investigation of the growth kinetics of tetra‑n ... · hydrate formation occurs within porous...

Investigation of the Growth Kinetics of Tetra‑n‑butylammoniumBromide Hydrate Formation in Small SpacesMeng Shi,†,‡ Xuemei Lang,† Yanhong Wang,† Nicolas von Solms,‡ and Shuanshi Fan*,†

†School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou 510640, China‡Center for Energy Resource Engineering, Department of Chemical and Biochemical Engineering, Technical University of Denmark,2800 Kgs. Lyngby, Denmark

ABSTRACT: The kinetics of tetra-n-butylammonium bromide (TBAB) hydrate formation orientated within the space of asmall dimensional tube is investigated through microscopic experiments in the temperature range of −5.5 to −9.7 °C. Based onthe experimental data, a kinetic model in a small dimensional space is proposed to describe the formation process. Hydratecrystals are observed uniformly growing in the small dimensional space. The experimental results show that the nucleation timeof TBAB hydrate increases from 9 to 25 min and the linear growth rate decreases from 16.36 to 9.66 μm/s with the increasingtemperature. Crystal morphologies show that the tube wall has less effect on the inner crystal growth when the temperature islower. Furthermore, the number of nucleation sites increases under even lower temperatures. The varying degree of brightnessof the crystals indicates that there is a variation of facets of hydrate crystals formed at different temperatures. Hydrate crystalsunder lower temperatures exhibit more growth points, and the linear growth rate of crystals in a tube is larger than that in thebulk because of heat-transfer effects. A negative activation energy during hydrate formation in this study is obtained accordingto the kinetic equation to be −58.27 kJ/mol.

1. INTRODUCTION

Clathrate hydrate crystals consist of cages composed of watermolecules, stabilized by other, small, molecules trapped insidethe cages as guest molecules.1−4 If a guest molecule is too largeto fit in a cage, semiclathrates may be formed by connectingionic guests and water molecules as hosts and with the cationembedded into the cages as a guest. Tetra-n-butylammoniumbromide (TBAB) is an example of a semiclathrate hydrateformer, where guest gas molecules are not required to form ahydrate structure, as is the case for normal clathrate hydrates.5

The formation conditions of TBAB hydrate are mild, and theycan form at atmospheric pressure.6

In recent years, TBAB hydrate has shown many advantagesfor various applications, such as gas storage/separationtechnologies, refrigeration technologies, etc.7−11 Recently,TBAB semiclathrate hydrate slurry has been proposed as apromising cold energy-storage medium in air-conditioningsystems for high cold storage capacity compared to othermedia such as water or ice slurry.12−14 TBAB hydrate usuallycannot be generated at equilibrium conditions; therefore,research on TBAB hydrate at different degrees of subcooling isnecessary for practical applications. Also, TBAB can act as anadditive to considerably reduce the equilibrium pressure of gashydrates commonly utilized in promoting the formation of gashydrates and in separating gas mixtures.15−19 The study of Leeet al.20 showed that the presence of TBAB at weightpercentages of 0.05−0.6 caused the H−Lw−V equilibriumline of the N2 + TBAB semiclathrates to be greatly shifted tohigher-temperature and lower-pressure regions when com-pared to that of pure N2 hydrates. They concluded that thehighest stabilization effect was at a mass fraction of 0.4. Toremove hydrogen sulfide from biogas, Kamata et al.15

confirmed that more than 90% of the H2S in the initial

vapor phase was separated from biogas by incorporating the 10wt % TBAB solution and found that TBAB hydrate was aneffective and economical desulfurization medium. Theseapplications are the direct result of the formation of TBABhydrate. Thus, nucleation and growth characteristics of TBABsemiclathrate hydrate are of vital importance in studiesinvolving TBAB. The morphology of TBAB hydrate is alsoworth studying. The investigations on TBAB hydrate growthbehavior are still limited, although some progress has beenmade during the last few years.21−23

