Article pubs.acs.org/EF
Kinetics of Carbon Dioxide Hydration Enhanced with a Phase-Change Slurry of n‑Tetradecane Bin Chen, Feng Xin,* Xiaofei Song, Xingang Li, and Muhammad Zeshan Azam School of Chemical Engineering and Technology, Tianjin University, Tianjin 300350, China ABSTRACT: CO2 capture based on hydrate formation is intensified by an oil-in-water phase-change slurry (PCS) in which the n-tetradecane particles are taken as nucleation centers and are used to directly remove the hydration heat through their solid-toliquid phase change. In this study, experiments on hydration were conducted at a temperature of 277.6 K and under isobaric pressures in the range of 2.1−2.4 MPa. All measurements were performed at a stirring speed of 450 rpm in PCSs of 25−45 wt % n-tetradecane. Two kinetics models, transport and reversible hydration, were established to regress and analyze the experimental data from the isothermal hydration of CO2 in a semibatch hydrator. For each model, the effects of pressure and PCS composition were examined in detail. As the experimental results show, the induction time before hydration initiated was less than 1 min for all runs, and the duration of the entire hydration process was approximately 13−15 min for each measurement. Furthermore, the average hydration rate reached 197 mol m−3 min−1 at 2.3 MPa in 45 wt % oil-in-water PCS, which demonstrates that the presence of n-tetradecane particles contributes significantly to the enhancement of hydrate formation rate. As the modeling results show, the parameters of the two models were determined by correlating the experimental data, and the interpretations of the measurements by the two models are satisfactory.
1. INTRODUCTION Increasing CO2 emissions have been caused by the excessive consumption of fossil fuels (coal, oil, natural gas) required to satisfy the growing energy demands of human society, which poses a series of challenges to ecological systems and the environment, such as global temperature rise, sea-level change, and ocean storms and floods.1 Therefore, dealing with CO2 emissions has become a common issue of global perspective and the focus of international concern.2 In the view of the global growth in energy demands, effective CO2 capture and storage methods are the mainly considered approaches. For different power plants, precombustion capture, postcombustion capture, and oxy-fuel combustion capture are the three typically used means to reduce the CO2 emissions,3 resulting in CO2 contents of 40 mol % (with 60 mol % H2), 15−20 mol % (with N2), and 70−90 mol %, respectively. Meanwhile, more substantial capture efficiencies can be obtained with higher concentrations of CO2,4 so oxy-fuel combustion capture has become a promising technology. The conventional available technologies for CO2 capture, such as physical and chemical absorption,5 adsorption,6 membrane, and cryogenic processes, have some limitations, such as high costs, low capture efficiencies, and complicated processing stages. Currently, hydrate-based CO2 capture (HBCC) and hydrate-based CO2 separation (HBCS) are widely considered to be promising technologies. Gas hydrates are nonstoichiometric cagelike crystals formed at relatively low temperatures and high pressures that are made of small-molecule gases and water.7 The primary forms of hydrate include structure sI (CH4, CO2 etc.), structure sII, and structure sH.8 A great number of studies have been published on the potential applications of HBCS and HBCC technologies, and the earlier research into hydrates focused mainly on the vapor− liquid−hydrate (V−L−H) equilibria of different gases.9−13 Owing to the distinct hydration heat released during the hydrate formation process14 and likely hydrate agglomeration, mass-transfer © XXXX American Chemical Society
resistance for gas molecules and heat-transfer resistance frequently arise during the hydrate formation process, seriously inhibiting the hydration rate and water conversion. As a result, more recently reported studies have focused on the enhancement of gas hydrate formation, with the selection of chemical additives and the design of novel hydrators being favored approaches. First, the widely used additives are divided into kinetic promoters and thermodynamic promoters, including polyoxyethylene sorbitan monooleate (Tween-80), dodecyl trimethylammonium chloride (DTAC), sodium dodecyl sulfate sodium salt (SDS)15 as common kinetic promoters, which are capable of accelerating hydration, and tetrahydrofuran (THF), cyclopentane (CP), propane (C3H8), and tetrabutylammonium bromide (TBAB)16,17 as common thermodynamic promoters, which can effectively reduce the hydrate phase equilibrium pressure. Second, the main purpose of novel hydrator design is to minimize the mass-transfer ̈ and heat-transfer resistances. Both Linga et al.18 and S. Douieb et al.19 constructed novel semibatch hydrators in which different impellers were employed to enhance the contact of gas and water to decrease hydrate agglomeration. Yang et al.20 employed a heat exchanger to decrease the heat-transfer resistance. Recently, water-in-oil21 and oil-in-water22 emulsions have been recognized as high-efficiency systems for hydration by relieving the hydrate agglomeration and enhancing the mass transfer. Thus, in view of industrial applications, novel hydrator designs combined with high-efficiency hydration systems will be the focus in the future. However, there are some other restrictions preventing the industrial application of HBCC, including the scarcity of reliable kinetic data and the lack of simplified rate equations to justify the formation of CO2 hydrate. After Glew and Haggett23 established Received: December 27, 2016 Revised: March 10, 2017 Published: March 13, 2017 A
DOI: 10.1021/acs.energyfuels.6b03477 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 1. Schematic diagram of the experimental setup.
