Numerical simulations of bubble behavior and mass transfer in CO2 capture system with ionic liquids

Chemical Engineering Science 135 (2015) 76–88

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Numerical simulations of bubble behavior and mass transfer in CO2 capture system with ionic liquids Di Bao a,b, Xin Zhang a,b, Haifeng Dong a, Zailong Ouyang a,b, Xiangping Zhang a, Suojiang Zhang a,n a Beijing Key Laboratory of Ionic Liquids Clean Processing, State Key Laboratory of Multiphase Complex System, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China b College of Chemistry and Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

H I G H L I G H T S








The The The The The

bubble behavior and mass transfer in IL-CO2 systems are numerical simulated. CFD method is improved by considering IL viscosity change during absorption. pressure gradient field analysis is applied to explain the bubble coalescence. CO2 mass transfer is kinetic-controlled in pure IL systems. CO2 mass transfer is thermodynamic-controlled in aqueous IL systems.

art ic l e i nf o

a b s t r a c t

Article history: Received 9 January 2015 Received in revised form 25 May 2015 Accepted 8 June 2015 Available online 24 June 2015

Ionic liquids (ILs) have exhibited excellent performance on CO2 capture. However, the lack of research on transport properties has become a bottleneck of industrial application. In order to understand the bubble behavior and mass transfer performance in CO2 capture systems with ILs, a computational fluid dynamics (CFD) method with two improvements is developed in this paper. One improvement is that a drag force equation suitable for IL systems is introduced into the hydrodynamics model, and the other one is that the influence of CO2 concentration in liquid phase on viscosity of ILs is considered in the mass transfer model. Based on the developed CFD method, the bubble behavior and mass transfer properties are accurately described. The simulation results of bubble diameter, velocity and aspect ratio agree well with the experimental data with the overall deviation of 7.52%, 12.17% and 5.17%, respectively. The bubble coalescence phenomenon is illustrated by pressure gradient field analysis rather than conventional pressure field analysis, which can represent the drag force and lift force directly. The simulation results also show that the CO2 mass transfer is kinetic-controlled in pure ILs and thermodynamic-controlled in aqueous ILs, respectively. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Computational fluid dynamics (CFD) Bubble behavior Coalescence Mass transfer Ionic liquid

1. Introduction As potential green solvents, ionic liquids (ILs) have gained increasing attention in recent years (Hallett and Welton, 2011; Plechkova and Seddon, 2008). Different from traditional organic solvents, ILs consist of cation and anion, which present unique properties, such as low melting point, high thermal stability, negligible vapor pressure and designable physicochemical characteristics. Due to these reasons, ILs show considerable potentials for industrial application in gas separation, especially CO2 capture

n

Corresponding author. Tel./fax: þ 86 10 8254 4875. E-mail address: [email protected] (S. Zhang).

http://dx.doi.org/10.1016/j.ces.2015.06.035 0009-2509/& 2015 Elsevier Ltd. All rights reserved.

(Kenarsari et al., 2013; Zhang et al., 2012b). Since Blanchard et al. (1999) first reported that CO2 possesses high solubility in [bmim] [PF6], extensive research has been carried out on designing new ILs (Bates et al., 2002; Zhang et al., 2013, 2009), aiming at overcoming some inherent defects such as high viscosity (Jiang et al., 2008; MacFarlane et al., 2001), high cost and poor mass transfer property (Morgan et al., 2005; Shiflett and Yokozeki, 2005). The recent research on ILs mostly focuses on the thermodynamic properties. However, the transport properties of IL-CO2 system, such as the bubble behavior and interfacial mass transfer have been lagged out, which become a bottleneck of industrial application of ILs. The transport properties of gas–liquid systems are usually studied through two methods, i.e., experiment method and computational fluid dynamics (CFD) method. As a common

