Kinetics of Hydrate Formation in the CO2+TBAB+H2O System at

In addition, the amounts of TBAB and water are accurately weighted with an electronic balance with an uncertainty of 0.01 g (Zhejiang Yuyao Jingming W...
0 downloads 0 Views 2MB Size
Download PDF
Article pubs.acs.org/IECR

Kinetics of Hydrate Formation in the CO2+TBAB+H2O System at Low Mass Fractions N. Ye,† P. Zhang,*,† and Q. S. Liu‡ †

Institute of Refrigeration and Cryogenics, MOE Key Laboratory for Power Machinery and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China ‡ Department of Marine Engineering, Kobe University, Kobe 658-0022, Japan ABSTRACT: In the present study, CO2 gas and tetra-n-butyl ammonium bromide (TBAB) is adopted to form CO2+TBAB double hydrate at mass fractions w = 0.05 and 0.10. The moles of CO2+TBAB double hydrate are calculated by the variation of pressure of CO2 gas from initial pressure at about 4.03 MPa and the solubility of CO2 in TBAB aqueous solution at various subcoolings of 2.0−5.0 K. In addition, the formation characteristics of CO2+TBAB double hydrate are observed by the visualization, and it is verified to be a type B double hydrate. The kinetics of CO2+TBAB double hydrate formation at w = 0.05 and 0.10 is determined by the normalized rate of hydrate formation in the hydration process.

1. INTRODUCTION With the help of van der Waals forces, the hydrogen bonds between water molecules hold them together and encage the gas molecules to form solid gas hydrate or clathrate hydrate under the appropriate condition. Gas hydrate shows cagelike inner structure and snowlike appearance.1 The hydration of gas hydrate is a phase-transition process similar to water changing from liquid to ice. By engaging gas molecules such as N2, CO2, and so forth into dodecahedral cages, gas hydrate can stabilize at the appropriate pressure and temperature. There are mainly three different structures of gas hydrate: structures I, II, and H.2 In recent years, gas hydrate is considered as not only a new energy source, for example, natural gas hydrate, but also a novel technique for gas separation and storage. Especially in modern society, the increasing emission of CO2 as the greenhouse gas due to the burning of fossil fuels has caused a serious greenhouse effect. So, CO2 hydrate is deemed as a potential measure to alleviate this problem.3,4 At present, about 15% of the power consumption in industrialized countries is consumed in cold production,5 which implies that the improvement of refrigerating efficiency is important. One solution is to use two-phase secondary refrigerant instead of single-phase secondary refrigerant because the former has larger heat storage capacity during phase transitions between solid and liquid states, which can decrease the pumping power consumption for the reduced flow rate. Simultaneously, the loading amount of primary refrigerant is reduced as well with the help of secondary refrigerant in a secondary loop refrigeration system for cold carrying, which results in the reduced leakage risk of the conventional primary refrigerants, such as chlorofluorocarbones (CFCs) and hydrofluorocarbones (HCFCs). CO2 hydrate is well suited for the secondary refrigerant because it can form at above 273.15 K and its dissociation enthalpy is 374.4 kJ/kg, which is even higher than that of ice of about 333.3 kJ/kg,6 but the rigorous formation condition is a bottleneck for application. Some quaternary salts can also form hydrate with water that is called semiclathrate hydrate because anions of these salts are a part of © 2014 American Chemical Society

cagelike structure. Due to the reason that these kinds of semiclathrate hydrates can form even at atmospheric pressure and room temperature,7−10 they are promising candidates as the secondary refrigerant. For example, tetra-n-butyl ammonium bromide (TBAB) semiclathrate hydrate is attractive due to the reason that it can be stable between 273 and 285 K with dissociation enthalpies of about 200 kJ/kg.8 Moreover, quaternary salts are used as additives to reduce the formation pressure of gas hydrate to make the application more feasible, where a kind of hydrate named as gas+salt double hydrate can form. For example, the equilibrium pressure of CO2+TBAB double hydrate is much lower than that of CO2 hydrate. In addition, the dissociation enthalpy of CO2+TBAB double hydrate is about 313.2 kJ/kg,11 which is close to that of CO2 hydrate. Although the acidity of CO2 and slight corrosive effect of TBAB may bring problems in practical applications, the moderate formation condition and large dissociation enthalpy make CO2+TBAB double hydrate slurry a potential candidate as the two-phase secondary refrigerant for cold carrying, and the above negative effects can be alleviated by using inhibitor. There are two types of TBAB semiclathrate hydrates, that is, types A and B, with different hydration numbers. Shimada et al.12,13 and Oyama et al.14 investigated the molecule structures by X-ray diffraction. For the appearance, type A semiclathrate hydrate crystal shows a columnar shape with better transmittance and higher regularity while type B semiclathrate hydrate crystal shows an undefined form composed of thin crystals with worse regularity and transmittance according to their results. The mass fraction of the hydrate slurry is an important parameter to clarify the cold carrying capacity of the hydrate slurry secondary refrigeration, and it is important to determine the moles of hydrate forming at different subcoolings in the Received: Revised: Accepted: Published: 10249