the first kinetics model for the hydration rate in 1968, Pangborn and Barduhn24 proposed another model. Although their models were relatively empirical, they both recognized that heat and mass transfer, which are critically affected by agitation speed, play significant roles during hydration. Afterward, based on the twofilm transport theory, Englezos et al.25 established several kinetics models to describe gas hydration using different driving forces with the quasisteady-state assumption. Then, on the basis of Englezos et al.’s model and in situ experiments, Herri et al.26 took the population balance for the hydrate crystals into account to characterize the nucleation, aggregation, and breakage of the hydrate formation. Although the mentioned models regress their experimental data well, they are not suitable for industrial applications because of various complexities. The main focus of this work was to study the kinetics of single CO2 under rapid hydration by direct heat removal through the phase change of solid n-tetradecane particles. In this work, a phase-change slurry of n-tetradecane, which was successfully applied to intensify methane hydrate formation in our previous work,22 was employed to enhance the CO2 hydration rate by abating the negative impacts of the mass-transfer and heattransfer resistances during the hydration process. Huang et al.27 reported that there was a distinct increase in viscosity with decreasing temperature; however, PCSs are required to have low viscosities for applications. Thus, the paraffin mass fraction of n-tetradecane should not be more than 50 wt %, so 25−45 wt % PCSs were applied to study CO2 hydration in our experiments. All measurements were performed at an agitation speed of 450 rpm and under pressures in the range of 2.1−2.4 MPa. The speed of 450 rpm was selected because agitation at this rate is sufficient to remove the hydrate from the gas−water interface and maintain the hydrate particles as small crystals in a slurry but not enough to induce excessive rippling at the surface or bubble entrapment by vortex.28 Although 0.1 MPa as the increment is relatively low, it is sufficient to indicate the influence of pressure on the CO2 hydration rate in our rapid hydration system. To regress the kinetics data, in our first mathematical model, the mass-transfer
resistances were assigned to each continuous mass transfer, and the effects of pressure and composition on the resistances were examined in detail. In the second mathematical model, upon the analysis of the hydrate growth reported in the literature, the hydration was processed as reversible hydration. Both of these models are relatively simplified.