D. Bao et al. / Chemical Engineering Science 135 (2015) 76–88

method, experiment provides reliable but limited information on bubble behavior, such as bubble size, velocity and shape. And our group has been working on bubble behavior in ILs in recent years (Dong et al., 2010; Zhang et al., 2014b, 2012a). Besides bubble behavior, the CO2 concentration distribution in the liquid phase in bubble column is also important for industrial scale-up. Therefore, researchers performed several experiments (Francois et al., 2011; Someya et al., 2005; Stöhr et al., 2009) to determine concentration distribution of the solute around a single bubble directly, and O2 was chosen as gas phase because of its oxidization on the fluorescent dye. But these methods are still difficult due to their limitations, such as the synthesis of fluorescent dye, using O2 as gas phase and its sensitivity to both gas and liquid. Thus, such experiments are not appropriate for mass transfer in IL-CO2 systems, and new method should be developed to investigate the CO2 concentration distribution in IL systems. Different from experimental measurement, CFD technique provides another effective method to study the transport properties (Ganapathy et al., 2013; Ganguli and Kenig, 2011; Khinast et al., 2003; Koynov et al., 2005), which overcomes the inherent difficulties of determining the flow field and concentration distribution around the bubbles by experiment. Some hydrodynamics models (Worner, 2012) were developed to simulate the bubble behavior, among which the volume-of-fluid (VOF) method (Hirt and Nichols, 1981) coupled with surface tension model (Brackbill et al., 1992; Lafaurie et al., 1994) was frequently used. The main reason is that the VOF method is appropriate in simulating bubble motion (Ma et al., 2012; Zhang et al., 2012c) and bubble coalescence (Islam et al., 2014; Liu et al., 2014), especially the cases with interfacial mass transfer (Zhu et al., 2011). Moreover, the bubble coalescence phenomenon can be explained by analyzing velocity field or pressure field. In the analysis of velocity field (Fan and Yin, 2013; Farhangi et al., 2010), the wake hypothesis is usually adopted to explain the coaxial bubble coalescence. Comparing with velocity field, the pressure field (Lin and Lin, 2009; Sanada et al., 2005) provides information on driven forces of bubbles. Besides the hydrodynamics model, the mass transfer model should be established to simulate the interfacial mass transfer phenomena. The mass transfer coefficient, a necessary parameter in the mass transfer model, should be measured before performing the simulation. However, the mass transfer coefficient is difficult to measure by experiment using a bubble column directly. Therefore, empirical or semi-empirical correlations (Akita and Yoshida, 1973; Ozbek and Gayik, 2001) were developed to calculate the mass transfer coefficient. In detail, the Sherwood number Sh, which is proportional to the mass transfer coefficient, is usually correlated as a function of Reynolds number Re and Schmidt number Sc. The involved parameters in Re and Sc, such as the bubble diameter and velocity, could be easily obtained by solving the hydrodynamics model. Thus, the mass transfer coefficient can be obtained through the above correlations and applied in the mass transfer model. However, the works related to CFD mostly focus on the traditional solvents, few research (Wang et al., 2010) was done on ILs, and the interfacial mass transfer of single bubble in ILs was never discussed. Especially, the effect of viscosity reduction of ILs after absorbing CO2 (Ahosseini et al., 2009; Tomida et al., 2007) has not been considered in the CFD method, which limits the understanding of bubble behavior and CO2 mass transfer in IL systems. In our previous work (Wang et al., 2010), the single bubble behavior in ILs was simulated, and a drag force source term which shows advantages on bubble velocity prediction was proposed. Based on the previous work, CO2 bubble coalescence and interfacial mass transfer in ILs are further simulated in this work. In order to simulate the bubble behavior and CO2 mass transfer in IL systems accurately, a new CFD method suitable for IL systems is developed. In this method, the IL-based drag force model and

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correlations of mass transfer coefficient are employed, and the viscosity of IL is considered as a function of the dissolved CO2 concentration. In order to verify this method, the bubble diameter, velocity and aspect ratio are measured experimentally by using high speed image pick-up system and compared with the simulation results. Then, the effects of pressure, temperature and water content on the bubble behavior and CO2 mass transfer properties are investigated based on the new method. In detail, the bubble behavior, such as the bubble velocity and coaxial bubble coalescence in different IL systems, is investigated through simulation, and the bubble coalescence phenomenon is explained by a new method of pressure gradient field analysis. The CO2 mass transfer properties, such as the CO2 mass transfer rate, mass flux and the CO2 concentration distribution, are predicted using the developed method in this work.

2. Methodology The numerical simulations on the bubble behavior and mass transfer properties in IL-CO2 systems are performed. These simulations are carried out with the following basic assumptions: 1) Both gas and liquid phase are considered as incompressible fluid. 2) The liquid density, viscosity and surface tension, as well as the gas viscosity, are regarded as pressure-independent physical properties. 3) The system temperature is assumed constant, and the absorption heat of interfacial CO2 mass transfer is ignored. 4) As the dissolved CO2 in ILs decreases the liquid viscosity obviously, the liquid viscosity is regressed as a function of liquid phase CO2 concentration (Ahosseini et al., 2009). Based on these assumptions above, the CFD models are established with the following improvements: 1) A bubble drag force model (Wang et al., 2010) suitable for IL systems is introduced to the momentum equation. 2) The mass transfer coefficients of CO2 in IL systems are correlated using the data in literature (Zhang et al., 2014a), and then the correlations are introduced to the CO2 mass fraction transport equation. 3) The liquid viscosity is considered as a variable, which is calculated by a function of CO2 mass fraction in liquid phase. With these improvements, the simulations are performed by solving the Navier–Stokes equations, i.e., the continuity and momentum equations, the VOF equation and the CO2 mass fraction transport equation. Fig. 1 shows the simulation procedure of this work and its differences from conventional CFD method. 2.1. Governing equations Based on the above assumptions and improvements, the governing equations are established as follows. First, the continuity and momentum equations for the incompressible two-phase flow can be written as
 ! ∇U ρ v ¼ 0 ð1Þ   
 ∂
! !! ! !T ! ! ρ v þ ∇ ρ v v ¼  ∇P þ ∇ μ ∇ U v þ ∇ U v þ ρ g þ F sf ∂t ! þ F LG

