Directional Solidification of Methane Hydrates with Controlled Crystal

Directional Solidiﬁcation of Methane Hydrates with Controlled Crystal Growth Velocities

Rafael Enrique Torres Blanco A thesis submitted to the Universidad de los Andes (Colombia) and the Royal Military College of Canada in partial fulﬁllment of the requirements of the degree of Chemical Engineer

Abstract Directional solidiﬁcation has been used in the past to control crystal growth velocity of low pressure systems such as ice and tetrahydrofuran hydrates. In this work, regulated growth of methane hydrates was achieved using a recently developed, high-pressure, temperature control stage. Experiments were run at a constant pressure of 4 MPa. Four temperature-adjustment strategies were used to achieve unidirectional crystallization and predictable growth velocities. Random formation of large crystals was observed during hydrate formation, which interfered with obtaining predictable growth velocities for some methods. Based on this observation, a temperature-adjustment method that minimizes large crystal formation and achieves unidirectional, controlled interface growth is proposed. Keywords: Methane hydrate, Growth rate, Directional solidiﬁcation

1. Introduction bulk phases. Deposits of gas hydrates have been discovered Natural gas hydrates are non-stoichiometric in oceanic sediment and in permafrost regions, compounds of water and gas with a crystalline where appropriate thermodynamic conditions ex- structure. The gas molecules are located inside a ist for hydrate formation[1]. This regions are es- hydrogen bonded network that forms a cavity in timated to have at least the double of the energy which the gas molecule is trapped. Hydrates can of all fossil fuel reserves available combined [3]. form three diﬀerent crystal structures depending Understanding how hydrates interacts with par- on the guest size: structure I (sI), structure II ticles is important in order to be able to extract (sII) and structure H (sH) [1]. All these struc- the gas stored in natural reservoirs for future en- tures have as a common building block: pentago- 12 ergy demands. Tohidi et al. [4] performed a visual nal dodecahedron (5 ). study at a microscopic scale of hydrate growth Studying gas hydrates is of interest to indus- in a synthetic porous media with tetrahydrofu- try since hydrates can plug oil and gas pipelines. ran (THF), CH4 and CO2. It was observed that Hydrate plugs in pipelines generate considerable hydrate can be formed without the presence of a economical losses and are a safety concern [2]. For free-gas phase and that hydrate nucleates in the this reason, the mechanisms of hydrate growth center of the pores and not on the particles surface and the factors that control it have been studied. [4]. Three important processes during hydrate growth Beltran and Servio [5] examined methane hy- include: the kinetics of crystal growth at the hydrate formation and decomposition in interaction drate surface, mass transfer of the from the bulk with ﬁne grains of silica gel. However, local tem- phases to the growing solid interface, and transfer perature control was not possible with this setup of heat generated by the growing crystals to the and crystal growth velocity could not be controlled.