March 25, 2014 May 17, 2014 May 26, 2014 May 26, 2014 dx.doi.org/10.1021/ie5012504 | Ind. Eng. Chem. Res. 2014, 53, 10249−10255

Industrial & Engineering Chemistry Research

Article

atures of the gas and liquid phases are measured by two PT100 thermometers (Shanghai Institute of Process Automation Instrumentation, China) with an uncertainty of 0.1 K. The CR is immersed in a constant temperature bath, and the temperature in the CR is controlled by a thermostatic bath (Shanghai Hengping Instrument Co., Ltd., China). An electric motor (Shanghai Meiyinpu Instrument, Ltd., China) underneath the CR is used to drive a magnetic stir bar in the CR to agitate the fluid. In addition, the amounts of TBAB and water are accurately weighted with an electronic balance with an uncertainty of 0.01 g (Zhejiang Yuyao Jingming Weighing Scale Co., Ltd., China) for aqueous solution preparation during the experiments, and 350.0 mL of TBAB aqueous solution measured by a graduated cylinder with an uncertainty of 5.0 mL is loaded for experiments. 2.2. Experimental Procedure. 2.2.1. Dissolution Process of CO2 Gas in TBAB Aqueous Solution. In the experiments, approximate 350.0 mL of liquid (water or TBAB aqueous solution) is loaded into the CR. When the liquid temperature in the CR reaches the designated value, the CR is purged three times using CO2 gas directly from gas cylinder to remove any gas remained in the CR. Then, CO2 gas is charged into the CR until a desired initial pressure is reached. After the gas purging is finished and the pressure and temperature of the gas stabilize in the sealed CR, the time is set as the initial time, t0 = 0 h, when CO2 in the gas phase charged in the CR has not begun to dissolve into liquid. Agitation starts at t0, and the pressure and temperature are recorded. As shown in Figure 2, gas pressure

hydrate slurry. Marinhas et al. calculated the moles of CO2 hydrate formed in a loop system by the pressure and temperature in the experiments, in which the solubility of CO2 in water was necessary.5 The estimation of the moles of CO2+TBAB double hydrate needs the information on the solubility of CO2 and composition of hydrate. Simultaneously, the difference between the equilibrium temperatures of CO2+TBAB double hydrate and TBAB semiclathrate hydrate increases with the increase of pressure of CO2. In order to avoid the appearance of TBAB semiclathrate hydrate, higher pressure is necessary. Therefore, the pressure of about 4.03 MPa is adopted in the present study. In the experiments, we use the isochoric experimental method to obtain the moles of CO2+TBAB double hydrate at different subcoolings by the pressure variation of CO2 gas. At the same time, we experimentally measure the solubility of CO2 gas in TBAB aqueous solution of mass fractions w = 0.05, 0.10, and 0.19 and in pure water, and the verification of the type of CO2+TBAB double hydrate with agitation by visualization is also carried out. Moreover, the kinetics of CO2+TBAB double hydrate formation at w = 0.05 and 0.10 is determined in the hydration process.

2. EXPERIMENTAL SETUP AND PROCEDURE 2.1. Apparatus and Materials. CO2 gas (>0.999 mole fraction) from Shanghai Cheng Gong Gas Industry Co., Ltd., China, and TBAB (>0.99 mass fraction) from Shanghai Richness Chemical Co., Ltd., China, are used without further purification. Distilled water is used in the present study. Table 1 reports the purity and sources of these chemicals used in the experiments. Table 1. Purities and Sources of Materials chemical name TBAB carbon dioxide

source Shanghai Richness Chemical Co., Ltd., China Shanghai Cheng Gong Gas Industry Co., Ltd., China

purity >0.99 mass fraction >0.999 mole fraction

The schematic diagram of the experimental apparatus is shown in Figure 1. The experiments are all conducted in a stainless steel crystallizer (CR) of 1050.0 cm3 in volume. Two circular glass windows are installed in the CR for visual observation. The pressure is measured by a pressure transducer (Dinkey Instrument Co. Ltd., China), and the uncertainty for pressure measurement is less than 0.015 MPa. The temper-