ð2Þ ! ! where v is the velocity vector and P is the pressure. F sf stands

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The drag force source term is defined as follow, which is based on our previous work (Wang et al., 2010). !! 2f ρg v v ! F LG ¼ ð7Þ db where f is the friction factor and db is the equivalent bubble diameter. The above source term is valid just in the cells containing the interface between gas and liquid. The friction factor f in the above equation is represented as ( 1 þ 0:15Re0:687 Re r 1000 f¼ ð8Þ 0:0183Re Re 4 1000 where Re is the Reynolds number of the bubbles. The mass fraction of CO2 dissolved in IL is solved by a scalar transport equation, which can be written as
     ∂ ! αl ρl ω þ ∇ U αl ρl ω v ¼ ∇ U Dl ∇ αl ρl ω þ SLG ð9Þ ∂t where ω is CO2 mass fraction in liquid phase, and SLG is the mass transfer source term which involves the gas–liquid interfacial mass transfer. For IL-CO2 systems, SLG can be defined as   ð10Þ SLG ¼ kl a M g cI  ρl ω where kl is the liquid-side mass transfer coefficient in IL systems, which is obtained from experiments; a is the specific interfacial area of the bubble; M g is the molecular mass weight, and for CO2 it is 0.044 kg mol  1; cI is molecular concentration of CO2 at the gas– liquid interface. At the interface, cI is the CO2 concentration at equilibrium, which can be calculated by the Henry’s law: cI ¼

Fig. 1. Framework of simulation procedure (n refers the differences compared with the conventional CFD method).

! for the surface tension source term, and F LG represents the drag force source term. The fluid density ρ and viscosity μ in the above equations are defined as follows X X ρ¼ αq ρq μ¼ αq μq ð3Þ q

q

where α is the volume fraction, and the subscripts q ¼ l ; g represent liquid phase and gas phase, respectively. The VOF method (Hirt and Nichols, 1981) is a flexible and efficient approach to the fluid–fluid interface tracking. In VOF method, the volume fraction equation is solved, which is represented as
 ∂  ! α q þ ∇ U αq v ¼ 0 ∂t

ð4Þ

For two phase flow, the volume fraction of both gas and liquid phase obey the following expression: αg þαl ¼ 1

ð5Þ

where αg and αl are the volume fractions of the gas and liquid phase, respectively. The continuum surface stress (CSS) model (Lafaurie et al., 1994) is employed to define the surface tension source term, which can be written as    ! ∇α  ∇α F sf ¼ ∇ U σ j∇αjI  j∇αj

ð6Þ

P KH

ð11Þ

where K H is the Henry’s constant of CO2 in IL systems. The CO2 diffusion coefficient in ILs Dl is calculated by Wilke– Chang equation (Wilke and Chang, 1955), which is defined as follows: pffiffiffiffiffiffiffiffiffi 7:4  10  12 φM l T Dl ¼ ð12Þ μl V g 0:6 where φ is an association factor that equals 0.15 for imidazoliumbased ILs according to Morgan et al. (2005)’s work. M l is the average molecular weight of IL systems. V g is the molecular volume of the gas at boiling point, and for CO2 V g equals to 34 cm3 mol  1. As the CO2 dissolved in ILs decreases the liquid viscosity significantly, the viscosity is set to be a function of CO2 mass fraction in liquid phase. The liquid viscosity is given by (Arrhenius, 1887):       ln μl ¼ ωln μCO2 þ ð1  ωÞln μIL ð13Þ where μIL is the viscosity of the IL system without CO2 dissolved in it, and μCO2 is the viscosity of CO2, which equals to 0.0137 mPa s. 2.2. Model geometry and solution strategies The cylindrical bubble column is simplified as a rectangle with 40 mm width and 80 mm height. The 2D geometry model is built with the mesh number of 100,000 which gives satisfactory simulation results. The bubbles are generated from a single vertical orifice, which is the gas inlet with 0.5 mm diameter at the bottom of the column. The rest of the bottom is specified as liquid velocity inlet with a velocity of zero. The gas inlet is set as velocity inlet with a gas velocity of 0.21 m s  1, and the pressure outlet with backflow of ILs is applied for the top of the column. In order to eliminate the influence of unconcerned bubbles, the supply of CO2 at the orifice is stopped after the bubble detachment. No-slip wall boundary condition is employed to specify the

D. Bao et al. / Chemical Engineering Science 135 (2015) 76–88

two sides of the column. The pressure, gas and liquid velocities and the volume fraction of the gas phase are initialized with a value of zero. The VOF model is employed to simulate the multiphase flow in bubble column, and explicit scheme is applied to solve the volume fraction equation. The pressure–velocity coupling method is SIMPLE scheme, and a body force weighted scheme is used for pressure discretization. The flow equations are discretized with QUICK scheme, which can provide high accuracy, and the CO2 mass fraction equation is discretized with the first order upwind scheme due to its high stability. The iteration time step is set as 1.0  10  4 s. The numerical simulation was performed with the CFD software FLUENT 6.3.2. A pressure-based time-dependent solver provided by FLUENT is applied to solve the equations. The drag force and surface tension source term for momentum equation, the mass transfer source term for CO2 mass fraction transport equation, and the liquid viscosity equation are implemented into the software by User Defined Functions (UDF).

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3.3. Experiment and model validation In order to verify the models, several experiments are carried out using a bubble column employed by our group previously (Dong et al., 2010; Zhang et al., 2014b). The CO2 gas is supplied with a linear velocity of 0.21 m s  1, though an orifice of 0.5 mm inner diameter at the bottom of the bubble column. Detailed experiment procedures and image analysis methods can be seen in our previous work (Dong et al., 2010; Zhang et al., 2014b). The simulation results of bubble size, velocity and aspect ratio are compared with the experiment results. The comparisons are presented in Table S3 in Electronic Supplementary information. The average relative errors of bubble diameter, velocity and aspect ratio are 7.52%, 12.17% and 5.17%, respectively, which means that the models are valid for ILs-CO2 systems. Furthermore, the bubble diameter and velocity at elevated pressure can be predicted by simulations using the developed method.