Preprint submitted to Elsevier May 28, 2016 Previous studies analyzed the growth of THF hydrates with a directional growth apparatus [6]. In this apparatus, a motorized stage moved the sample over two copper blocks. One copper block was maintained at temperature above hydrate equilibrium temperature, while the other was kept below the equilibrium value. The experiments with Tetrahydrofurancould be performed at at- mospheric pressure, whereas CH4 and CO2 have to be performed in pressurized apparatus. The same directional growth apparatus has been used to observe the interaction of THF hydrates growing in presence of silica beads at different formation velocities [7][8][9]. A critical hydrate growth velocity (v c) was identified: below v c beads were pushed by the growing crystal, while Figure 1: Schematic of the setup of the reactor. (A) 316 above the critical velocity the beads were engulfed stainless steel pressure vessel. (B) Sapphire windows. (C) Video camera. (D) Cold light source. (E) Coolant jacket. by the hydrate film. (F) Refrigerated circulator. (G) PID temperature con- The same behaviour of gas hydrates engulfing trollers. [12] and pushing particles was observed [Watanabe et al. [10]] using a different apparatus for directional 2. Experimental growth. Recently, a novel high pressure system, ca- 2.1. Apparatus pable of localized temperature control, has been The experimental apparatus consisted of a pres- developed by DuQuesnay et al. [11]. With this sure vessel made of 316 stainless steel (Figure1) system, constant local temperatures and temper- that contained a stage where a water droplet is ature gradients can be applied to water droplets placed on a sapphire slide. The vessel has sap- in a pressurized atmosphere. phire windows on the top and the bottom. A As described above, there are several studies PCO.edge sCMOS 5.5 camera equipment with a that reports the growth of gas hydrates in the Nikon AF-Micro-Nikkor 60 mm lens was used to presence of particles. In order to study hydrate in- acquire the images. A Schott KL 1500LCD lamp teraction with particles at different growth rates, was used to illuminate through the bottom win- it is necessary to control the hydrate crystalliza- dow. The vessel’s temperature was controlled by tion velocity. circulating a 50 % ethylene glycol aqueous solu- The objective of this work was to achieve reg- tions through copper tubing coiled around the ap- ulated growth of methane hydrate using a recently paratus. Refrigeration was supplied by Thermo developed, high-pressure, temperature control stage. Scientific AC200 chiller. Temperature inside the Four temperature-adjustment strategies were used reactor was measured with a platinum RTD (Omega to achieve unidirectional crystallization and pre- Engineering, QC, Canada). The temperature of dictable growth velocities. High resolution video the coolant was controlled using a Thermo Sci- microscopy was utilized to analyze the crystal mor- entific AC200 refrigerated circulator. The vessel phology and hydrate-growth velocites. temperature was measured with a platinum resistance temperature detector probe (± 0.32 oC). The pressure inside the cell was measured by a Rosemount 3051s transmitter with an accuracy of ± 0.025 % of the span.

2 푇 the vessel was cooled to 275 K using the refrigerated circulator (Figure 3-4 A). The stage was then

푇퐻퐿푉 uniformly cooled to 260 K for ice formation (Fig-

푇퐻 ∆Tsub ure 3-4 B). After this, the pressure was increased (A) 푇퐶 (B) to reach the experimental pressure (4 MPa) (Fig- 푇퐿 ure 3-4 C). Then, the ice was heated to 274 K to 푙gap 푥 form hydrate from ice (Figure 3-4 D). After all the droplet was covered with hydrate the system was heated to 278 K to dissociate the hydrate (Figure 3-4 E). The stage temperature was cooled again to 274 K to obtain the desired hydrate from water with previous hydrate formation history. Finally, a gradient of 4 K was applied on the stage and Figure 2: Simplified representation of the temperature profiles in the High-Pressure Bilateral Temperature Con- temperature was increased until only half of the trol Stage (HP-BTCS). (A) Temperature in the sapphire droplet was covered by hydrate (Figure 3-4 F). slide when a constant temperature T C is applied on the Methane hydrate density is lower that that of slide. (B) Temperature profile in the sapphire slide when water at experimental conditions. Therefore, hy- a gradient (∆T =T H -T L) is applied on the slide. drates crystals can float on the water surface as has been reported [13]. During the initial mo- The temperature on the sapphire slide was ments of the hydrate growth, small crystals move controlled with a bilateral temperature control towards the center of the droplet due to buoy- stage or HP-BTCS (Figure 2). On each side of ancy. This phenomenon impedes unidirectional the stage, a thermoelectric cooler (TEC) is placed film growth. For this reason, it was found that between two copper plates transferring heat from controlled growth velocity was only possible if about the top to the bottom of the stage. The TEC are half of the droplet remained covered with hydrates controlled by two bi-polar PID temperature con- (Figure 4 F) trollers allowing an independent control on each Four different methods were tested in order to side of the stage. Therefore, a constant tempera- control the hydrate growth velocity. The basic ture (Figure 2-A) or a gradient (Figure 2-B) can idea of every method is to increase the supercool- be applied to the sample. The temperature is ing1 in the droplet, and as a consequence, gener- measured by fast response thermistors elements ate the driving force to make the hydrate grow with an accuracy of ± 1oC. from the center of the droplet toward the desired direction. 2.2. Methods A schematic representation of method A is shown Before each experiment, the sapphire slide was in Figure 5. In this method, an increasingly steep cleaned with detergent, distilled water, acetone temperature gradient is applied from the colder and isopropanol. Then, thermal paste was applied side of the stage while the temperature of the in the copper plates of the stage and the sapphire opposite side is maintained constant. The decre- slide was placed on top of it. A 20 µL sample of ments are made at constant time intervals (∆t=10 distilled and deionized water was placed on the s) center of the slide between the two copper plates. In method B (Figure 6). The temperature gra- After that, the vessel was sealed and purged three dient applied to the slide remains constant. Tem- times with N2 and three times with CH4 (99.99 % peratures at both sides of the slide are simulta- mol). Finally the system was pressurized with CH up to 0.25 MPa. 4 1Supercooling is defined as the difference between the In order to facilitate hydrate formation, wa- experimental temperature and the equilibrium tempera- ter droplets were pretreated by forming ice. First ture at the experimental pressure (∆Tsup=Texp-Teq). 3 (A) (B-C) (D) (E) (F)