2. EXPERIMENTAL METHOD 2.1. Setup. As shown in Figure 1, the experimental setup consisted of a hydration unit, a feeding unit, and a data acquisition unit. The hydration occurred in a cylindrical stainless steel vessel with an inner volume of 61.3 cm3 and a vertically mounted magnetically driven stirrer with a maximum attainable rotation speed of 1200 rpm. The hydrator could withstand pressures up to 10 MPa and temperatures down to 233.15 K and was enclosed with a cooling jacket through which aqueous ethylene glycol was circulated continuously. The top of the hydrator was insulated with polyurethane foam. For accurate temperature measurements, two temperature sensors with Pt100 resistance and an uncertainty of ±0.1 K were placed at top and bottom of the hydrator to monitor the temperatures of the gas phase and slurry, respectively. A pressure transducer (CYB-20S, Beijing WESTZH Machine and Technology) was set on top of the hydrator to gauge its internal pressure. The prepared phase-change emulsion (PCE) was pumped into the hydrator with a constant-flow pump (P230 II, Dalian Elite Analytical Instruments) with an uncertainty of 0.3% at a flow rate between a realistic feed flow rate and the setup flow rate. The control uncertainties of the mass flow controller (MFC) and mass flow meter (MFM) (Beijing Seven Star Electronics) were 1%, and gaseous carbon dioxide was fed into the hydrator through the MFC and piped out through the MFM. The temperature, pressure, and instantaneous and cumulative volume flows of carbon dioxide were measured with secondary instruments and recorded by the data acquisition unit of computer. 2.2. Materials. Carbon dioxide (99.99 wt %) was obtained from Liufang Inc., Tianjin, China. Span 80 (chemical grade) and Tween 60 (chemical grade) were obtained from Guangfu Chemical Plant, Tianjin, China. n-Tetradecane (98 wt %) was obtained from Aladdin Inc., Shanghai, China. 2.3. PCS Preparation. Two steps were necessary to prepare the PCSs. First, Tween 60 (2.92 wt %) and Span 80 (1.08 wt %) as the B
DOI: 10.1021/acs.energyfuels.6b03477 Energy Fuels XXXX, XXX, XXX−XXX
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Energy & Fuels surfactants were weighed precisely, and then n-tetradecane (25, 35, or 45 wt %) and the rest of deionized water were added. The prepared mixtures were emulsified with a high-performance disperser (T25 Digital) at 10000 rpm for 5 min to obtain the phase-change emulsion (PCE). Afterward, the PCE (30 mL) was charged into the hydrator with the coolant circulated at 268.8 K (−4.4 °C). To ensure that the n-tetradecane droplets in the emulsion solidified completely, the agitator was operated for at least 1 h. The fusion point of the solid n-tetradecane particles in the PCS was already characterized to be 277.6 K in our previous work.22 2.4. Experimental Procedure. Prior to feeding, the constant-flow pump, MFC, and MFM were cleaned and calibrated accordingly. Then, deionized water and carbon dioxide were alternately introduced into the hydrator and evacuated; this step was repeated at least five times to ensure that there was no longer any contamination in the hydrator. Then, the prepared PCE was charged into the hydrator. After the PCS preparation had been completed, the hydrator was heated to a temperature (∼277.5 K) that was slightly lower than the fusion point of solid n-tetradecane particles. Then, the hydrator was pressurized to reach the fixed pressure, and the agitator was started. Isobaric hydration was allowed to proceed, with all of the necessary information being recorded, until the instantaneous flow difference between the MFC and the MFM was zero. 2.5. Data Analysis. In the prepared PCSs of n-tetradecane, water as the continuous phase came into contact with the absorbed carbon dioxide. As the carbon dioxide molecules were encapsulated by water molecules to form a hydrate, the released hydration heat was directly absorbed by solid n-tetradecane particles through a solid-to-liquid phase change, and then the carbon dioxide molecules in the water rapidly diffused into the melted n-tetradecane. Therefore, carbon dioxide molecules were present in the water, melted liquid n-tetradecane, and hydrate phase. Because strong agitation was applied, it was assumed that the system reached a quasisteady state. Because the solubility of carbon dioxide in water29,30 is far less than that in liquid