Figure 2. Variation of gas pressure and liquid temperature in the dissolution and hydration processes of CO2+TBAB double hydrate (w = 0.10).

drops and liquid temperature rises due to the dissolution of CO2 into liquid. As time elapses, the pressure of CO2 and the temperature of the liquid in the CR no longer change from the time t1 to t2, and it reaches a steady state (stage A), indicating that the dissolution process finishes. Δt1 = t1 − t0 is defined as the dissolution time. For example, Δt1 ≈ 1.0 h, as shown in Figure 2, can be taken as the dissolution time. The moles of CO2 at t0 and t1 in the gas phase can be obtained by eqs 1 and 2: nt0 =

Figure 1. Schematic diagram of the experimental apparatus.16 PT, pressure transducer; T, thermometer; V1−V4, valves. 10250

Pt0VCO2 Z t0Tt0R

(1)

dx.doi.org/10.1021/ie5012504 | Ind. Eng. Chem. Res. 2014, 53, 10249−10255

Industrial & Engineering Chemistry Research

nt1 =

Article

Pt1VCO2 Z t1Tt1R

The moles of CO2 at t3 in the gas phase can be obtained by eq 6:

(2)

n t3 =

where P is the pressure of CO2 gas, T is the temperature of CO2 gas, VCO2 is the volume of the gas phase in the CR, R is the gas constant (8.314 J/(mol·K)), and Z is the compressibility factor of CO2 gas obtained from the Soave−Redlich−Kwong equation of state (SRK EoS).15 As a result, the moles of total dissolved CO2 from t0 to t1, nCO2,dis, can be obtained as follows: nCO2,dis = nt0 − nt1

xCO2 =

Z t3Tt3R

(6)

So, the moles of CO2 gas consumed in the hydration process, nCO2,hyd, can be obtained by eq 7 as follows: nCO2,hyd = nt1 − nt3 (7) where the subscript hyd denotes the hydration process. The volume of the gas phase in the CR is assumed to be constant throughout the hydrate formation process.

(3)

where the subscript dis denotes the dissolution process of CO2 in TBAB aqueous solution. Then, the solubility of CO2 in TBAB aqueous solution is given by eqs 4 and 5: L L nsol = n TBAB + nW

Pt3VCO2

3. RESULTS AND DISCUSSION In the present study, the total moles of CO2 in the isochoric CR is constant in the dissolution and hydration processes, and the pressure drops because CO2 dissolves into the TBAB aqueous solution and forms hydrate. The schematic illustration for the hydration formation process is shown in Figure 3. The TBAB

(4)

nCO2,dis L nCO2,dis + nsol

(5)

where nLW and nTBAB are the moles of water and TBAB salt, respectively. 2.2.2. Hydration process of CO2+TBAB Double Hydrate. The experimental procedure for the hydration of CO2+TBAB double hydrate is similar to that for the solubility of CO2 as mentioned above. When the bath temperature is set lower than the equilibrium temperature of CO2+TBAB double hydrate, formation of hydrate may occur. As shown in Figure 2, the dissolution process begins at t0 = 0 h with agitation. The rising of the initial temperature with falling pressure is caused by the dissolution of CO2. The dissolution is equilibrated at t1 ≈ 1.0 h, which indicates that there is no more CO2 gas dissolving into aqueous solution. At t2 ≈ 1.6 h, the temperature of the aqueous solution rises again due to hydration, where the temperature of the TBAB aqueous solution increases sharply within a short time and then decreases gradually. In this period, the pressure in the CR reduces quickly with the rapid increase of moles of the gas consumption for hydrate formation. This period is a process of the phase transformation of the gas and the TBAB aqueous solution to solid hydrate, which releases the heat of hydrate formation and results in the temperature rise in the system, even leading to a slight pressure rise of gas at the beginning of the hydrate process, as shown in Figure 2. Then, from t3 ≈ 3.0 h, it enters stage B where the hydration is equilibrated and the formation of CO2+TBAB double hydrate completes. The duration from t2 to t3, Δt2, is defined as the hydration time, for example, Δt2 ≈ 1.4 h, as shown in Figure 2, can be taken as the hydration time. The amount of total consumed CO2 from t0 to t1 is for dissolution and that consumed from t2 to t3 is for hydration. The subcoolings are about 2.0−5.0 K for hydration of CO2+TBAB double hydrate in the experiments and measured by ΔTsub = Teq − Tt1, where Teq is equilibrium temperature corresponding to the pressure of CO2 gas Pt1 and Tt1 is the temperature of the TBAB aqueous solution at t1. As can be seen in Figure 2, the average pressure is about 4.03 MPa. At w = 0.05 and 0.10, values of Teq are 286.83 and 289.06 K, respectively, which are obtained by the same method as in the previous study.16