4. Results and discussion 3. Improvement and validation of numerical models 4.1. Bubble velocity and bubble coalescence 3.1. Physical properties measurement Three pure ILs ([bmim][BF4], [omim][BF4], [bmim][NO3]) and two aqueous ILs (95 wt% [bmim][BF4] þ5 wt% water and 90 wt% [bmim][BF4]þ 10 wt% water) are chosen as the liquid phase. The densities, viscosities and surface tensions of the IL systems are measured using the method in literature (Zhang et al., 2014b) with a density meter (Anton Paar DMA 5000), an automated microviscometer (Anton Paar AMVn) and a tensiometer (Krüss K100), respectively. The properties of IL systems are shown in Table S1 in Electronic Supplementary information. In addition, the gas densities at different pressure are calculated by the Redlich–Kwang equation. The Henry’s constants of CO2 in IL systems are measured using the method in our previous work (Zhang et al., 2014a), and the data are shown in Table S2 in Electronic Supplementary information. 3.2. Mass transfer coefficient correlation In this work, the liquid-side mass transfer coefficients of CO2 in IL systems are calculated by the following correlation: Sh ¼ aReb Scc

ð14Þ

The above correlation is proposed based on the data reported by our previous work (Zhang et al., 2014a). In order to ensure the physical correctness of the correlations, the parameters b and c were limited in the region from 0 to 1. The parameters for each IL in the above equation are shown in Table 1. It can be seen that for all IL systems, the index of Re equals to 0.5 coincidently, which means the mass transfer coefficient is related to the gas–liquid contact time and physical properties of ILs. It implies that the correlations, which are independent of the structure of reactors, are able to be applied in bubble columns. Moreover, this correlation shows a relatively low standard deviation rather than penetration theory, which is shown in Fig. S1. Thus, the application of Eq. (14) improves the simulation accuracy. Table 1 Parameters of Eq. (14). Ionic liquid

a

b

c

[bmim][BF4] [omim][BF4] [bmim][NO3]

0.1031 0.4818 0.2974

0.5 0.5 0.5

0.6963 0.6036 0.5476

4.1.1. Bubble diameter and bubble velocity The simulated CO2 bubble diameters and terminal bubble velocities in different IL systems are shown in Fig. 2. The results reveal that the bubble diameter, which is mainly affected by the surface tension and liquid viscosity, decreases with the increase of temperature in both pure and aqueous ILs. For pure ILs, the terminal bubble velocity increases significantly when the temperature increases. The main reason is that the liquid viscosity is significantly influenced by temperature. By contrast, the terminal bubble velocity reaches a maximum in the range of temperature from 303 to 343 K in aqueous ILs, which is caused by the difference of bubble diameter. Since the larger bubbles reach higher terminal velocity (Kulkarni and Joshi, 2005), the bubbles aqueous [bmim][BF4] exhibit a higher terminal velocity at 333 K rather than 343 K. Fig. 2(a) also shows that the bubble diameter decreases with the increase of temperature. Comparing with the difference of bubble diameter, the slight difference of liquid viscosity at high temperature does not affect terminal bubble velocity visibly. Therefore, the terminal bubble velocity depends on both bubble diameter and liquid viscosity. However, for most cases, the bubble diameter shows a positive correlation with liquid viscosity (Kulkarni and Joshi, 2005). Thus, the liquid viscosity has both positive and negative effect on terminal bubble velocity. The terminal bubble velocity increases with decreasing liquid viscosity at low temperature, and decreases at high temperature due to the smaller bubble size. The contrast of terminal bubble velocities in pure and aqueous [bmim][BF4] shows that a small amount of water increases the terminal bubble velocity dramatically. Water containing in IL decreases the liquid viscosity significantly, but has little effect on the surface tension. The water changes the structure of the ILs through the water–cation interaction, which weakens the hydrogen-bond in ILs (Mele et al., 2003) and decreases viscosity of ILs. Comparing with pure IL, the weak interaction in aqueous IL reduces caging, which also leads to low viscosity. Therefore, adding a small amount of water, rather than increasing temperature, is a more effective way to decrease the viscosity and increase the bubble velocity. 4.1.2. Coaxial bubble coalescences in pure and aqueous [bmim][BF4] The simulation results reveal that the second bubble generated on the orifice will overtake the first bubble, as shown in the video in Electronic Supplementary Information. A comparison between the bubble coalescence phenomena in pure and aqueous [bmim] [BF4] is carried out by the simulation results. At the beginning, the

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Fig. 2. Temperature effect on (a) bubble diameter and (b) terminal bubble velocity (P¼ 2 MPa).

