This text will appear in all images where the checkbox (15) was activated.

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Figure E.3: Representative diagram of the input and output data linking different parts of the experimental setup reported in ongoing thesis Dyhia Atig LFCR

In an experimental setup, which is part of an on-going doctoral thesis, Resistance Temperature Detectors ’PT100’ are used to measure the temperature via a ’National In- strument’ acquisition card. National Instrument provides library files to exchange with this acquisition card. Some functions used in the application developed here are present in the files ’NIDAQmx.h’ and ’NIDAQmx.lib’. I included in Qt project this files in order to use these functions.

In this example (Figure E.4), two temperature sensors are installed. The graph (14) shows the evolution in real time of the temperature measured by these sensors if the cor- responding check box (9 and 11) is activated. After each experiment, the graphic is saved in ”.png” format. Two labels (10 and 12) are used to display in real time the temperature measured by the corresponding sensor.

[2]Tow Projects are available to download in https://mega.nz/#F!iZImQDpZ! Nqqr93jNUkiFD4ChzU5gYQ and https://mega.nz/#F!TZQzFbrD!M6qvQPySSWbqKnOXHlCrTw

l APPENDIX E. DEVELOPMENT OF A HOMEMADE SOFTWARE

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N◦ QObject Descreption 1 QLabel label displays information about the camera type 2 QPushButton button to start video recording 3 QPushButton button to stop video recording and save the video in ”.avi”format 4 QPushButton button to close connection and exit the application 5 QLineEdit number editor to modify the time between two successive images 6 QPushButton button to transmit time step to the timer 7 QLabel label displays the number of images that have been added to the current movie 8 QLabel label displays the elapsed time of the experience in ”hh/mm/ss” format 9 QCheckBox when is activated, the port of the first temperature sensor is opened 10 QLabel label displays the temperature measured by the first temperature sensor 11 QCheckBox when is activated, the port of the second temperature sensor is opened 12 QLabel label displays the temperature measured by the second temperature sensor 13 QScrollArea visualizes, in real time, the sample with a frequency of 20 frame/s 14 QwtPlotGrid draws temperature versus time plot

Figure E.4: Graphical user interface of an application for video, temperature acquisition

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