n-tetradecane31,32 during hydrate growth, the former was neglected in our calculations. In addition, the following assumptions were employed for further calculations and modeling: • The carbon dioxide molecules can transfer quickly from water to liquid n-tetradecane, so the mass-transfer rate of CO2 is controlled by the absorption rate in water. • During the isothermal hydration process, only the hydration heat and latent the heat of solid n-tetradecane phase change are considered. The number of moles of carbon dioxide encapsulated by the hydrate was calculated using the molar and heat balance equations. The general mole balance is given by n T(t ) = nCO2(hg)(t ) + nCO2(o)(t )
water-to-hydrate phase inversion process into account. When water inverts to the hydrate phase, the molar volume of the formed hydrate is 1.25 times the molar volume of water.33 The general heat balance is given by
nCO2(hg)(t )(−ΔHhg) = nn‐tetra(t )ΔHe
where ΔHhg is the molar hydration heat, ΔHe is the molar enthalpy change of solid n-tetradecane, and nn‑tetra(t) denotes the number of moles of melted liquid n-tetradecane at time t. In the following equation, x expresses the solubility (molar fraction) of carbon dioxide in n-tetradecane x=
nCO2(o)(t ) + nn‐tetra(t )
(4)
where x was calculated with the Peng−Robinson equation. In eqs 1−4, there are four variables, namely, nCO2(o)(t), nn‑tetra(t), nCO2(hg)(t) , and nT(t). Therefore, we combined In eqs 1−4 to obtain the number of moles of carbon dioxide encapsulated in hydrate at time t, nCO2(hg)(t), expressed as nCO2(hg)(t ) =
nMFC(t ) − nMFM(t ) 1+
x 1−x
(
−ΔHhg ΔHe
)−
0.25PNMW ZRTρW
(5)
To compare the numbers of moles of carbon dioxide absorbed by liquid n-tetradecane and encapsulated in hydrate, a simple calculation was performed. It was found that, in the experimental pressure range, 0.73−0.89 mol of CO2 dissolved into liquid n-tetradecane for each 1 mol of hydrate formed. This means that the quantity of CO2 encapsulated in the hydrate was greater than the amount absorbed by liquid n-tetradecane.
3. RATE LAW The CO2 hydration rate is defined as rhg =
1 dnCO2(hg)(t ) VW,0 dt
(6)
where VW,0 is the initial volume of water in the slurry. 3.1. Model of Transport in Hydration. Hydrate formation is similar to crystallization generally, which is controlled by the crystallization kinetics.25 The nucleation of CO2 hydrate crystals can be induced by the solid n-tetradecane particles, and the growth of these crystals can be accelerated by the direct removal of heat through the phase change of the solid n-tetradecane particles. A brief schematic of the hydration process is presented in Figure 2. According to eq 3, the relative rates of the fusion of solid n-tetradecane (re) and the hydration of CO2 (rhg) can be expressed as
(1)
⎛ −ΔHhg ⎞ re = ⎜ ⎟rhg ⎝ ΔHe ⎠
0.25nCO2(hg)(t )PNMW ZRTρW
nCO2(o)(t ) 35
where nT(t) denotes the total number of moles of carbon dioxide transferred from the gas to the liquid bulk at time t, nCO2(hg)(t) denotes the number of moles of carbon dioxide encapsulated in hydrate at time t, and nCO2(o)(t) denotes the number of moles of carbon dioxide absorbed by liquid n-tetradecane at time t. Furthermore, nT(t) can be calculated as
n T(t ) = nMFC(t ) − nMFM(t ) +
(3)
(7)
Thus, the hydration rate of CO2, rhg, can be expressed as the total transfer rate of CO2 from the gas to the liquid bulk, rT, minus the x rate of the absorption of CO2 by liquid n-tetradecane, 1 − x re , resulting in the expression x rhg = rT − re (8) 1−x
(2)
where nMFC(t) denotes the number of moles of carbon dioxide piped into the hydrator through the MFC at time t; nMFM(t) denotes the number of moles of carbon dioxide piped out of the hydrator through the MFM at time t; P and T are the experimental pressure and temperature, respectively; N is the hydration number of CO2 hydrate; MW and ρW are the molar weight and density, respectively, of water; and R and Z are the universal gas constant and the compressibility factor calculated using the P−T equation of state, respectively.34 In eq 2, the third term on the right-hand side expresses the volume shift of the vapor taking the molar volume change during the
The rate of CO2 transfer from the gas to the liquid bulk is given by sat b rT = k TAg − W (c W − cW )
C
(9) DOI: 10.1021/acs.energyfuels.6b03477 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 3. Analog electrical circuit of hydrate growth.