Figure 4: Images of the pretreatment process and initial methane hydrate formation (A) The vessel is cooled below 280 K. (B) The HP-BTCS is cooled to 260.15 K. until ice forms (C) The Pressure is increased to 4 MPa. (D) The HP-BTCS is heated to 274.15 K when ice melts and hydrate forms. (E) The HP-BTCS is heated past H-LW -V curve dissociating the hydrate. (F)A temperature gradient is applied to the sample. The left half of the water droplet remains below

TH−L−V and solid. The right half of the water droplet is mantained above TH−L−V and in the liquid state.

− W

L Hydrate Water

− 푡 = 푡0 Sapphire (C) I (D) (E) 4 (F) Hydrate Hydrate Water

푡 = 푡푛 Sapphire

MPa / /

V 푇

−

Pressure

L −

I 푇퐻

푇퐻퐿푉 푡0 푇퐿0 0.25

(B) (A) 푡푛 푇퐿푛 260.15 273.15 282.5 푡푓 푇퐿푓 Temperature / K 푥 0 푥퐼0 푥퐼푛 푥퐼푓 푙푔푎푝

Figure 3: Pretreatment and methane hydrate formation superimposed on a partial phase diagram for the wa- Figure 5: Method A, used to control methane hydrate ter+methane system. (A) The vessel is cooled below 280 growth at constant pressure. An increasingly steep of tem- K. (B) The HP-BTCS is cooled to 260.15 K. (C) The Pres- perature is applied from the colder side of the stage while sure is increased to 4 MPa. (D) The HP-BTCS is heated the temperature of the opposite side is maintained con- to 274.15 K when ice melts and hydrate forms. (E) The stant. The decrements are made at constant time inter- HP-BTCS is heated past H-LW -V line dissociating the hy- vals. drate. (F) The HP-BTCS is cooled again below H-LW -V line and then with a gradient of temperature in the slide the hydrate dissociates until only half of the droplet is covered.

4 Hydrate Water Hydrate Water

푡 = 푡0 Sapphire 푡 = 푡0 Sapphire

Hydrate Water Hydrate

푡 = 푡푛 Sapphire 푡 = 푡푓 Sapphire

푇 푇

푇 푇퐻0 퐻0

푇퐻푛

푇퐻푓 푇퐻퐿푉 푇퐻퐿푉

푡0 푡0 ∆T 푇 sub 퐿0 푇퐿 , 푇퐻 푡 0 푓 푛 푡푓 푇퐿 푛 푡 푓 푇 푇 퐿푓 퐿푓 푥 푥 푥 푥 푥 0 퐼0 퐼푛 퐼푓 푙푔푎푝 0 푥퐼0 푥퐼푓 푙푔푎푝