Figure 3. Schematic diagram of CO2 molecule migration in the hydration process. CO2 molecules in the gas phase (black); CO2 molecules dissolved in solution (white); TBA+ ions in solution (orange); Br− ions in solution (blue).

aqueous solution is saturated by CO2 at t1, and in the hydration process from t2 to t3, a portion of water with TBAB and CO2 dissolved form hydrate. As the mass fractions of TBAB and CO2 in the aqueous solution at t1 are lower than those in CO2+TBAB double hydrate at t3, more dissolved CO2 and TBAB in the remained aqueous solution are gradually used to form CO2+TBAB double hydrate from t2 in the hydrate process, which causes the pressure drop and decrease of mass fraction of TBAB in aqueous solution. As a result, the pressure drop from t2 to t3 is due to two reasons: one is for the moles of CO2 entering hydrate, and the other is for the variation of solubility of CO2 in the remaining aqueous solution because the pressure drops and the mass fraction of the TBAB aqueous solution decreases. The impact of the variation of the mass 10251

dx.doi.org/10.1021/ie5012504 | Ind. Eng. Chem. Res. 2014, 53, 10249−10255

Industrial & Engineering Chemistry Research

Article

fraction of the aqueous solution and pressure drop on the solubility of the remaining aqueous solution is necessarily determined. So, the experimental data for the solubility of CO2 gas in water and the TBAB aqueous solution is presented. Shown in Figure 4 is the solubility of CO2 in pure water and the TBAB aqueous solution with mass fractions w = 0.05, 0.10,

nCO2,CW =

H nCW xCO2

1 − xCO2

(9)

where xCO2 is the solubility of CO2 in the TBAB aqueous solution obtained by eq 5. In the hydration process, the solubility of CO2 in the remaining TBAB aqueous solution, xCO2, is affected by the decrease of mass fraction of the TBAB aqueous solution and the pressure variation. However, it is understood from Figure 4 that the salting-out effect of the TBAB salt on the solubility of CO2 in pure water and the TBAB aqueous solution at w = 0.05 and 0.10 is very small and the solubility becomes less sensitive to pressure in the highpressure range, so these impacts from the decrease of mass fraction of the TBAB aqueous solution and the pressure on the solubility of CO2 in the TBAB aqueous solution for hydrate formation are negligible in the present study. Therefore, the solubility of CO2 in eq 9 can be taken as that in pure water for simplification. Moreover, a clear composition of CO2+TBAB double hydrate is necessary for estimating the moles of CO2+TBAB double hydrate because there are two types of hydrates forming in the CO2+TBAB+H2O system with two different compositions. Lin et al.11 have experimentally examined the composition of CO2+TBAB double hydrate forming in 9.01 wt % TBAB aqueous solution with CO2 using DTA, and the results showed that the moles of type A CO2+TBAB double hydrate was far less than that of type B CO2+TBAB double hydrate. Moreover, the composition of type B CO2+TBAB double hydrate was determined as 2.51CO2·TBAB·38H2O in which 38 is the hydration number and 2.51 is the encaged gas number. However, CO2+TBAB double hydrate formation in the present study is with agitation at higher pressure, where the hydration number might be different from that in ref 11. Therefore, the visualization of CO2+TBAB double hydrate is necessary to clarify the type of double hydrate first. For visualizing CO2+TBAB double hydrate, the morphologies of hydrate crystals in the formation and growth processes are presented and discussed in comparison with those without agitation.16 For better presenting the morphologies of CO2+TBAB double hydrate in the hydration process, the time thyd is set as 0 s when the hydration begins. Figure 5 presents a sequence of photos of CO2+TBAB double hydrate forming at ΔTsub = 3.0 K and P = 4.03 MPa. As seen from the photos, the regular columnar-shaped double hydrate crystals with high transmittance forming in the TBAB aqueous solution with agitation at thyd = 10 s. Then, a portion of the hydrate crystals grow irregularly at thyd = 300 s and become thin cylinder shape with high transmittance at thyd = 660 s. In addition, the amount of hydrate crystals increases apparently without apparent size increase from 10 to 300 s. In the end of the hydration process at thyd = 1560 s, all hydrate crystals stop

Figure 4. Solubility of CO2 in the TBAB aqueous solution and pure water at 283.0 and 293.0 K.