Over the years, studies of TBAB hydrate kinetics have beenmainly concerned with bulk systems, e.g., stainless vessels andglass tubes.24−32 There is little literature focused on hydrategrowth in small dimensional spaces. However, in many cases,hydrate formation occurs within porous media, pores inpacking materials, microchannels of heat transfer, valves for gaspipelines, or gaps in transfer equipment, in which the space forhydrate growth is limited. The mechanism of hydrate growthin small dimensional spaces is unclear, making this a naturaland important aspect to investigate. There are difficultiesinvolved in investigating hydrate growth properties duringhydrate formation in pore-sized spaces, compared within thebulk, due to the limitation of the nontransparency of porewalls, especially hydration processes that occur on the surfaceof the pore wall. Because of these issues, a visual and directstudy of hydrate growth behavior in pore-sized spaces is verychallenging.In this study, a self-made transparent perfluoroalkoxy

ethylene (PFA) tube is employed to investigate overall growth

Received: November 20, 2018Revised: February 27, 2019Published: February 28, 2019

Article

pubs.acs.org/EFCite This: Energy Fuels XXXX, XXX, XXX−XXX

© XXXX American Chemical Society A DOI: 10.1021/acs.energyfuels.8b04042Energy Fuels XXXX, XXX, XXX−XXX

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processes and kinetics of TBAB hydrate, where a 40 wt %TBAB solution is injected, which fits mostly the TBAB-relatedapplication systems. The corresponding phase equilibriumtemperature for 40 wt % TBAB solution is 12 °C. Amicroscopic hydration system is introduced to gain insightsinto the growth process and growth kinetics of TBAB hydrateformation in confined pore-sized spaces. A growth model isproposed for the mechanism of the growth process. Based onthe growth kinetics and the Arrhenius equation, activationenergy is calculated here for the formation process. Also,formation properties of TBAB semiclathrate hydrates, namely,formation morphology and nucleation time, are obtained.

2. MATERIALS AND METHODS2.1. Materials. TBAB (99% pure) from Kermel Chemical Reagent

Co., Ltd was dissolved in distilled water so that the mass fraction inTBAB·nH2O corresponded to a hydration number n = 26.33,34

Anhydrous ethanol was provided by Nanjing Chemical Reagent Co.,Ltd to function as a cooling medium.2.2. Nucleation Time Measurement. The common method to

obtain nucleation time is to monitor the variation of temperature andpressure in the system. In the case where an extremely small amountof hydrates is formed, the hydration heat produced is too small tocause a change on the transducer and no temperature change can beobserved. Another method of determining nucleation time is by visualinspection. A typical temperature profile in the low-temperature cell isshown in Figure 1. The photograph in Figure 1 shows the initial

formation of TBAB hydrate. It can be seen that the temperature of thecell decreased from ambient temperature of around 29 °C to the setpoint of −5.5 °C within a time of tc (about 35 min). Thecorresponding phase equilibrium temperature of 40 wt % TBABsolution is 12 °C.13 At the time of td (60 min), a TBAB crystal wasfirst observed by the microscope. The nucleation ti is defined as thetime interval between td and tc,i.e.,

t t ti d c= − (1)

2.3. Kinetic Measurement and Apparatus. Figure 2 shows aschematic diagram of the microscopic imaging and data logger systememployed in the study, mainly consisting of an inverted lightmicroscope (Carl Zeiss Axio Observer A1), a programmed thermo-static bath (Huber Minisbat 240Cl), a low-temperature cell, and animaging and data logger.A piece of transparent PFA tube with an inner diameter of 580 μm

is placed into a low-temperature cell (Φ50 × 30 mm2, made ofstainless steel). TBAB solution is injected inside the transparent PFA

tube with a length of around 17 mm (Figure 3). The inverted lightmicroscope is employed to observe the growth process and measure

the kinetics combined with an imaging unit (Imaging Micro Publisher5.0RTV). The low-temperature cell is placed under the microscopeand filled with anhydrous ethanol to ensure a stable temperatureenvironment for the hydrate to form in the tube. The temperature ofthe cell is recorded by a thermocouple and a corresponding datalogger. A schematic representation of the formation process andkinetic measurements of TBAB hydrate used in this study is shown inFigure 4.