R hg =
⎡ x ⎛ −ΔHhg ⎞⎤ 1 R g − W = ⎢1 − ⎜ ⎟⎥ ⎢⎣ 1 − x ⎝ ΔHe ⎠⎥⎦ k TAg − W
where kT is the mass-transfer coefficient of CO2 absorbed in the bulk liquid, Ag−W is the gas−water interface area per unit volume of water, csat W is the saturated concentration of CO2 in water, and cbW is the CO2 concentration in the bulk water. csat W can be expressed as f (T , P exp) cW H(T , P exp)
where cW is the concentration of pure water; the fugacity of carbon dioxide, f, can be calculated using the Peng−Robinson equation of state;35 and Henry’s law constant, H, was reported by Anderson.29 As shown in Figure 2, an ultrathin diffusion layer surrounding the hydrate crystal limits the formation rate of CO2 hydrate, so the hydration rate can be expressed as b eq rhg = k hgA p(c W − cW )
(11)
ceq W
where khg is the global hydrate growth rate coefficient; is the CO2 concentration near the hydrate;30 and Ap is the surface area of hydrate particle per unit volume of water, which is given by (12)
A0p
where is the initial surface area of the hydrate nuclei per unit volume of water, X is the water conversion to hydrate, and j is an exponent. By combining eqs 7−12, the variable cbW in eq 11 can be substituted, and eq 11 can be transformed as follows rhg =
sat eq − cW cW
1 khgA p0(1 + X ) j
⎡ + ⎢1 − ⎣
x 1−x
(
−ΔHhg ΔHe
⎤ 1 ⎥⎦ k TA g−W
)
sat rhg = kac W (P , T )(1 − X )z − kdX q
(13)
U R overall
4. RESULTS AND DISCUSSION 4.1. Model of Transport in Hydration. 4.1.1. Number of Moles of CO2 Consumed during Hydrate Formation. The effects of the PCS composition [ i.e., different mass fractions of n-tetradecane (φ) and water (φW)] and the experimental pressure on CO2 hydrate formation were investigated. As shown in Figure 5, CO2 hydrate formation in PCSs of 25−45 wt % n-tetradecane was measured at 2.3 MPa. It was found that an increase in the n-tetradecane mass fraction increased the number of moles of CO2 consumed during hydrate growth and that the
(14)
with sat eq U = cW − cW
(15)
R overall = R hg + R g − W
(16)
(19)
where ka and kd are the formation rate constant of CO2 molecules adsorbed in the empty hydrate lattice and the disappearance rate constant of CO2 molecules desorbed from the hydrate, respectively, and z and q are exponents.
To simplify the mathematical model of transport, the masstransfer resistances were assigned to each continuous masstransfer process as for an electrical circuit. As a result, the hydrate growth can be represented as an analog electrical circuit, as shown in Figure 3. Equation 13 can be simplified as I = rhg =
(18)
where Roverall is the overall resistance, Rhg is the resistance near a hydrate particle, R0hg is the initial resistance near a hydrate nucleus, and Rg−W is the resistance at the gas−liquid interface. 3.2. Model of Reversible Hydration. Currently, most available thermodynamic models for predicting V−L−H equilibria are modifications based on the van der Waals− Platteeuw (vdW−P) model. In the vdW−P model,36 similarities between the hydrate formation process and the physical adsorption process are assumed. Although some other thermodynamic models for hydrate formation have been proposed7,37 and hydrate formation is regarded as a multistep processes, it has also been confirmed that the occupation of empty hydrate lattice sites by gas molecules is a critical step. In the work of Sugaya and Mori,38 it was found that, depending on the saturation conditions of the gas molecules, the hydrate morphology can convert during the hydration process. Hydrate growth undergoes a dynamic equilibrium: that is, in unsaturated water, the hydrate tends to decompose, whereas in saturated water, hydrate tends to form. According to our small-scale hydration measurements, in the case of disperse PCSs under strong agitation, a satisfactory hydration homogeneity can be achieved. Thus, based on the similarities between hydrate growth and physical adsorption, in our second mathematical model, we assumed that hydrate growth can be modeled as a reversible hydration process. A simplified model of hydrate growth is depicted in Figure 4. In this case, the CO2 hydration rate is given by
(10)
A p = A p0(1 + X ) j
(17)
and
Figure 2. Brief schematic of the hydration of CO2.
sat cW =
1 0 = R hg (1 + X )−j k hgA p0(1 + X ) j
D
DOI: 10.1021/acs.energyfuels.6b03477 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 6. Experimental and modeled numbers of moles of CO2 consumed during hydrate formation at different pressures as functions of time (T = 277.6 K, φ = 35 wt %, agitation speed = 450 rpm), modeled by eq 13. Figure 4. Simplified model of hydrate growth as reversible hydration.