and 0.19 measured at 283.0 and 293.0 K at 0.3−4.0 MPa in the present study. The data of CO2 solubility in pure water at 283.0 K agree well with those from the literature.17−20 Simultaneously, the solubility data of CO2 in the TBAB aqueous solution at w = 0.19 at 293.0 K are close to those at w = 0.20 at 290.0 K presented by Lin et al.20 It is indicated that the apparatus and the procedure adopted in the present study are reliable. Apparently, CO2 solubility in pure water and the TBAB aqueous solution increases with the increase of CO2 gas pressure. The solubility becomes less sensitive to pressure variation in the high-pressure range. In addition, the solubility of CO2 in pure water and TBAB aqueous solution decreases with the increase of temperature. The solubility in TBAB aqueous solution usually decreases due to the salting-out effect.21 When adding TBAB salt, the reduction of solubility due to the salting-out effect is apparent at w = 0.19 at high pressure. However, the salting-out effect appears too weak to make an obvious impact on the difference of the solubilities for pure water and the TBAB aqueous solution at w = 0.05 and 0.10. Suppose nHCW is the moles of water combined into double hydrate in the hydration process, then the moles of CO2 dissolved in the combined water is formulated as

Figure 5. Sequential photos of CO2+TBAB double hydrate crystal growth at w = 0.10, ΔTsub = 3.0 K, and P = 4.03 MPa. 10252

dx.doi.org/10.1021/ie5012504 | Ind. Eng. Chem. Res. 2014, 53, 10249−10255

Industrial & Engineering Chemistry Research

Article

Table 2. Solubility of CO2 in Water and the Moles of CO2+TBAB Double Hydratea w

ΔTsub (K)

xCO2,dis

nDH1 (mol) (2.51CO2·TBAB·38H2O)

nDH2 (mol) (3CO2·TBAB·38H2O)

Δdmax ((nDH1 − nDH2)/(nDH1) × 100%)

0.05

2.0 3.0 4.0 5.0 2.0 3.0 4.0 5.0

0.0220 0.0225 0.0228 0.0230 0.0201 0.0221 0.0222 0.0224

0.0214 0.0333 0.0499 0.0663 0.0541 0.0695 0.0807 0.0947

0.0165 0.0256 0.0383 0.0509 0.0422 0.0536 0.0622 0.0729

22.84% 23.06% 23.19% 23.27% 22.07% 22.88% 22.93% 23.01%

0.10

a

Uncertainties for solubility, u(xCO2), and the moles of CO2+TBAB double hydrate, u(nDH) are estimated to be less than 2.14% and 3.24%, respectively. The moles of CO2+TBAB double hydrate in the present study nDH is between nDH1 and nDH2.

hydrate.22 If the composition is not 2.51CO2·TBAB·38H2O but 3CO2·TBAB·38H2O, eq 12 is changed as follows:

growing, and the CR is full of the irregular thin cylinder-shaped crystals that show type B characteristic.12−14 Compared to the morphology of CO2+TBAB double hydrate forming without agitation in our previous paper,16 the morphologies of hydrate crystals are similar, and the differences are the size and number of hydrate crystals because better heat exchange condition and disturbance with agitation are favorable for the formation of nucleus of hydrate to increase the number and reduce the size of crystals. From the above visualization, formation of type B CO2+TBAB double hydrate with agitation is clarified in the present study, so the composition of 2.51CO2·TBAB·38H2O is adopted, and the moles of CO2 gas encaged in double hydrate is formulated by eq 10: H nCO = 2 ,tot

H 2.51nCW 38

nDH =

(10)

H nCW 38

(11)

Eventually, the formula for the moles of CO2+TBAB double hydrate can be written as

nDH =

⎛ Pt VCO (1 − xCO2)⎜ Z1 T R2 − ⎝ t1 t1

3 − 41xCO2

Pt3VCO2 ⎞ ⎟

Z t3Tt3R ⎠

(13)

The results from eqs 12 and 13 and the relative deviation are listed in Table 2. As presented in Table 2, the solubility of CO2 in pure water and the moles of CO2+TBAB double hydrate forming in the TBAB aqueous solution at w = 0.05 and w = 0.10 increase with the increase of subcooling ΔTsub. Meanwhile, at the same subcooling, the number of moles of CO2+TBAB double hydrate forming at w = 0.10 are more than that forming at w = 0.05. However, for the TBAB aqueous solution of w = 0.05 at ΔTsub = 5.0 K obtained from eq 12, the moles of CO2+TBAB double hydrate forming in the hydration process is 0.0663 mol and more than 0.0543 mol, which is the moles of TBAB in aqueous solution at w = 0.05, whereas the moles of CO2+TBAB double hydrate forming at w = 0.05 at ΔTsub = 5.0 K obtained from eq 13 is 0.0509 mol. As a result, the encaged gas number of CO2+TBAB double hydrate forming in the present study might be between 2.51 and 3. The kinetic characteristics of CO2+TBAB double hydrate formation are important to the performance of the hydrate slurry secondary refrigeration system. CO2 consumption rate can be determined from the slope of gas uptake curves in the hydration process presented in Figure 6. As can be seen, the moles of consumed CO2 in the hydration process increase with