The space for crystal growth is confined, and only a cross section ofthe hydrate is observed by the microscope. When the crystal isoriginally formed, it grows in all three dimensions. When the crystalmeets the tube wall or another crystal, the growth in that directionstops. Hence, a linear growth rate is represented by the crystal surfacemoving in the direction from the crystal core to the farthest point ofthe solution in the microscopic view, which is vertical to the face ofthe crystal measured. Figure 5 shows a typical crystal growth process.Pc is the core of the crystal, and Pf is the farthest point in the solutionrelative to Pc. At time ti, the distance between Pc and the crystalsurface Si in the direction of Pc−Pf is li. Hence, the linear growth ratecan be calculated by

lt

l lt t

dd

i i

i i

1

1=

−−

+

+ (2)

2.4. Experimental Section. The 40 wt % TBAB solution (about0.3 μL) is injected into the 580 μm diameter tube via a microinjector.The injected liquid is placed under the microscope field of view. Bothends of the 580 μm diameter tube are sealed. The tube of TBABsolution is then placed into the low-temperature cell, and the

Figure 1. Typical temperature profile of the low-temperature cell andthe initial formation of 40 wt % TBAB hydrate (T = −5.5 °C).

Figure 2. Schematic diagram of the microscopic imaging and datalogger system.

Figure 3. PFA tube sealed with TBAB solution.

Figure 4. Experimental setup for TBAB hydrate formationobservation, with a zoomed-in view of the PFA tube (×50).

Energy & Fuels Article

DOI: 10.1021/acs.energyfuels.8b04042Energy Fuels XXXX, XXX, XXX−XXX

B


microscope aperture is adjusted to give an appropriate brightness inthe view. The low-temperature cell is maintained at 29 °C for 1 h toeliminate the so-called “memory effect”35−37 of TBAB hydrate andthen the temperature is decreased to the desired value and maintaineduntil the observation ends. The video camera is started, and thehydrate formation processes until the hydrate growth ends arerecorded. The data of temperature and time are acquired by a datalogger. Afterward, a Raman spectroscopy device is employed toidentify and analyze the TBAB hydrates in the tube.2.5. Raman Spectroscopy Measurement. To confirm that the

crystal in the transparent tube is TBAB hydrate, Raman spectroscopy(Renishaw inVia-Reflex) is used. During the measurement, while thetube sealed with 40 wt % TBAB solution is placed into the coolingcell, its temperature is set to the experimental temperature. Thetemperature is set to decrease at a rate of about 10 °C/min. AfterTBAB hydrate is observed in the tube through the microscope, theRaman spectroscopy test is started. The light is provided by a 532 nmDPSS laser with 50 mW power, and the scan is performed from 2800to 3700 cm−1 for 10 s with a band resolution of 0.5 cm−1.

3. RESULTS AND DISCUSSION3.1. Raman Spectroscopy. Since the TBAB crystal is

formed in water at temperatures below 0 °C, it is necessary toconfirm that the solid formed in the tube is TBAB hydraterather than simply ice. Raman spectroscopy is an effectivemethod to provide information on the structure, occupancy,and composition of hydrates and on molecule dynamics.Figure 6 shows the Raman spectra of 40 wt % TBAB solutionat 26 °C and TBAB hydrate at −5.5 °C in the range 2800−3700 cm−1. It can be seen that the peak bands between 2850and 3050 cm−1 are typical for TBAB.38 For the TBAB aqueous

solution, the widths of the TBAB characteristic peaks arerelatively large and overlap with each other, but for the hydratesample, the signal peaks are sharp and isolated.39 The rangeshows the symmetric and asymmetric stretching vibrations of−CH3 and −CH2− in TBAB.40,41 The broad peak from 3100to 3500 cm−1 corresponds to the O−H vibration of waterlocated next to the TBAB peak. Hashimoto et al.42 reportedthat the characteristic peaks of TBAB constitute strongevidence for this study. Formation of TBAB hydrate is thusconfirmed for T = −5.5 °C, as well as for other temperatures,whose Raman spectra are not presented here.

3.2. Nucleation Time. The nucleation time is exper-imentally accessible and contains valuable information aboutthe dynamics of new phase nucleation and/or growth.43

Nucleation times for the TBAB solution are measured by themethod described by eq 1 for T = −9.7, −8.8, −7.8, −6.5, and−5.5 °C at atmospheric pressure. Corresponding subcoolingdegrees are 21.7, 20.8, 19.8, 18.5, and 17.5 °C. The results areshown in Figure 7. It can be seen that nucleation time rapidlyincreases from 9 to 25 min with the temperature increasingfrom −9.7 to −5.5 °C.