Table 2 Bubble diameters, velocities and Reynolds numbers during bubble coalescence (T ¼313 K, P ¼2 MPa). Ionic liquid

[bmim][BF4] [omim][BF4] [bmim][NO3] 95 wt% [bmim][BF4] 90 wt% [bmim][BF4]

The first bubble

The second bubble

The merged bubble

Diameter (mm)

Velocity (m s  1)

Re

Diameter (mm)

Velocity (m s  1)

Re

Diameter (mm)

Velocity (m s  1)

Re

2.781 3.573 3.085 2.153 1.983

0.1546 0.1190 0.1439 0.1909 0.2107

8.74 3.24 5.95 33.59 61.95

2.784 3.696 3.090 2.142 1.969

0.1904 0.1450 0.1744 0.2545 0.2639

10.77 4.08 7.22 44.55 77.04

3.935 5.156 4.367 3.081 2.802

0.1728 0.1332 0.1605 0.2276 0.2459

13.82 5.23 9.40 57.31 102.16

two bubbles form at the orifice and rise independently; then the second one accelerates until the bubble coalescence takes place. Finally, the bubbles experience coalescence, and the merged bubble keeps rising like a single bubble. Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.ces.2015.06.035. The bubble coalescence process in pure and aqueous [bmim] [BF4] reveals the disparity between the two cases. The two bubbles keep rising straightly until the bubble coalescence takes place. In pure [bmim][BF4], the merged bubble moves straightly after coalescence; while in aqueous [bmim][BF4], it deforms and experiences horizontal displacement after coalescence. The Reynolds number, an important parameter to describe the flow behavior, is employed to explain this phenomena. The bubbles tend to rise stably at low Reynolds number; when the Reynolds number increases, the bubbles lose stability and experience a plume movement. Table 2 shows the diameters, velocities and Reynolds numbers of the bubbles at the moment exactly before and after coalescence. As shown in the table, the Reynolds number of the merged bubble is larger than that of the bubbles before coalescence. For bubbles in [bmim][BF4] with 10 wt% water, the Reynolds number of merged bubble is 102.16, much higher than those of the two bubbles before coalescence, which are equal to 61.95 and 77.04, respectively. Due to its high Reynolds number, the merged bubble in aqueous [bmim][BF4] exhibits an unstable flow, namely the bubble deformation and plume movement.

4.1.3. Bubble velocity during coaxial bubble coalescence The local velocities of bubbles during bubble coalescence in pure [bmim][BF4] are shown in Fig. 3. The local bubble velocities during coalescence are similar in pure [bmim][NO3] and [omim] [BF4], but different from single bubble velocities. The single bubble

quickly reaches the terminal velocity after a short distance of acceleration (Wang et al., 2010). However, during bubble coalescence, both the two bubbles keep accelerating until the coalescence takes place, which is also observed in non-Newtonian fluid (Frank et al., 2013). Then the merged bubble reaches the terminal velocity after a short distance of deceleration and acceleration. This indicates that the variation of bubble velocity during coalescence is very complex, and the velocity field and pressure field should be analyzed to elucidate this problem.

4.1.4. Velocity field analysis of bubble coalescence Information on velocity field can be helpful for understanding the bubble flow behavior, especially for the bubble coalescence. The velocity field around the single bubble and bubbles during coalescence are shown in Figs. 4 and 5, respectively. As shown in Fig. 4(a), the velocity of the gas in the region above the orifice reaches up to 0.25 m s  1. After contacting the gas–liquid interface, the gas flows back along the side of the bubble. Comparing Fig. 4 (b) with Fig. 5(a) which shows the acceleration of bubbles, the bubble in Fig. 5(a) reaches a higher velocity due to the formation of the second bubble. At the same time, two eddies form on the sides of the detached bubble and a wake region is generated under the bubble. Then the second bubble detaches from the orifice, as shown in Fig. 5(b and c). It is obvious that the velocity of second bubble, as high as 0.22 m s  1 in the center of the bubble, is higher than that of the first bubble. The wake flow of the first bubble plays an important role in this phenomenon. Fig. 5(b) shows that the eddies on the sides of the first and second bubble connect with each other, which is clearly different from the velocity field of around the single bubble shown in Fig. 4 (c). The connection of eddies affects the velocities of both the first and second bubble. As shown in Fig. 5(d), when the second bubble

D. Bao et al. / Chemical Engineering Science 135 (2015) 76–88

touches the first one, the resistance of the liquid between two bubbles disappears. Thus, the gas in the second bubble accelerates to more than 0.25 m s  1, tending to flow towards the sides of the merged bubble. Then the merged bubble shown in Fig. 5 (e) deforms and rises at a constant velocity, which is similar to the single bubble shown in Fig. 4(c). According to the analyses above, the phenomena of bubble formation and coalescence is understood. Nevertheless, how the second bubble affects the motion of the first one is still not clear just with the analyses on velocity field. Thus, the pressure gradient field analysis is proposed and applied in this work to explain the interaction between two axial bubbles, which discussed in Section 4.1.5.

Fig. 3. Local bubble velocity during bubble coalescence in [bmim][BF4] (T ¼ 313 K, P¼ 2 MPa).