Figure 6: Method B, used to control methane hydrate Figure 7: Method C, used to control the methane hydrate growth at constant pressure. The temperature gradient growth at constant pressure. The temperature gradient applied to the slide remains constant. Temperatures at applied to the slide is forced to invert signs. The temper- both sides of the slide are simultaneously lowered, in con- ature on the left side of the stage remains constant, while stant decrements, and at constat time intervals. the temperature of the opposite side is decreased in a single step change. The temperature across the slide remains neously lowered, in constant decrements, and at below THLV constat time intervals (∆t=10 s). In method C (Figure 7), the temperature gradient applied to the slide is forced to invert signs. Hydrate Water The temperature on the left side of the stage re- 푡 = 푡0 Sapphire mains constant, while the temperature of the op- Hydrate Hydrate posite side is decreased in a single step change. 푡 = 푡푓 Sapphire The temperature across the slide remains below THLV 푇 Finally, in method D (Figure 8), the tempera- 푇퐿 ture proﬁle of the slide is changed from a gradient 0 to a constant temperature. Both sides of the stage 푇 are set to the same temperature in a simultane- 퐻퐿푉 ous step change. The temperature across the slide 푡0 ∆Tsub 푇퐻0 푡푓 remains below THLV . 푇퐿푓, 푇퐻푓

푥 2.3. Experimental Conditions 0 푥퐼0 푥퐼푓 푙푔푎푝 Table 1 shows the conditions of the experiments performed in this work. 5 replicates were made for each method at constant pressure with Figure 8: Method D, used to control the methane hydrate a total amount of 20 experiments. Also, the tem- growth at constant pressure. The temperature proﬁle of the slide is changed from a gradient to a constant temper- perature and the supercooling ranges are shown. ature. Both sides of the stage are set to the same temperature in a simultaneous step change. The temperature across the slide remains below THLV 5 Table 1: Conditions for controlled interfacial growth of methane hydrates. THLV , hydrate-liquid-vapor equilibrium temperature at the experimental pressure (from a best ﬁt regression of literature data compuled by Sloan and Koh [1]. ∆Tsup, supercooling degree for each temperature-adjustment method.

Method Replicates P /MPa THLV /K T range ∆Tsup range /K A 5 3.98 277.5 267.1 to 278.3 1.6 to 2.6 B 5 3.99 277.5 274.1 to 277.5 2.0 to 3.4 C 5 3.98 277.5 273.1 to 277.1 2.0 to 3.1 D 5 4.00 277.4 273.5 to 275.1 2.4 to 4.3 Total 20

3. Results Figure 11 shows the results of method C. (a- b) are the images of experiments under a 2 K 3.1. Hydrate Film Growth gradient applied between the sides of the stage Hydrate film growth results for every method and (c-e) are the images of the experiments under are shown in figures 9 to 12. A polycrystalline a 4 K gradient in the stage. In almost all the layer grew from the partially dissociated hydrate experiments (Figure 11 (a-b),(d-e)) a considerable towards the bottom of the droplet covering the amount of large hexagonals nucleated and grew gas/liquid interface. The hydrate observed on in the hydrate film. With method C only one the upper portion of each droplet on figures 9 experiment yielded growth without large crystals to 12 corresponds to the crystals obtained dur- (Figure 11 c). ing pretreatment. Analysis was limited to the Finally, method D, results are shown in Figure clathrate fronts that grew from this preexisting 12. Large crystals were also observed in the initial hydrate film. Hydrates that grew with a con- steps of growth. Similarly to the other methods, trolled velocity were mostly granular. However, the number, size and location of the large hexag- in most of the experiments, large crystals formed onal crystals was unpredictable. at different locations of the droplet. These larger The presence of large crystals affects signifi- crystals had hexagonal shapes in diverse sizes. cantly the shape of the interface of the hydrate Additionally, in some of the experiments a thin film during growth. In Figure 13 a comparison hydrate film grew outside of the original water between both types of growth is presented. Fig- boundary. ure 13 (left) shows the time-lapse images for an Figure 9 shows the growth replicates for method experiment with method D with large crystals for- A. The final temperature in the cold side, T Lf , in mation. Initially, the film started to grow from which the hydrate covered the droplet surface was the pretreated hydrate, forming a smooth and approximately the same for all the experiments. straight interface. Then, large crystals grew ahead In some of the replicates, the film grew without of the advancing crystal and the solid-liquid inter- the presence of big crystals generating a smooth face became rougher. The hydrate film continued and straight interface during growing (Figure 9a to grow but the interface was not straight any- and 9d). However, in other experiments, large more. The interface remained curved until the crystals appeared on the film (Figure 9b, 9c and hydrate covered the droplet at t=70 s. 9e). Nucleation of large crystals did not follow Figure 13 (right) shows the time-lapse images any trend respect to location or size. for an experiment without large crystal growth Figure 10 shows the results for method B ex- with method B. The interface in this experiment periments. Overall, very few large crystals were grew as a smooth film with a flat interface until observed with this method. When present, large the droplet was completely covered. crystal formed on the periphery on the droplet. 6 (a) (b) (c) (d) (e)(e)