Table 1. Summary of Modeled Parameters Rg−W, R0hg, and j for cc
durations of the three measurements were approximately 13− 15 min. Figure 6 shows the CO2 hydrate growth at 2.1−2.4 MPa
φ P run (wt %) (MPa) 1 2 3 4 5 6
45 35 25 35 35 35
2.3 2.3 2.3 2.4 2.2 2.1
Rg−W (min)
R0hg × 103 (min)
j
R2
0.163 0.409 0.536 0.539 0.304 0.178
7.56 1.63 1.48 0.48 0.27 0.43
−25.4 −41.7 −53 −47 −53.4 −49
0.988 0.996 0.999 0.998 0.997 0.998
induction time (min) ≤1
PCS and the experimental pressure, respectively, on the resistance near a hydrate particle. As shown in Figure 7, when the mass fraction of water in the PCS was increased, the initial resistance near the hydrate nuclei, R0hg, tended to decrease. This means that the hydrate growth was relatively easy to initiate; however, the absolute value of the exponent |j| increased correspondingly, which indicates that the variation in Rhg during hydrate growth became greater as the water content was increased. As a result, it was concluded that an increase in the water content of the PCS is not conducive to the continuation of hydrate growth. Figure 8 shows the influence of experimental pressure on Rhg. As can be seen, the initial resistance near the hydrate nuclei, R0hg, and the exponent j were found to be essentially constant at different experimental pressures. Therefore, it can be concluded that the resistance near the hydrate particles, Rhg, is mainly affected by the water content in the PCS. 4.1.3. Resistance at the Gas−Liquid Interface, Rg−W. Figure 9 shows the change in the resistance at the gas−liquid interface, Rg−W, as a function of the mass fraction of water in the PCS and the experimental pressure. Rg−W became greater as the water content in the PCS increased, because the quasisteady state in the PCS was more difficult to maintain during hydrate growth. Meanwhile, when the driving force was increased by increasing the experimental pressure, the mass-transfer resistance at the gas−liquid interface increased accordingly. The variation in Rg−W with the mass fraction of water in the PCS and the experimental pressure could be fitted using the equation
Figure 5. Experimental and modeled numbers of moles of CO2 consumed during hydrate formation in different PCSs as functions of time (T = 277.6 K, P = 2.3 MPa, agitation speed = 450 rpm), modeled by eq 13.
observed in the PCS with 35 wt % n-tetradecane. For all measurements, the number of moles of CO2 consumed during hydrate growth increased accordingly when the experimental pressure, that is, the driving force, was increased, and the duration of hydration was approximately 15 min. In addition, the agitation speed was selected as 450 rpm for all runs. It was also found that the induction time before the initiation of hydrate growth was less than 1 min under all conditions. Based on the model of transport in hydration in eq 13, the measurements of hydrate formation under all conditions were modeled. The modeling results are summarized in Table 1 and presented in Figures 5 and 6. As the modeling results show, the description of CO2 hydrate formation in PCSs by the model of transport in hydration was found to be satisfactory. 4.1.2. Resistance near a Hydrate Particle, Rhg. Figures 7 and 8 show the effects of the mass fraction of water (φW) in the
R g − W = 1.19P − 5.16 × 10−2φW −3 − 2.03 E
(20)
DOI: 10.1021/acs.energyfuels.6b03477 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 7. Influence of the mass fraction of water in a PCS on the resistance near a hydrate particle (Rhg).