The data presented indicate that the nucleation time isstrongly dependent on the experimental temperature. Thedifference between the experimental temperature and theequilibrium hydrate formation temperature provides thedriving force for hydrate formation. Under the same systemconditions, experiments with a high driving force show that thenucleation time varies exponentially with the size of the drivingforce.44

3.3. Growth Morphologies. TBAB hydrate generated by40 wt % TBAB solution is shown in Figures 8−12,corresponding to the temperatures of −5.5, −6.5, −7.8,−8.8, and −9.7 °C. The results of the camera observationsare presented below in the order of the increasing experimentaltemperature.Figure 8 shows a sequence of TBAB hydrate formation and

crystal growth in a single position at −5.5 °C (a subcooling of17.5 °C). Once the crystal phase is observed, meaning that theinduction period is completed. TBAB crystals are observedgrowing gradually from the one end of the PFA tube to theother. Hydrate crystals grow in the shape of cylinders with awidth of 240 μm. The contour and brightness from the imagesconfirm that the crystals in the tube center lead the growthwith the crystals near the tube wall growing behind the leadcrystals. Surface veins on the crystals grow alternatively,

Figure 5. Schematic for the measurement of the variation of TBABhydrate linear growth rate.

Figure 6. Raman spectra of (a) TBAB solution and (b) TBAB hydrategenerated by 40 wt % TBAB solution in the range of 2800−3700cm−1.

Figure 7. Nucleation time of TBAB hydrate at different experimentaltemperatures.



C


interactively, and unorderly, which lead to a reduction ofbrightness of hydrates.Figure 9 presents the TBAB hydrate formation and growth

at −6.5 °C. At 0 s, the crystal in the columnar is formed first in

the boundary of view and near the wall of the tube. It appearswith a width of 570 μm after 28.5 s as seen from the red cycle.After 19.1 s, another crystal at 138 μm is formed at a secondsite. Veins on the crystals are more regular and interlacedcompared to those under −5.5 °C, which makes thetransmittance of crystals formed at −6.5 °C greater than forthose formed at −5.5 °C.

Figure 10 shows the growth of TBAB hydrate, where theimages are obtained at −7.8 °C. The brightness at this

temperature is clearly higher than for the higher temperatures.Fewer and more uniform veins appear at the root of the crystal.The first crystal comes into view at 0 s. After 5.2 s, a convexsurface moves from the center to the wall in the tube andfinally flattens out at 15 s. It is concluded that the hydrategrowth surface becomes flat with the increasing subcooling(increased driving force). Finally, an even lower experimentaltemperature is used to confirm this conclusion. Experimentaltemperature has an effect on increasing nucleation sites.Crystals generated from more nucleation sites grow uniformlyalong the tube wall.As the temperature decreases, the leading crystals became

more obscure. Figure 11 shows that all TBAB crystals growconsistently and the front edge is nearly a smooth surface. Inaddition, veins on the bulk hydrate disappear at this condition.These morphologies give us information that the tube wall hasless effect on the inner crystal growth when the temperature islower. Furthermore, the number of nucleation sites increases asthe temperature is lowered. The hydrate crystals at eachnucleation site grow at similar rates, presenting a smooth,nearly planar front edge.As shown in Figure 12, for the experiment carried out at a

temperature of −9.7 °C (the lowest temperature), TBABhydrate is initially formed inside the solution at time t = 0 s.The crystals radiate out from the initial crystal. At the sametime, another crystal may be seen nucleating at the edge of theview, since at time t = 7.0 s, crystals show up at a second siteand their boundaries meet. Both crystals continue growingsubsequently. At 15.8 s, crystals from the second site meet thetube wall. Growth continues along the tube together with thecrystals from the first site. At 27.9 s, the surface of the firstcrystal reaches the tube wall and the view boundary. Asubcooling of 20.8 °C (the lowest temperature) led to themost crystal growth points in this study. Since the number of

Figure 8. TBAB hydrate formation and growth in the PFA tube at−5.5 °C.