2 mm

Figure 9: Replicates for methane hydrate growth using Method A. Pretreatment hydrate appears at the top, darker section of the droplet. Controlled crystallization started in the middle of the droplet. The white arrow on the left shows the direction of controlled hydrate growth. (a-e) T Lf =267.3 ± 0.6 K, T H =278.3 K ± 0.1 K, p=3.97 ± 0.01 MPa, T HLV = 277.4 K

(a) (b) (c) (d) (e)

2 mm

Figure 10: Replicates for methane hydrate growth using Method B. Pretreatment hydrate appears at the top, darker section of the droplet. Controlled crystallization started in the middle of the droplet. The white arrow on the left shows the direction of controlled hydrate growth. (a-e) T Lf =271.2 ± 0.3 K, T Hf =274.9± 0.5 K, p=3.98 ± 0.02 MPa, T HLV = 277.4 K

(a) (b) (c) (d) (e)

2 mm

Figure 11: Replicates for methane hydrate growth using Method C. Pretreatment hydrate appears at the top, darker section of the droplet. Controlled crystallization started in the middle of the droplet. The white arrow on the left shows the direction of controlled hydrate growth. (a-b) T L=275.0 K, T H =277.1 K, (c-e) T L=273.1 K, T H =277.1 K, p=3.98 ± 0.01 MPa,T HLV = 277.4 K

7 (a) (b) (c) (d) (e)

2 mm

Figure 12: Replicates for methane hydrate growth using Method D. Pretreatment hydrate appears at the top, darker section of the droplet. Controlled crystallization started in the middle of the droplet. The white arrow on the left shows the direction of controlled hydrate growth. (a-c) T L=275.1 K, T H =275.1 K, (d-e) T L=273.5 K, T H =273.5 K, p=3.98 ± 0.02 MPa,T HLV = 277.4 K.

3.2. Apparent Kinetics 120 The hydrate-ﬁlm-growth velocity was calculated using equation 1. 100

xi − xi−1 vfilm = (1) 80

∆ti,i−1 −1 m s µ

Where x and x are the interface positions in / i i−1 60 v the time i and i-1 respectively and ∆ ti,i−1 is the elapsed time between steps. Obtained velocities 40 are shown in Figure 14. The interface temperature for method A, B 20 and C experiments were obtained following DuQu- esnay et al. [11] work. DuQuesnay et al. demon- 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 ∆T / K strated that the temperature profile in the tem- sup perature control stage was linear. Therefore, know- ing the temperature of both sides of the stage and Figure 14: Film velocity vs supercooling for methane hy- the length of the slide, it was possible to obtain drate growth. ∗ Method A results. 4 Method B results. the value of the temperature at any position on + Method C results. Method D results. the stage. Figure 14 shows methane hydrate growth velocities as a function of supercooling. Velocities of previous work as a function of supercooling. increased with increasing supercooling in the sys- The film velocity data is shown as a function tem; however, considerable scatter in the data was of the solubility index developed by Ohmura and obtained for all the methods, except method B. co-wokers [14] : The presence of large crystals was identified as the source of this scatter (see discussion). Therefore, n∆xg (2) images were reanalized without taking into ac- Where n is the hydration ratio, or the ratio count interfacial growth where large crystals were between water molecules and guest molecules in present (Figure 15). In this way, scatter was con- a hydrate unit cell, and ∆x g is defined as the siderably reduced for methods C and D, while difference between the composition of the guest methods A and B remained unchanged (Figure x eq,int in liquid water at the gas-liquid interface 15). Figure 16 shows film shows film growth ve- and the composition of the guest x eq,hyd in water locities from this study together with the results at the hydrate equilibrium temperature. The as- 8 (a) (b) (f) (g)