Figure 8. Influence of the experimental pressure (P) on the resistance near a hydrate particle (Rhg).
to eq 19. The modeling results are summarized in Table 2 and presented in Figures 10 and 11. As shown in Figures 10 and 11, the data on CO2 hydration were regressed better when the process was treated as reversible hydration than when the process was modeled based on transport in hydration. According to the modeling results in Table 2, good agreement between the experimental measurements and modeling results was obtained under all conditions, when the exponents z and q were determined as 0.82 and 1, respectively. Figures 12 and 13 show the effects of the experimental conditions on the formation rate constant of CO2 molecules adsorbed Table 2. Summary of Modeling Parameters ka, kd, z, and q for All Measurements
Figure 9. Effects of the mass fraction of water in a PCS and the experimental pressure (P) on the resistance at the gas−liquid interface (Rg−W).
where φW is the mass fraction of water in the PCS. 4.2. Model of Reversible Hydration. The measurements of hydrate formation were regressed in a reversible way according F
run
φ (wt %)
P (MPa)
ka (min−1)
kd × 10−3 (mol m−3 min−1)
z
q
R2
1
45
2.3
0.625
2.28
0.82
1
0.994
2
35
2.3
0.355
1.797
0.82
1
0.999
3
25
2.3
0.286
1.672
0.82
1
0.997
4
35
2.4
0.364
1.642
0.82
1
0.998
5
35
2.2
0.358
1.731
0.82
1
0.998
6
35
2.1
0.354
1.581
0.82
1
0.997
DOI: 10.1021/acs.energyfuels.6b03477 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 10. Experimental and modeled numbers of moles of CO2 consumed during hydrate formation in different PCSs as functions of time (T = 277.6 K, P = 2.3 MPa, agitation speed = 450 rpm), modeled by eq 19.
Figure 13. Effects of the mass fraction of n-tetradecane in the PCS and the experimental pressure (P) on the disappearance rate constant (kd).
Figure 11. Experimental and modeled numbers of moles of CO2 consumed during hydrate formation at different pressures as functions of time (T = 277.6 K, φ = 35 wt %, agitation speed = 450 rpm), modeled by eq 19.
Figure 14. CO2 hydration rate rhg as a function of time measured in different PCS (T = 277.6 K, P = 2.3 MPa, agitation speed = 450 rpm).
Figure 12. Effects of the mass fraction of n-tetradecane in the PCS and the experimental pressure (P) on the formation rate constant (ka).
Figure 15. CO2 hydration rate rhg as a function of time measured at different pressures (T = 277.6 K, φ = 35 wt %, agitation speed = 450 rpm). G
DOI: 10.1021/acs.energyfuels.6b03477 Energy Fuels XXXX, XXX, XXX−XXX
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Table 3. Comparison of Average Hydration Rate, Hydration Duration, and Induction Time between the Present Work and Previous Works conditions of hydrate formation
average hydration rate (mol m−3 min−1)
hydration duration (min)
induction time (min)
ref
2.3 MPa, 450 rpm, 45 wt % o/w PCS, semibatch 2.5 MPa, 500 rpm, pure water, semibatch with Dispersimax 3.5 MPa, 277.2 K, pure water, porous media 3.25 MPa, 500 rpm, pure water, semibatch 3 MPa, pure water, circulation flow loop
197 7.5 0.64 8 25.4
13 ≥180 5400 60 60
≤1 180 360 40 35
this work 19 39 40 41
in the empty hydrate lattice, ka, and the disappearance rate constant of CO2 molecules desorbed from the hydrate, kd, respectively. It can be seen that ka and kd are mainly related to the properties of the PCS and are essentially independent of the selection of experimental pressure. With more of the phasechange material (PCM) n-tetradecane in the PCS, the hydrate growth was enhanced through improvements in the formation rate constant, ka, and the disappearance rate constant, kd. Consequently, the description of CO2 hydrate formation in PCSs by the model of reversible hydration was substantially satisfied owing to the definite similarities between hydrate growth and physical adsorption. 4.3. Effects of Pressure and Slurry Composition on the Hydrate Formation Rate. The CO2 hydration rate, rhg, was measured under different conditions. Figure 14 shows the influence of the addition of n-tetradecane to the PCS on the hydration rate. Through a comparison of the CO2 hydration rates in PCSs with different mass fractions of n-tetradecane, it was verified that the addition of n-tetradecane had a significant effect on the promotion of the hydration rate. Higher hydration rates were obtained in PCSs containing more n-tetradecane, and the average hydration rate in the PCS with 45 wt % n-tetradecane reached 1.97 × 102 mol m−3 min−1. Figure 15 shows the influence of experimental pressure on the hydration rate; as can be seen, increasing the experimental pressure was found to be conducive to increasing the hydration rate, although the effect was not that significant owing to the selected 0.1 MPa increment in pressure. To compare the hydration process used in this work with those reported in the literature, the average hydration rate, hydration duration, and induction time are listed in Table 3. The hydration durations were approximately 15 min in this work compared to several hours or days for other proposed methods, meaning that the hydration rate was effectively enhanced. The maximum average hydration rate in the PCS with 45 wt % n-tetradecane reached 1.97 × 102 mol m−3 min−1, which is 26 times that reported in ref 19 and 308 times that reported in ref 39. Moreover, the induction time was also markedly reduced. Based on their advantages, PCSs are promising for the extension of CO2 capture based on hydrate formation, even in large-scale industrial applications.