Figure 9. TBAB hydrate formation and growth in the PFA tube at−6.5 °C.

Figure 10. Growth process of TBAB hydrate in the PFA tube at −7.8°C.



D


crystal growth points is increasing, the crystals at thistemperature present the smoothest surface.It is interesting to note that with the reduction of

temperature, the brightness of TBAB hydrate increases. Asthe light source intensity is maintained constant in allexperiments, the different brightnesses of the photographstaken from the microscopic view may indicate that the crystalsformed under different temperatures have different structures,with different light transmittances. Shimada et al.44 observedthat the TBAB hydrates were columnar and had differentmorphologies at different temperatures. The facets thatcompose the column changed with temperatures. Some sidefacets of the column vanished at lower temperatures. In this

study, the brightness of the crystals detected from the imagingsystem indicates that the crystals also have various facets. Forthese experiments, some crystals appear dark (Figures 8 and 9)and other crystals appears light (Figures 10 and 12). Thisindicates that there are more facets on the column for thehigher temperature range (−5.5 to −6.5 °C) than for the lowertemperature range −7.8 to −9.7 °C. The connection betweenthe crystal brightness in the images and the single crystalstructure is worthy of further study. Based on heat-transferconsiderations in this study, we concluded that hydrate crystalgrows with a convex front edge to enlarge the contact area withTBAB solution, which is beneficial for heat transfer at lowsubcooling (ΔT < 18.5 °C). At higher subcoolings (18.5 °C <ΔT < 21.7 °C), where heat transfer is not an issue, hydratecrystals grow with a flat front surface.To compare with TBAB hydrate growth in a tube, we also

conducted a hydrate growth experiment in bulk, using a cooledreactor made of stainless steel with a silica glass base at atemperature of −8.8 °C. The images of hydrate morphologiesobtained focus on a spot of TBAB solution in the cooledreactor (Figure 13a). Figure 13c shows typical morphologies ofTBAB hydrate free-growth formation in TBAB solution fromthe study of Shimada et al.44

3.4. Growth Kinetics and Model of TBAB HydrateFormation. The growth kinetics of TBAB hydrate isinfluenced by the heat-transfer, mass-transfer, and intrinsichydrate formation kinetics. In Section 3.3, we concluded thatmorphology is mainly controlled by heat transfer when TBABhydrate grows in a large-scale environment. In the conditionsof our experimental setup, heat-transfer effects are eliminatedwhen the small dimensional tube is placed in a bulk coolingsystem. During the hydrate formation process, TBAB hydrateis formed on the surface of a crystal. A formation kineticsmodel describing the interface between TBAB hydrate andTBAB solution is thus proposed as follows. Considering theeffect of heat-transfer, mass-transfer, and intrinsic hydrateformation kinetics, an expression for the growth rate of TBABhydrate under experimental temperature can be formulated

nt

K T Tdd

( )sceq exp= −

(3)

where nt

dd

sc is the molar growth rate of TBAB semiclathrate in

mol/s. The temperature of TBAB hydrate facially on thehydrate solution is the equilibrium temperature of TBABhydrate, Teq. Both Teq and constant experimental temperatureTexp are in K. K is the growth rate constant in mol/(s K). Sincethe overall growth resistance is influenced by the three transferprocesses, an expression can be written as follows



Figure 13. (a) Morphology of TBAB hydrate on a flat surface in thisstudy, (b) growth in a microtube, and (c) free-growth forms in bulksolution from literature.44



E


K h k k1 1 1 1

aψ= + +

(4)

where h is the heat-transfer rate constant during hydrateformation, W/s; k is the mass-transfer rate constant, L/s; andka is the reaction rate constant in mol/s. Figure 14 illustrates

this model. Figure 14a depicts TBAB hydrate growth in a tube,and Figure 14b is an enlarged picture of the interface betweenTBAB hydrate and TBAB solution. At the constantexperimental temperature Texp, semiclathrate hydrate growsforward at the surface temperature Teq. The temperature ofTBAB solution is considered to be the same as that of the tubewall and ethanol cooling bath and is fixed at Texp. Lateraltemperatures at the interface between the hydrate phase(solid) and the residual solution phase (liquid) are Teq and TL,respectively.The kinetic model is based on the following assumptions:

(1) the density of TBAB hydrate is constant with time; (2) thegrowth volume of hydrate in the PFA tube is equivalent to thatof a cylinder; (3) in the small space, all crystals are consideredto have the same, constant growth rate. The TBAB hydrategrowth rate can thus be expressed as

nt

R

MLt

D

Mlt

dd

dd 4

dd

sc SC e2

SC

SC e2

SC

ρ π ρ π= · = ·

(5)

where ρsc is the density of TBAB hydrate, kg/m3; Msc is themolecular molar mass of TBAB hydrate, g/mol; De can beapproximated by the diameter of cylindrical TBAB hydrategrowth in the PFA tube, m; and l

tdd

is the face growth rate of

TBAB hydrate, m/s. The TBAB hydrate growth rate can thenbe expressed as

lt

K T TM

Ddd

( )4

( )eq expSC

SC e2ρ π

= − ·(6)

For the sake of simplicity, it is assumed that thethermophysical properties of TBAB hydrate [hsc, ksc, 0 < l <li(t)] and TBAB solution [hL, kL, li(t) < l < l1] are constants.For a cylindrical geometry, we have

T

l h

T

tl l t

1(0 ( )) (TBAB hydrate)i

2eq2

sc

eq∂

∂= ·

∂∂

< <(7)

Tl h

Tt

l t l l1

( ( ) ) (TBAB solution)i

2L

2L

L1

∂∂

= ·∂∂

< <(8)

where hsc and hL are the thermal diffusion coefficients of TBABhydrate and TBAB solution, respectively, in eqs 7 and 8 andli(t) is the position of the interface with time. The overallenergy equation at the interface is given by

lt

hTl

l t hTl

l tdd

( , ) ( , )i isc scsc

LLρ λ =

∂∂

+∂∂ (9)

where ρsc and λ are the density and heat of TBAB hydrateformation, respectively. Finally, the control functions can bewritten in a dimensionless form

LSt

tL L(0 ( ))i

2sc2

scθ θτ

∂∂

=∂∂

< <(10)

LSt

ht

L L( ( ) 1)i

2L

2sc

L

Lθα

θτ

∂∂

=∂∂

< <(11)

where St is the Stefan number. Dimensionless variables andparameters are defined by

T T

T TT TT T

, i

isc

sc exp

eq oL

L

eqθ θ=

−−

=−− (12)

Lll

St hl

t StC T T

, ,( )

1

s

12

P eq expsτλ

= =·

=−

(13)

where CPsis the specific heat capacity of TBAB hydrate.

Finally, the energy conversion equation is simplified to

LL

HLL

L( , ) ( , ) dd

i i is Lθ τ θ ττ

∂∂

+∂

∂=

(14)

Hh T T

h T T

( )

( )iL eq

sc eq o=

−− (15)

Considering the following equation representing solid TBABand liquid water to TBAB hydrate as structure A

x xTBAB H O TBAB H O2 2+ = · (16)

After TBAB hydrate formation has taken place, theconcentration of residual TBAB solution can be obtainedbased on mass conservation where the initial amounts ofTBAB and water are nTBAB,0 and nH2O,0, respectively.

cn n

n xn1000

18TBABTBAB,0 sc

H O,0 sc2

=−

−·

(17)

Figure 15 shows the concentration distribution of TBAB at theinterface of the TBAB hydrate−TBAB solution. The growthproceeds under a driving force of concentration gradientsbetween the content of TBAB in solution and in hydrate (Δc)at a given T. In the small space, all crystals are considered tohave the same growth rates. With these assumptions, theintrinsic kinetics of TBAB hydrate formation can be written as

nt

k c cdd

( )scTBAB 0= −

(18)

where cTBAB and c0 are the concentrations of TBAB at theTBAB solution−hydrate interface and hydrate−TBAB solutioninterface, respectively, in mol/L.

Figure 14. Conceptual diagram of TBAB hydrate formation based ontemperature. (a) Growth process of TBAB hydrate in the PFA tubeand (b) interface between TBAB hydrate and TBAB solution.