2 mm 2 mm 푡 = 0 s 푡 = 18 s 푡 = 0 s 푡 = 24 s (c) (d) (h) (i)

푡 = 24 s 푡 = 45 s 푡 = 44 s 푡 = 60 s (e) (j)

푡 = 70 s 푡 = 72 s

Figure 13: Hydrate growth sequences with big crystals (left) and without big crystals appearance (right).(a-e) Method D replicate T =275.1 K, p=3.98 MPa,T HLV = 277.45 K. (f-j) Method B replicate T H =275.0 K, T H =271.1 K, p=3.99 MPa,T HLV = 277.46 K. (a) Hydrate ﬁlm starts to grow from the partially dissociated hydrate forming a smooth interface. (b) First big crystals to appear in the interface. (c)Increasing number of big crystals. (d) Big crystals generate an irregular interface. (e) Hydrate covers the droplet. (f) Hydrate ﬁlm starts to grow from the partially dissociated hydrate forming a smooth interface. (g-i) Hydrate interface grow without big crystals formation. (j) Hydrate covers the droplet.

9 1000

120 100

100

−1 10 m s µ

80 /

v −1

m s µ

60 v 1

20 0 0 5 10 15 20 25 30 35 40 45 4 n∆x / ×10 g 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 ∆T / K sup Figure 17: Film velocity vs the diﬀerence in solubility index (n∆x g) for methane hydrate growth. Film velocity Figure 15: Film velocity vs supercooling for methane hy- was plotted on logarithmic scale for clarity in the low drate growth removing big crystals formation data. ∗ supercooling region. × This work. F Kishimoto and Method A results. 4 Method B results. + Method C Ohmura 2012 [14]. ∇ Freer et al. 2001 [15]. Kita- mura and Mori 2013 [16]. results. Method D results.

sumption made by Englezos et al. [18] was used to calculate the solubility of gas dissolved in the liquid in equilibrium with gas hydrates, deﬁned as: 1000 f(P,T ) x = (3) eq H 100 Where f is the fugacity of the pure gas at the temperature and pressure of the system and H is

−1 Henry’s constant. For x eq,int, the fugacity was

m s 10 µ

calculated at T and P . On the other hand / exp exp

v for x eq,hyd , the fugacity was calculated at T HLV and P exp. The film velocity results versus the 1 difference in solubility index is shown in figure 17.

0 0 2 4 6 8 10 12 4. Discussion ∆T / K sup As shown in Figure 15 each of the four meth- Figure 16: Film velocity vs supercooling for methane hy- ods seemed to be more suitable for a speciﬁc driv- drate growth. Film velocity was plotted on logarithmic ing force. The method A results were in the lower scale for clarity in the low supercooling region. × This range of supercooling from 1.5 to 2.5 K, this means work. Kishimoto and Ohmura 2012 [14]. Freer et al. B that the experimental temperature was very close 2001 [15]. Kitamura and Mori 2013 [16]. ♦ Li et al. 2014 [17] to the equilibrium value. Thus, increase the temperature gradient by changing only the decreasing the temperature of the cold side of the stage only 10 (Figure 15) would be convenient when velocities from 20 µm s−1 to 40 µm s−1 are desired. Film velocities obtained with method A de- 3.5 creased with increasing supercooling, which was

3.0 unexpected and contrary to all the other methods results (Figure 15) and to trends observed in 2.5 the literature [1]. Method A was the only method

2.0 where active cooling was not promoted via the / K /

sub sub thermoelectric module on the liquid side of the

ΔT 1.5 droplet. It is plausible then that hot spots re-

1.0 mained in the liquid ahead of the interface and thus the assumed profiles shown in figure 15 could 0.5 be erroneous. 0.0 On the other hand, in method B and C the 0 20 40 60 80 100 120 film velocity increased with increasing supercool- t / s ing. Both methods can be used to obtain velocities from 20 to 90 µm s−1 while operating from Figure 18: Supercooling in the interface vs time of growth 2.5 to 3.5 K of supercooling. for all the methods. Method A experiment. Method B experiment. 4 Method C experiment. × Method D One of the most relevant advantages of the experiment. previous mentioned methods based on a temperature gradient is the acquisition of several growth rates in a single experiment. In contrast, in the traditional method where a constant temperature is applied during growth, rate measurements are recorded individually for each driving force to obtain a trend. Method D is based on the traditional method 3.0 (hydrate grows under a constant driving force), for this reason only a few points are obtained 2.5 with the same amount of experiments as the other