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4.1.5. Pressure gradient field analysis of bubble coalescence As the driving force of bubble rising is provided by the pressure gradient, the analysis of pressure gradient field around bubbles is applied to explain the bubble behavior intuitively. Fig. 6 shows the pressure gradient field around the single bubble and bubbles during coalescence. In order to eliminate the influence of the pressure gradient caused by the surface tension, the bubbles which are a bit larger than the actual bubbles are used as shown in Fig. 6. In these figures, the positive value stands for the pressure gradient with a vertical upwards direction, which means the lift force, while the negative value stands for a vertical downwards pressure gradient, i.e. the drag force. Fig. 6(a) shows the pressure gradient field of the single bubble motion at the terminal velocity. It is known that there are three liquid regions providing lift forces and two regions providing drag forces. With these forces, the bubble rises at a constant velocity and keeps its shape. Fig. 6(b–f) shows the pressure gradient field during the bubble coalescence. When the bubbles rise independently, as shown in Fig. 6(b), the two regions under the first bubble connect with the region above the second one. And the merged region provides larger lift forces for both two bubbles. With these enhanced lift forces, both the two bubbles experience an acceleration, and become close to each other. As shown in Fig. 6(c), when the second bubble almost touches the first one, the liquid region between the bubbles, which provides lift forces, gets smaller and disappears. Therefore, the second bubble begins to slow down until the bubble coalescence takes place. The merged bubble deforms and accelerates in a short distance due to the lift forces, which is shown in Fig. 6(d). With the deformation of the merged bubble, a region that provides drag forces forms right under the bubble, as shown in Fig. 6(e). As a result, the merged bubble decelerates in a short distance until the bubble shape is preserved, and then it performs uniform motion as the single bubble does, which is shown in Fig. 6(f).

velocity magnitude (m∙s-1)

Fig. 4. Velocity field around single bubble in pure [bmim][BF4]: (a) t¼ 0.05 s, (b) t¼ 0.1 s, (c) t ¼0.3 s (T ¼ 313 K, P¼ 2 MPa).

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velocity magnitude (m∙s-1)

Fig. 5. Velocity field around bubbles in pure [bmim][BF4]: (a) t¼ 0.1 s, (b) t ¼0.2 s, (c) t ¼0.3 s, (d) t¼ 0.32 s, (e) t¼ 0.4 s (T ¼ 313 K, P¼ 2 MPa).

4.2. CO2 interfacial mass transfer and distribution 4.2.1. Effect of pressure and water content on CO2 mass transfer rate Operating parameters, such as pressure and temperature, have significant influences on both the physical properties of ILs and gas–liquid mass transfer properties. In this work, the physical properties, except the gas density, are set as pressure-independent variables. As a result, the pressure has a significant influence only on the driving force of gas–liquid mass transfer. Fig. 7 shows the quantity of CO2 dissolved in [bmim][BF4] under different pressures. In this figure, linear fits of the data points are shown as the solid lines. The slopes of the lines represent the CO2 mass transfer rate. Due to the remarkable effect of pressure on the mass transfer driving force, which can be inferred from Eq. (10) and Eq. (11), the CO2 mass transfer rate is significantly affected by the operating pressure. The global mass flux of the single bubble is calculated by the following equations: 2

J U πdb ¼

dm dt

ð15Þ

where ðdm=dtÞ is the slope of the lines in Fig. 7. Here, the data collected from detached bubble are adopted to calculate the mass flux. The mass flux of single bubble in IL systems under different

pressure is shown in Fig. 8. As shown in the figure, the mass flux increases with elevated pressure, which is similar to the mass transfer rate. Since the CO2 mass flux is the product of mass transfer coefficient and mass transfer driven force, the increasing of CO2 mass flux at high operating pressure is caused by the increase of mass transfer driven force, which depends on the operating pressure significantly. As shown in Fig. 8, the mass flux of CO2 in [bmim][BF4] increases with the increase of water content due to the high mass transfer coefficient of CO2 in aqueous ILs. The CO2 solubility under different conditions and the average mass transfer coefficients calculated by Eq. (14) are shown in Fig. 9. The results reveal that the solubility decreases and the mass transfer coefficient increases with the increase of water content. Therefore, when the water content changes, the CO2 solubility competes with the mass transfer coefficient to affect the mass flux of CO2. The results shown in Figs. 8 and 9 imply that the mass transfer coefficient dominates the mass flux when the water content increases.

4.2.2. Effect of temperature on CO2 mass flux Similar to the water content, the temperature has an impact on both the mass transfer coefficient and the CO2 solubility. When temperature increases, the CO2 solubility decreases and the mass

D. Bao et al. / Chemical Engineering Science 135 (2015) 76–88

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Vertical pressure gradient magnitude -1

(Pa∙m )

Fig. 6. Pressure gradient field around bubbles in pure [bmim][BF4]: (a) single bubble: t ¼0.3 s; (b)–(f) bubble coalescence, (b) t¼ 0.2 s, (c) t ¼0.3 s, (d) t ¼ 0.32 s, (e) t ¼0.33 s, (f) t ¼0.4 s (T ¼313 K, P¼ 2 MPa).

Fig. 7. Dissolved CO2 in pure [bmim][BF4] at 313 K.