As all CO2 from the two parts mentioned above is encaged into H hydrate, the total amount of CO2 is nCO = nCO2,CW + nCO2,hyd. 2,tot Then, according to the composition of type B CO2+TBAB double hydrate, that is, 2.51CO2·TBAB·38H2O, the moles of CO2+TBAB double hydrate can be estimated as follows: nDH =

⎛ Pt VCO (1 − xCO2)⎜ Z1 T R2 − ⎝ t1 t1

Pt3VCO2 ⎞ ⎟

Z t3Tt3R ⎠

2.51 − 40.51xCO2

(12)

where xCO2 is the solubility of CO2 gas in pure water. CO2+TBAB double hydrate forming in Lin et al.11 was at about 2.0 MPa without agitation, which is different from that in the present study; thus, the encaged gas number of 2.51 might be different. The moles of encaged CO2 in CO2+TBAB double hydrate is affected by several factors, and high pressure with agitation may increase the moles of encaged CO2. For example, more CO2 will dissolve in aqueous solution at higher pressure, and consequently, more CO2 might be encaged into hydrate. Furthermore, agitation might be favorable for increasing the occupation of dodecahedral cages in TBAB semiclathrate hydrate by CO2 molecules, that is, the encaged gas number might be larger than that in Lin et al.11 As a result, the encaged gas number might be in the range 2.51−3 in which 3 is the maximum value of dodecahedral cages in TBAB semiclathrate

Figure 6. Variation of the consumed CO2 with time in the hydration process. 10253

dx.doi.org/10.1021/ie5012504 | Ind. Eng. Chem. Res. 2014, 53, 10249−10255

Industrial & Engineering Chemistry Research

Article

the subcooling at w = 0.05 and 0.10, which indicates that more CO2+TBAB double hydrate forms when subcooling increases. However, with a vigorous agitation, that is, 700 r/min in the present study and in a dissolution equilibrium condition before hydration, the CO2 consumption rate in the hydration process can be assumed to be equal to the growth rate of CO2+TBAB double hydrate.23 Simultaneously, the driving force for the growth of hydrate decreases as approaching the end of the hydration process that results in the decrease of the growth rate of CO2+TBAB double hydrate. In the experiments, the time durations of the hydration processes are all about 1.0 h, and we use the growth rate of CO2+TBAB double hydrate in the first 10 min to present the kinetics of hydration. The slope of gas uptake curves in the hydration process is defined as the normalized rate of hydrate formation in the first 10 min, NR10, which can be used to measure the kinetic characteristics of hydration. Under those experimental conditions, the normalized rate of CO2+TBAB double hydrate formation can be expressed by24 R NR10 = 10 L Vsol (14)

Figure 8. Temperature rise of the aqueous solution versus subcooling in the hydration process.

of w = 0.05, and the differences of temperature rise between them increase with the increase of subcooling. Higher initial solution concentration, for example, w = 0.10, leads to a larger NR10 than that of w = 0.05, which indicates that higher initial mass fraction is more favorable for increasing the formation rate of hydrate. However, with the increase of subcooling, ΔTsub, the difference between the temperature rise of w = 0.05 and 0.10 increases, and the effect on the hydrate formation rate augments, which results in that the value of NR10 of w = 0.05 is larger than that of w = 0.10.

where R10 is the moles of CO2 uptake for hydrate growth versus time for the first 10 min in the hydration process and VLsol is the volume of the TBAB aqueous solution. The effect of subcooling of the aqueous solution on the normalized rate of CO2+TBAB double hydrate for the first 10 min in the hydration process is shown in Figure 7. As seen in

4. CONCLUSIONS In the present study, the moles of CO2+TBAB double hydrate are estimated by the variation of pressure and solubility at about 4.03 MPa at w = 0.05 and 0.10. The solubility of CO2 in pure water and the TBAB aqueous solution at w = 0.05, 0.10, and 0.19 increases with the increase of pressure but becomes less sensitive to pressure in the high pressure range. The difference between the solubilities of CO2 in pure water and the TBAB aqueous solution at w = 0.05 and 0.10 is negligibly small. Furthermore, the formation of type B CO2+TBAB double hydrate is verified. The moles of CO2+TBAB double hydrate forming at w = 0.05 and 0.10 increase with the increase of subcooling of 2.0 to 5.0 K, and the encaged gas number of CO2+TBAB double hydrate forming in the present study is confirmed between 2.51 and 3. The formation rates of CO2+TBAB double hydrate at w = 0.05 and 0.10 increase with the increase of subcooling of 2.0 to 5.0 K. Higher initial mass fraction of the TBAB aqueous solution is more favorable for increasing the formation rate of hydrate. But, higher initial mass fraction may lead to higher temperature rise of the aqueous solution especially at high subcooling. Such a large temperature rise in turn hampers the formation of hydrate, which leads to that the formation rate of w = 0.10 is less than that of w = 0.05 at larger ΔTsub.