2.0 methods. An advantage of this method compared to the others is the direct measurement of the ex-

1.5 perimental temperature. Tsub / K / Tsub

Δ Another way to analyze the methods in terms 1.0 of supercooling is shown in ﬁgure 18, where supercooling of the interface is shown as a function 0.5 of time for each method. A diﬀerent trend is ob-

0.0 served in method A, where the supercooling de- 0 20 40 60 80 100 120 creases as the experiment proceeds. t / s Figure 19 shows that this trend is observed in all the replicates for this method. One of the Figure 19: Supercooling in the interface vs time of growth causes for this behavior might be that the re- for method A replicates. • Replicate 1. × Replicate 2. 4 sponse time of the system is greater that the time Replicate 3.− Replicate 4. Replicate 5 ♦ steps defined for the experiments (∆t =10 s). To estimate this characteristic time, the response time of the slide could be estimated by performing a scaling analysis on a steady-state, unidirectional 11 energy balance on the sapphire slide. the detached seed to grow to a larger size without impinging on other grains. k 1 As shown in figure 13, the presence of large ∼ ρCp (4) τ L2 crystals generate an irregular interface in subse- Where τ is the characteristic time of the sys- quent growth. As discussed previously, these large tem, k is the thermal conductivity, ρ is the density crystals generated considerable scatter on film- of the sapphire slide and Cp is the specific heat of growth-rate values. This is easily observed by the sapphire slide, this values were extracted from comparing figure 13 to figure 14.The smaller scat- Green [19]. L is the characteristic length, defined ter observed in figure 14 was obtained by using as the gap length of the stage. only the portions of the advancing hydrate that The obtained value of τ was 7 s, which gives did not contain large crystals. Thus, having least a sense of the order of magnitude of the response amount of large crystals became a criterion to time of the system. Because this value is close to chose the best crystallization velocity control me- the value of the defined time step, it is possible thod. that the hydrate growth occurred under a tran- Size and number of large crystals seemed to sient temperature profile. This means that the occur randomly, independent of the chosen method temperature in the stage is actually higher than or supercooling. Method B was the exception: the the desired one. Hence, the supercooling in the formation of large crystals was minimal and the system is lower. growing hydrate interface was remained straight In method A the droplet is cooled from the cold throughout the entire growth process. side instead of both sides as in the other meth- Several authors have studied hydrate growth ods, where cooling is actively occurring ahead of in order to find the best represantation of the driv- the interface. As a consequence, the temperature ing force for this process [15][22][21][23]. Compar- decreases at a lower rate and driving force is ob- ing figures 16 and 17 it can be observed that film served to decrease with time in method A, but velocity behaves in the same manner with respect not the other methods (Figure 18). to ∆Tsup and n∆xg. Thus, both supercooling and Figure 16 shows the film growth data from this the solubility index are valid representations of work compared to other studies available in the the hydrate growth driving force for the methane literature. The obtained growth rates follow the + water system. A reason for this is strong re- same trend and agree within uncertainty to pre- lation of the solubility of methane as a function vious works[15][14][16][17]. of the temperature of the system. Hence, can be Hydrate morphology was found to be uniform concluded that both factors can be used to predict across methods (Figure 9-12) and similar to the the crystal growth. one described by other authors at similar driving Previously proposed models for hydrate film forces [17][20][21]. growth centered either on mass transfer [14], heat Small grain-like crystals grew in the hydrate transfer [15][24][25] or both transport processes film. According to Li et al. [17] and Sloan[1], this [26], are based on a two-dimensional analysis and phenomenon is due to a high rate formation of a single direction growth. Hence, the obtained crystal nucleation sites due to high supercooling. hydrate formation in this work with a straight in- The emergence of new crystals on the surface of terface, growing in a single direction could be used the growing film hinders continued growth of some for model validation. Furthermore, the methods large crystals at the expense of many small ones. shown here allow for controlled directional crys- Nevertheless, some large crystals appeared at the tallization of methane hydrates which could im- interface. It is possible that this large crystals prove previous efforts to study interaction of hy- formed by the detachment of a crystal seed from drates with particles [5][8]. the solid-liquid interface [17]. This would allow