Meanwhile, the experimental measurements were regressed well with both a model of transport in hydration and a model of reversible hydration. With a resistance assigned to each continuous mass-transfer process, the model of transport is beneficial for the analysis of the impacts of different factors on the hydration process. Through the simplified format of an analog circuit for hydrate growth, the practicality can be promoted greatly by establishing a database of resistances in industrial applications. However, better modeling agreement was obtained using the model of reversible hydration than the model of transport in hydration, and the former provides a better description of the CO2 hydration process according to our experimental measurements. Both of the mathematical models were relatively simplified and were capable of predicting the CO2 hydration process to some extent. Based on the modeling results, the descriptions for CO2 hydrate formation in PCSs are satisfied, and the two models are promising for industrial applications of CO2 capture.
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AUTHOR INFORMATION
Corresponding Author
*Tel.: +86 22 27409533. E-mail:
[email protected]. ORCID
Bin Chen: 0000-0002-2501-2804 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Basic Research Program of China (973 Program, No. 2012CB215005).
5. CONCLUSIONS The CO2 hydrate formation process in PCSs of n-tetradecane was studied in a semibatch hydrator. As the experimental results demonstrate, solid n-tetradecane particles as the phase-change material contribute significantly to the enhancement of CO2 hydration. Using a PCS of n-tetradecane, the hydration duration can be reduced greatly to 13−15 min, and the hydration rate can also be improved markedly compared to that in pure water. Under all of the experimental conditions tested, the induction time was less than 1 min.
ABBREVIATIONS CP = cyclopentane DTAC = dodecyl trimethylammonium chloride HBCC = hydrate-based CO2 capture HBCS = hydrate-based CO2 separation MFC = mass flow controller MFM = mass flow meter PCE = phase-change emulsion PCS = phase-change slurry SDS = sodium dodecyl sulfate sodium salt TBAB = tetrabutylammonium bromide THF = tetrahydrofuran Tween-80 = polyoxyethylene sorbitan monooleate V−L−H = vapor−liquid−hydrate
List of Symbols
A = surface area per unit volume of water (m2 m−3) c = concentration (mol m−3) f = fugacity (MPa) H = Henry’s law constant (MPa) j = exponent in eq 12
H
DOI: 10.1021/acs.energyfuels.6b03477 Energy Fuels XXXX, XXX, XXX−XXX
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k = rate coefficient M = molecular weight (kg mol−1) N = hydration number P = pressure (MPa, gauge) q = exponent in eq 19 r = rate (mol min−1 m−3) R = universal gas constant (J mol−1 K−1) Ri = resistance of component i (min) t = time (min) T = temperature (K) V = volume (m3) x = molar fraction X = water conversion z = exponent in eq 19 ΔH = molar enthalpy change (kJ mol−1) ρ = density of water (kg m−3) φ = mass fraction of n-tetradecane in slurry (wt %) φW = mass fraction of water in slurry (wt %) Superscripts and Subscripts
0 = initial state when hydrate growth begins a = hydrate formation b = liquid bulk d = hydrate disappearance e = fusion of a solid particle of n-tetradecane eq = equilibrium g−W = gas−liquid interface hg = hydrate growth MFC = mass flow controller MFM = mass flow meter n-tetra = n-tetradecane o = oil (liquid n-tetradecane) overall = overall resistance p = particle sat = saturated T = total amount of CO2 transferred W = water
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