F


For reaction kinetics of TBAB hydrate, growth rate equationcan be expressed as

nt

k a add

m nsca TBAB H O2

= · ·(19)

where aTBAB and aH2O are the activities of TBAB and H2O insolution, respectively. m and n represent the reaction orders ofTBAB and H2O, respectively. In the condition of ourexperimental setup, the heat-transfer effect is eliminatedwhen the small dimensional tube is placed in a bulk coolingsystem since the heat-transfer coefficient approaches infinity h→ ∞. As hydrate formation proceeds, TBAB hydratecontinues to form on the surface of the crystal. Variations ofK under different temperatures can be obtained fromexperimental data according to eq 5. Crystal growth lengthsincrease linearly with time and are summarized in Figure 16.The fitted lines are presented with different colors for eachtemperature. The results show that the growth increases for thedecreasing temperature.The linear growth rates of TBAB hydrate under correspond-

ing experimental conditions and subcooling/driving force arelisted in Table 1.

Figure 17 shows an Arrhenius plot for the growth rateconstant K

K K e E RT0

( / )a exp= · −(20)

where Ea is the activation energy of TBAB hydrate in J/moland K0 is the pre-exponential factor. R is the universal gasconstant. T is the absolute temperature (K). From eq 20, theobtained activation energy is −58.27 kJ/mol determined by thesolid line in Figure 17, indicating a negative correlation withtemperature.Negative activation energies for TBAB hydrate have not

been reported before, although Shimada et al.44 observed thatTBAB hydrate growth rate has a negative correlation withtemperature that is not characterized by its activation energy.Chen et al.45 also found that faster rates of methane hydratewere obtained with lower initial temperatures. Nguyen et al.46

investigated the effects of temperature on the formationkinetics of difluoromethane hydrate from CF2H2 gas and founda positive activation energy of 7.2 kJ/mol. A negative activationenergy occurs when the stability of a state is higher than that ofthe reactants. A possible explanation is proposed that thereexists a state that is metastable compared to the products at alower energy than the initial status. It is assumed that a largenumber of empty cages for semiclathrate hydrate appear duringthe metastable state, which is more stable than randomlydistributed TBA+, Br−, and water molecules. This idea isdepicted in Figure 18.Figure 19 shows the growth length of TBAB hydrate as a

function of time at the same temperature of −8.8 °C in a tubeand in a bulk system of a cooling reactor. As can be seen fromthe regression analysis of the series, shown as solid lines,hydrate crystals in the cooling reactor grow linearly at a rate of10.49 μm/s within the observation view. Hydrate grows in thetube with a constant linear rate of 15.67 μm/s, which is fasterthan in the cooling reactor at the same temperature. The linear

Figure 15. Conceptual model of TBAB hydrate formation based onconcentration. (a) Growth process of TBAB hydrate in the PFA tubeand (b) magnification of the interface of TBAB hydrate and TBABsolution.

Figure 16. Growth lengths of TBAB hydrate with lapsed time atexperimental temperatures ( l

tdd

is the slope of the line and represents

the linear growth rate of the hydrate).

Table 1. Linear Growth Rates of TBAB Hydrate in SmallSpaces with Variation of Conditions

experimental temperature Texp(°C)

subcooling ΔT(°C)

linear growth rate lt

dd

(μm/s)

−5.5 17.5 9.66−6.5 19.5 10.37−7.8 19.8 13.48−8.8 20.8 15.67−9.7 21.7 16.36

Figure 17. Correlation of ln K with 1/Texp. The solid line is a linearfit.



G


growth rate of hydrate crystals in the cooling reactor is nearlycoincident with that of crystals in the tube at a highertemperature. Compared with crystal growth in the bulk system,crystals grow faster in a small dimensional tube. These resultsare in accordance with those of Li et al.47 In the bulk system,heat produced by partial hydrate formation contributes to atemperature increase, delaying hydrate formation, whereas thiseffect is eliminated in the current small dimensional formationcrystallizer. Heat generated in the tube is transferred to thecooling environment immediately upon hydrate formation.The small dimensional tube is thus a more convenient methodfor the investigation of hydrate kinetics.