12 5. Conclusions [3] C. A. Koh, E. D. Sloan, A. K. Sum, and D. T. Wu, “Fundamentals and applications of gas hydrates,” Four methods, based on different temperature Annual review of chemical and biomolecular engineer- management strategies, were used to control growth ing, vol. 2, pp. 237–257, 2011. of methane hydrates on water droplets. Random [4] B. Tohidi, R. Anderson, M. B. Clennell, R. W. Bur- formation of large crystals was observed during gass, and A. B. Biderkab, “Visual observation of gas-hydrate formation and dissociation in synthetic hydrate growth, which interfered with obtaining porous media by means of glass micromodels,” Geol- predictable film velocities for some methods. ogy, vol. 29, no. 9, pp. 867–870, 2001. Based on this observation, a temperature ad- [5] H. Bruusgaard, J. G. Beltrán,and P. Servio, “Vapor- justment method that minimizes large crystal for- liquid water- hydrate equilibrium data for the system N2+ CO2+ H2O,” Journal of Chemical & Engineer- mation and achieves unidirectional, controlled in- ing Data, vol. 53, no. 11, pp. 2594–2597, 2008. terface growth is proposed. This method oper- [6] K. Nagashima, Y. Yamamoto, M. Takahashi, and ates by maintaining a constant temperature gra- T. Komai, “Interferometric observation of mass trans- dient across the sample. Film velocity regulation port processes adjacent to tetrahydrofuran clathrate is achieved by decreasing temperature in simulta- hydrates under nonequilibrium conditions,” Fluid phase equilibria, vol. 214, no. 1, pp. 11–24, 2003. neous steps at both ends of the sample stage. Ve- [7] K. Nagashima, T. Suzuki, M. Nagamoto, and −1 locities from 20 to 40 µm s were obtained when T. Shimizu, “Formation of periodic layered pattern a supercooling varying from 1.5 to 2.5 K was ap- of tetrahydrofuran clathrate hydrates in porous me- plied, and 40 to 90 µm s−1 with a supercooling dia,” The Journal of Physical Chemistry B, vol. 112, from 2.5 to 3.5 K. These growth velocities were in no. 32, pp. 9876–9882, 2008. [8] T. Suzuki, M. Muraoka, and K. Nagashima, “For- agreement with literature values. Finally, it was eign particle behavior at the growth interface of found that both supercooling and the solubility tetrahydrofuran clathrate hydrates,” Journal of Crys- index are valid representations of the driving force tal Growth, vol. 318, no. 1, pp. 131–134, 2011. for methane hydrate film growth. [9] M. Muraoka and K. Nagashima, “Growth pattern de- pendence of tetrahydrofuran hydrates in glass beads of two sizes on growth rate and glass bead mix- 6. Acknowledgments ing ratio,” Crystal Growth & Design, vol. 14, no. 8, pp. 3813–3824, 2014. I am deeply grateful to my advisor Dr. J.G. [10] K. Watanabe, K. Yokokawa, and Y. Muto, “Observa- Beltránfor his valuable support and ideas that tion of frost heave of thf clathrate hydrate on porous helped me in this study. I would like to thank glass powder,” Current Practices in Cold Regions En- the staff of the Chemistry and Chemical Engineer- gineering, pp. 1–10, 2006. [11] J. R. DuQuesnay, J. G. Beltrán, and M. C. ing department of RMC for their support. This D´ıazPosada, “Novel gas hydrate reactor design: 3- project would not have been possible without the in-1 assessment of phase equilibria, morphology and financial support of the Natural Sciences and En- kinetics.,” Fluid Phase Equilibria, vol. 413, p. 148, gineering Research Council of Canada and The 2016. Canadian Foundation for Innovation. Thanks to [12] J. R. 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