Figure 7. Effect of subcooling on the normalized rate of CO2+TBAB double hydrate.

the figure, the normalized rates of CO2+TBAB double hydrate formation at w = 0.05 and 0.10 increase as subcooling increases. Moreover, as shown in Figure 7, the gradient of NR10 of w = 0.05 is larger than that of w = 0.10 with the increase of subcooling. We believe that this is due to the temperature rise in the hydration process as shown in Figure 2, because hydration is an exothermic process that leads to the temperature rise. However, the temperature rise in the hydration process reduces the driving force for hydrate formation, and the higher the temperature rise, the less the driving force is. Larger subcooling leads to a greater hydrate formation rate, and accordingly, the temperature rises for hydration of w = 0.05 and 0.10 increase at the subcooling of 2.0−5.0 K, as shown in Figure 8. Moreover, at the same subcooling, the temperature rise of w = 0.10 is larger than that

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-21-34205505. Fax: +86-21-34206814. E-mail: [email protected]. Notes

The authors declare no competing financial interest. 10254

dx.doi.org/10.1021/ie5012504 | Ind. Eng. Chem. Res. 2014, 53, 10249−10255

Industrial & Engineering Chemistry Research

■

Article

(8) Oyama, H.; Shingo, T. Air-conditioning system using clathrate hydrate slurry. JFE Tech. Rep. 2004, 3, 1−5. (9) Lin, W.; Dalmazzone, D.; Fürst, W.; Delahaye, A.; Fournaison, L.; Clain, P. Accurate DSC measurement of the phase transition temperature in the TBPB−water system. J. Chem. Thermodyn. 2013, 61, 132−137. (10) Fukushima, S.; Takao, S.; Ogoshi, H.; Ida, H.; Matsumoto, S.; Akiyama, T.; Otsuka, T. Development of high-density cold latent heat with clathrate hydrate. In NKK Technical Report (in Japanese); JFE Steel Corporation: Tokyo, Japan, 1999; Vol. 166, pp 65−70. (11) Lin, W.; Delahaye, A.; Fournaison, L. Phase equilibrium and dissociation enthalpy for semi-clathrate hydrates of CO2 + TBAB. Fluid Phase Equilib. 2008, 264, 220−227. (12) Shimada, W.; Ebinuma, T.; Oyama, H.; Kamata, Y.; Takeya, S. Separation of gas molecule using tetra-n-butyl ammonium bromide semi-clathrate hydrate crystals. Jpn. J. Appl. Phys. 2003, 42, 129−131. (13) Shimada, W.; Ebinuma, T.; Oyama, H.; Kamata, Y.; Narita, H. Free-growth forms and growth kinetics of tetra-n-butyl ammonium bromide semi-clathrate hydrate crystals. J. Cryst. Growth 2005, 274, 246−250. (14) Oyama, H.; Shimada, W.; Ebinuma, T.; Kamata, Y.; Takeya, S.; Uchida, T.; Nagao, J.; Narita, H. Phase diagram, latent heat, and specific heat of TBAB semiclathrate hydrate crystals. Fluid Phase Equilib. 2005, 234, 131−135. (15) Soave, G. Equilibrium constants from a modified RedlichKwong equation of state. Chem. Eng. Sci. 1972, 27, 1197−1203. (16) Ye, N.; Zhang, P. Equilibrium data and morphology of tetra-nbutyl ammonium bromide semiclathrate hydrate with carbon dioxide. J. Chem. Eng. Data 2012, 57, 1557−1562. (17) Houghton, G.; McLean, A. M.; Ritchie, P. D. Compressibility, fugacity, and water-solubility of carbon dioxide in the region 0−36 atm. and 0−100°C. Chem. Eng. Sci. 1957, 6, 132−137. (18) Diamond, L. W.; Akinfiev, N. N. Solubility of CO2 in water from −1.5 to 100° C and from 0.1 to 100 MPa: Evaluation of literature data and thermodynamic modeling. Fluid Phase Equilib. 2003, 208, 265− 290. (19) Stewart, P. B.; Munjal, P. Solubility of carbon dioxide in pure water, synthetic sea water and synthetic sea water concentrates at −5° to 25° C. and 10- to 45-atm. pressure. J. Chem. Eng. Data 1970, 15, 67−71. (20) Lin, W.; Dalmazzone, D.; Fürst, W.; Delahaye, A.; Fournaison, L. Thermodynamics studies of CO2 -TBAB-water system. In Proceedings of the 7th International Conference on Gas Hydrate; Edinburgh, Scotland, United Kingdom, July 17−21, 2011. (21) Liu, Y.; Hou, M.; Yang, G.; Han, B. Solubility of CO2 in aqueous solutions of NaCl, KCl, CaCl2 and their mixed salts at different temperatures and pressures. J. Supercrit. Fluids 2011, 56, 125−129. (22) Shimada, W.; Shiro, M.; Kondo, H.; Takeya, S.; Oyama, H.; Ebinuma, T.; Narita, H. Tetra-n-butylammonium bromide-water (1/ 38). Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 2005, 61, 65−66. (23) Fan, S. S.; Li, S. F.; Wang, J. Q.; Lang, X. M.; Wang, Y. H. Efficient capture of CO2 from simulated flue gas by formation of TBAB or TBAF semiclathrate hydrates. Energy Fuels 2009, 23, 4202− 4208. (24) Babu, P.; Yao, M.; Datta, S.; Kumar, R.; Linga, P. Thermodynamic and kinetic verification of tetra-n-butyl ammonium nitrate (TBANO3) as a promoter for the clathrate process applicable to precombustion carbon dioxide capture. Environ. Sci. Technol. 2014, 48, 3550−3558.