Fig. 8. Effect of pressure on mass flux of single CO2 bubble at 313 K.

transfer coefficient increases. The mass flux, depending on both the solubility of CO2 and the mass transfer coefficient, affected by temperature is shown in Fig. 10. For pure [omim][BF4] and [bmim] [NO3], the mass flux of CO2 increases with raising temperature. As for pure [bmim][BF4], the mass flux increases until the temperature reaches 318 K, and remains steady at higher temperature. It is a result of trade-off between increasing mass transfer coefficient and decreasing CO2 solubility. However, for aqueous [bmim][BF4], the mass flux decreases with raising temperature. The results imply that for pure ILs, the mass transfer coefficient dominates the mass flux under different temperatures; while for aqueous ILs, the CO2 solubility dominates the mass flux. In other words, the CO2 mass transfer is kinetic-controlled in pure ILs and thermodynamic-controlled in aqueous ILs. The results can be ascribed to the fact that the temperature has little impact on the bubble velocity in aqueous ILs and the liquid viscosities which affect the mass transfer coefficient significantly.

Moreover, comparing with the CO2 diffusivity in pure ILs, CO2 diffusivity in aqueous ILs is not sensitive to temperature. As a result, the CO2 solubility, rather than the mass transfer coefficient, has more influence on the mass flux of CO2 in aqueous ILs, which is the reason for the mass flux reduction when the temperature rises. Consequently, although both raising water content and temperature are effective approaches to enhancing mass flux, applying these two methods simultaneously is not a reliable way to maximize the mass flux. In terms of the results shown in Fig. 10, absorbing CO2 with aqueous ILs at low temperature is the optimized strategy for CO2 capture using ILs.

4.2.3. Effect of coaxial bubble coalescence on CO2 mass transfer rate The CO2 interfacial mass transfer during bubble coalescence is simulated. Fig. 11 shows the mass transfer rates during single bubble rising and bubble coalescence in pure [bmim][BF4]. Similar

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Fig. 9. CO2 solubility (a) and mass transfer coefficients (b) in ILs (P¼ 2 MPa).

Table 3 Comparisons of mass transfer rate between single bubble and bubbles coalescence in ILs (T¼ 313 K, P¼ 2 MPa). Ionic liquid

[bmim][BF4] [omim][BF4] [bmim][NO3]

Fig. 10. Effect of temperature on mass flux of single CO2 bubble at 2 MPa.

Fig. 11. Comparison of mass transfer rate between single bubble rising and bubble coalescence in [bmim][BF4] (T ¼ 313 K, P¼ 2 MPa).

results can be obtained in pure [bmim][NO3] and [omim][BF4]. The vertical coordinates represent the quantity of dissolved CO2 in liquid phase. The slope of the points stands for the average mass transfer rate, which is shown in Table 3. The horizontal coordinate

Mass transfer rate  106 (kg s  1) Before coalescence

After coalescence

Single bubble

13.90 10.60 2.83

6.75 5.01 1.34

6.82 4.95 1.37

of the vertical dotted line represents the time of bubble coalescence. The coalescence takes place at 0.32 s, 0.42 s and 0.46 s in [bmim][BF4], [bmim][NO3] and [omim][BF4], respectively. Moreover, the coalescence time follows the opposite order of terminal bubble velocity, which means the coalescence between bubbles with high velocity takes place earlier. As shown in Table 3, the mass transfer rate of CO2 in bubbles before coalescence is almost twice as that in single bubble and the merged bubble after coalescence. It implies that the mass transfer rates of CO2 in different individual bubbles are independent of each other, and the difference of the mass transfer rate between the small single bubble and big merged bubble is not obvious. Therefore, the big merged bubble is not conductive to the interfacial mass transfer due to its small specific surface area. Small bubbles without coalescence are expected to enhance interfacial mass transfer. As a result, although high liquid viscosity is not efficient to improve interfacial mass transfer, it delays the coalescence of small bubbles. Comparing with big merged bubbles after coalescence, these small bubbles lead to higher mass transfer rate. Moreover, since low viscosity is often accompanied by low CO2 solubility, the mass transfer in liquids with low viscosity is not as good as it should be. Therefore, in the cases with bubble coalescence, [omim][BF4] exhibits a comparative CO2 mass transfer effect as [bmim][BF4].

4.2.4. Distribution of CO2 concentration in ILs CO2 concentration field in ILs is obtained by simulations for further understanding of the interfacial mass transfer. Fig. 12 presents the CO2 concentration distribution in liquid phase at 343 K. The results illustrate that the dissolved CO2 is distributed behind the bubble and forms a straight line in pure ILs, which is shown in Fig. 12(a–c). However, the radial motion of the bubble in aqueous ILs leads to vortex

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Fig. 12. CO2 mass fraction field in IL systems: (a) [bmim][BF4]; (b) [omim][BF4]; (c) [bmim][NO3]; (d) 95 wt% [bmim][BF4]; (e) 90 wt% [bmim][BF4] (T ¼343 K, P ¼2 MPa).