4. CONCLUSIONSIn this work, a small dimensional tube is utilized to investigatethe growth kinetics of TBAB hydrate. A growth kinetic modelis constructed based on the experimental data.At the experimental conditions studied, nucleation time

increases from 9 to 25 min with an increase in temperaturesfrom −9.75 to −5.5 °C. Crystal linear growth rate decreasesfrom 16.36 μm/s at a temperature of −9.7 °C to 9.05 μm/s ata temperature of −5.5 °C. Morphologies of the hydrate underdifferent temperatures changed in the tube. Crystal morphol-ogies give us information that the hydrate grows in a shapebeneficial for heat transfer when the temperature is lower. Inaddition, the number of nucleation sites increased at a lowertemperature. The transmittance of TBAB hydrate crystalincreases with the reduction of temperature. This indicates that

some side facets, which compose the column, vanish at a lowertemperature.In this study, the experimental tubes of small dimensional

spaces immersed in a bulk cooling system eliminate the effectof heat transfer, which otherwise makes the investigation ofhydrate growth kinetics difficult. Growth kinetics equationsand mathematical models are introduced to describe theformation of TBAB hydrate. It is found that the crystallizationrate constant of TBAB hydrate formation increases withtemperature and that it follows an Arrhenius relationship.Activation energy is calculated to be −58.26 kJ/mol. Thekinetic models developed in this work may provide assistancein revealing hydrate formation mechanisms.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected]. Tel: + 86-20-22236581.ORCIDMeng Shi: 0000-0002-1298-2852Yanhong Wang: 0000-0002-0059-8159Shuanshi Fan: 0000-0002-2227-7620NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was supported by the National Key Research andDevelopment Programme of China (2016YFC0304006,2017YFC0307303-2 and 2017YFC0307302-2), and the Na-tional Natural Science Foundation of China (21736005 and2176005).

■ SYMBOLSaTBAB = activity of TBAB in solutionaH2O = activity of water in solutioncTBAB = concentrations of TBAB at the TBAB solution−hydrate interface, mol/Lc0 = concentrations of TBAB at the TBAB hydrate−solutioninterface, mol/LCPs

= specific heat capacity of TBAB hydratelt

dd

= face growth rate of TBAB hydrate crystals, m/snd

dtsc = molar growth rate of TBAB hydrate crystals, mol/s

De = diameter of cylindrical TBAB hydrate growth in a PFAtube, mEa = activation energy of TBAB hydrate, J/molh = heat-transfer rate constant, L/shsc = thermal diffusion coefficient of TBAB hydratehL = thermal diffusion coefficient of TBAB solutionK = growth rate constant, mol/(s K)ka = reaction rate constant, mol/sK0 = pre-exponential factor, mol/(s K)Li = at time ti, the distance between Pc and Pf, as shown inFigure 5, μmMsc = molecular molar weight of TBAB·26H2O, g/molm and n = reaction orders of TBAB and H2O, respectivelynTBAB,0 = initial amount of TBAB in solution, molnH2O,0 = initial amount of water in solution, molPc = hydrate growth core as shown in Figure 5Pf = farthest point in the solution relative to Pc, as shown inFigure 5P = pressure, PaR = universal gas constant, 8.314 J/(mol K)

Figure 18. Concept of an energy barrier of a TBAB hydrate growthprocess in a tube.

Figure 19. Growth lengths of TBAB hydrate as a function of time inthe PFA tube (▼), in a cooling reactor (◆) at −8.8 °C, and (●) in atube at −6.5 °C.



H

mailto:[email protected]

http://orcid.org/0000-0002-1298-2852

http://orcid.org/0000-0002-0059-8159

http://orcid.org/0000-0002-2227-7620


Si = hydrate crystal surface, as shown in Figure 5St = Stefan numbertc = period of cooling stage, mintd = time from the start of the cooling to the appearance ofhydrate, minti = nucleation time, minT = temperature, °CΔT = subcooling, °CTL = temperature of solution phase, KTeq = equilibrium temperature of TBAB hydrate, K

Greek Lettersρsc = density of TBAB hydrate, kg/m3

λ = heat of TBAB hydrate formation, kJ/kg

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