ACKNOWLEDGMENTS This research is jointly supported by the National Natural Science Foundation of China under the contract no. 51176109 and the NSFC-JSPS cooperative project under the contract no. 51311140169.

■

NOMENCLATURE w mass fraction of TBAB in aqueous solution P pressure T temperature V volume R universal gas constant Z compressibility factor u uncertainty R10 mole of gas consumed for the first 10 min NR10 normalized rate of hydrate formation n moles x solubility of gas in aqueous solution Δt time interval ΔT temperature difference Subscripts

W CW TBAB CO2 DH r sol t eq sub tot dis hyd

water combined water tetra-n-butyl ammonium bromide carbon dioxide double hydrate temperature rise aqueous solution time equilibrium condition subcooling total dissolution process hydration process

Superscripts

L liquid phase H hydrate phase

■

REFERENCES

(1) Sloan, E. D. Clathrate hydrates of natural gases. In Chemical Industrial Series:119, 3rd ed.; Koh, C. A., Ed.; CRC Press: Golden, CO, 2008. (2) Englezos, P. Clathrate hydrates. Ind. Eng. Chem. Res. 1993, 32, 1251−1274. (3) Du, J. W.; Liang, D. Q.; Li, D. L.; Chen, Y. F.; Li, X. J. Phase equilibrium conditions of tetrabutyl ammonium nitrate + CO2, N2, or CH4 semiclathrate hydrate systems. Ind. Eng. Chem. Res. 2011, 50, 11720−11723. (4) Linga, P.; Kumar, R.; Lee, J. D.; Ripmeester, J.; Englezos, P. A new large scale apparatus to enhance the rate of gas hydrate formation: Application to capture of carbon dioxide. Int. J. Greenhouse Gas Control 2010, 4, 630−637. (5) Marinhas, S.; Delahaye, A.; Fournaison, L.; Dalmazzone, D.; Fürst, W.; Petitet, J.-P. Modelling of the available latent heat of a CO2 hydrate slurry in an experimental loop applied to secondary refrigeration. Chem. Eng. Process. 2006, 45, 184−192. (6) Kang, S. P.; Lee, H.; Ryu, B.-J. Enthalpies of dissociation of clathrate hydrates of carbon dioxide, nitrogen, (carbon dioxide + nitrogen), and (carbon dioxide + nitrogen + tetrahydrofuran). J. Chem. Thermodyn. 2001, 33, 513−521. (7) Kamata, Y.; Yamakoshi, Y.; Ebinuma, T.; Oyama, H.; Shimada, W.; Narita, H. Hydrogen sulfide separation using tetra-n-butyl ammonium bromide semi-clathrate (TBAB) hydrate. Energy Fuels 2005, 19, 1717−1722. 10255

dx.doi.org/10.1021/ie5012504 | Ind. Eng. Chem. Res. 2014, 53, 10249−10255