shedding in the wake of bubbles, and the CO2 is distributed along the vortex in a wide region. Comparing Fig. 12(d) to Fig. 12(e), it can be observed that the bubbles experience an irregular radial movement. The bubble swings to one side in 95 wt% [bmim][BF4] while the bubble in 90 wt% [bmim][BF4] swings to the other side. The reason for the bubble irregular movement in aqueous ILs is the low viscosity and relative high bubble Reynolds number. Otherwise, it can be seen from Fig. 12(d and e) that the swinging of the bubble contributes to the uniform CO2 distribution. The CO2 concentration distribution in [bmim][BF4] during coaxial bubble coalescence is shown in Fig. 13. The two bubbles form on the orifice originally, and then the second bubble surrounded by the dissolved CO2 in the wake of first bubble rises independently. The dissolved CO2 is left behind in the wake of second bubble. When the bubble coalescence takes place at 0.32 s, the merged bubble deforms and enlarges, leading to broaden the wake of dissolved CO2. In addition, similar phenomena are observed in other IL systems. The CO2 concentration distribution in liquid phase after coalescence is shown in Fig. 14. All the merged bubbles shown in Fig. 14 are at the height of 0.07 m. As the merged bubble is almost twice as large as the single bubble, the width of its wake is extended when the bubble coalescence takes place. Seen from Fig. 14, a mutation of the dissolved CO2 wake width is observed where the coalescence occurs. And for aqueous ILs, it is seen that the dissolved CO2 covers a straight line at the initial stage, and then the bubble experiences a radial movement

after coalescence due to the increased bubble Reynolds number, which is further discussed in Section 4.1.2 before. The maximum of CO2 concentration shown in Figs. 12 and 14 appears in pure [bmim][BF4], reaching a mass fraction of 0.02%. While the CO2 solubility in [bmim][BF4] at the same conditions reaches a mass fraction of 4.79%, which is more than 200 times of the CO2 concentration around the bubbles. In consideration of the CO2 solubility, the results presented in Figs. 12 and 14 imply that the dissolved CO2 is extremely unsaturated in the IL systems. Similar results are obtained even at the operating pressure of 5 MPa, which is shown in Fig. S1. That means the dissolved CO2 of individual bubbles has negligible effect on the mass transfer driving force, so that the conclusions on CO2 mass transfer properties are also suitable for the cases of multi-bubble systems.

5. Conclusion A CFD method is developed to investigate the bubble behavior and mass transfer properties of IL-CO2 systems. The results demonstrate that the liquid viscosity dominates the bubble behavior. Moreover, the bubble coalescence phenomenon is deeply analyzed through pressure gradient field. In the bubble coalescence process, the bubbles present different phenomena from the single bubble. The two coaxial bubbles keep accelerating until coalescence, while the single bubble quickly reaches the

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Fig. 13. CO2 mass fraction field during bubble coalescence in pure [bmim][BF4] (T ¼ 313 K, P ¼2 MPa).

Fig. 14. CO2 mass fraction field after bubble coalescence in IL systems: (a) [bmim][BF4]; (b) [omim][BF4]; (c) [bmim][NO3]; (d) 95 wt% [bmim][BF4]; (e) 90 wt% [bmim][BF4] (T¼ 313 K, P¼ 2 MPa).

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terminal velocity after a short distance of acceleration. These phenomena are further explained by velocity field and pressure gradient field analysis. As for the mass transfer aspect, the numerical simulations indicate that mass flux is influenced significantly by water content, operating pressure and temperature. Increasing water content of the IL systems will enhance the mass flux, which can be attributed to the decrease of viscosity. Besides, elevating pressure will improve the CO2 solubility, which is also favorable for the mass flux. In contrast, the bubble coalescence is negative for mass transfer because of the low specific surface area of the merged bubble after coalescence. The influence of temperature on CO2 mass flux in pure ILs is different from that in aqueous ILs. In detail, the CO2 mass transfer is kinetic-controlled in pure ILs and thermodynamic-controlled in aqueous ILs, respectively. The optimized strategy for CO2 capture is to perform absorption at low temperature using aqueous ILs.

Nomenclature a cI D do db ! F f ! g I KH kl M P SLG T t Ug V0 Vg VT ! v

specific interfacial area (m2 m  3) CO2 mole fraction at gas–liquid interface (mol m  3) CO2 diffusion coefficient (m2 s  1) diameter of gas inlet (m) equivalent diameter of bubble (m) source term of momentum equation (N m  3) friction factor (–) gravitational acceleration (m s  2) unit tensor (–) Henry’s constant (Pa m3 mol  1) liquid side mass transfer coefficient (m s  1) molecular weight (kg mol  1) pressure (Pa) source term of scalar transport equation (kg m  3 s  1) temperature (K) time (s) gas superficial velocity (m s  1) gas intel velocity (m s  1) CO2 molecular volume (cm3 mol  1) terminal bubble velocity (m s  1) velocity vector (m s  1)

Dimensionless numbers Eo Fr o Mo Re Sc Sh

ðρ  ρ Þgd 2 Eötvös number, Eo ¼ l 2 μg b l U Froude number, Fr o ¼ dogg ðρl  ρg Þgμl 4 Morton number, Mo ¼ σ3 ρ 2 ðρ  ρl Þd V Reynolds number, Re ¼ l μg b T l μl Schmidt number, Sc ¼ ρ Dl l Sherwood number, Sh ¼ kDl dl b

Greek symbols α μ ρ σ φ ω

volume fraction (–) viscosity (Pa s) density (kg m  3) surface tension (N m  1) association factor (–) CO2 mass fraction (–)

Subscripts g l

gas phase liquid phase

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Acknowledgments This work was financially supported by the National Basic Research Program of China (no. 2013CB733506, no. 2014CB744306), The National Natural Science Fund for Distinguished Young Scholars (no. 21425625), and the National Natural Science Foundation of China (no. 21376242).

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