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Influence of membrane module geometry on SO removal: A numerical study Zhien Zhang, Yunfei Yan, David A. Wood, Wenxiang Zhang, Lixian Li, Li Zhang, and Bart Van der Bruggen Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b03374 • Publication Date (Web): 03 Nov 2015 Downloaded from http://pubs.acs.org on November 8, 2015
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Influence of membrane module geometry on SO2 removal: A numerical study Zhien Zhanga, Yunfei Yana,*, David A. Woodc, Wenxiang Zhangd, Lixian Lib,*, Li Zhanga, Bart Van der Bruggene a
Key Laboratory of Low-grade Energy Utilization Technologies and Systems (Chongqing University), Ministry of Education of PRC, Chongqing 400030, China b
Chongqing Key Laboratory of Translational Research for Cancer Metastasis and Individualized Treatment, Chongqing Cancer Hospital & Institute & Cancer Center, Chongqing 400030, China c
d
e
DWA Energy Limited, Lincoln, United Kingdom
EA 4297 TIMR, Technological University of Compiegne, 60205 Compiegne Cedex, France
Department of Chemical Engineering, ProcESS, KU Leuven, W. de Croylaan 46, B-3001 Leuven, Belgium
Abstract
SO2 emissions to the atmosphere result in acid rain, which is a key issue for the environment. Membrane gas absorption (MGA) is a novel approach to minimize the SO2 emissions to the atmosphere. A comprehensive mass transfer model considering the non-wetting mode is proposed to observe the SO2 absorption performance. A physical solvent of H2O and a chemical solvent of N,N-dimethylaniline (DMA) are utilized as the aqueous absorbents. The calculated results are verified against the available experimental data derived from two different modules, demonstrating a good consistency. The effects of inside membrane diameter, membrane thickness, porosity, fiber length, number of fibers and inside module diameter on removal of SO2 were simulated. The results show that an improvement in the absorption performance can be achieved by increasing the number of *Corresponding author email address: [email protected] (YY) , [email protected] (LL); Other authors email address: [email protected] (ZZ), [email protected] (DW), [email protected] (WZ), [email protected] (LZ), [email protected] (BVB). 1 ACS Paragon Plus Environment
fibers and porosity, and decreasing the membrane thickness and inner contactor radius. Furthermore, a longer module length (corresponding to a higher gas-liquid contact area) results in a sharp decline of the SO2 removal efficiency, while the SO2 flux increases. Finally, the model provides guidelines for the selection of optimum module parameters for SO2 absorption. Keywords: SO2 capture; Hollow fiber membrane; Structure; Numerical simulation
1. Introduction Fossil fuels like oil, natural gas and coal have been applied for many decades to many fields but they come with serious environmental problems. SO2 is one of the gaseous contaminants mainly originating from the burning of fossil fuels by industry including coal-fired power plants, petroleum refining, H2SO4 production and smelting of non-ferrous metals. Indeed, the amount of SO2 in the atmosphere is still continually increasing. SO2 mixing with water vapor in the atmosphere produces acid rain, which causes soil acidification and crop damage. Capturing SO2 is a high priority, in attempts to reduce air pollution.1,2 Encompassing wet and dry forms of desulfurization product, SO2 removal methods consist of three approaches: dry desulphurization, semi-dry desulphurization and wet desulphurization. All three of these methods involve a high capital cost, incomplete decontamination, and the possibility of secondary pollution. Another key issue is the regeneration of sulfur. Processes like Wellman-Lord or Westvaco process would recycle the sulfur either in elementary form or as sulfuric acid, while the common lime scrubbers would generate it as waste.3 Among them, the Wellman-Lord process, with more than 30 commercial units worldwide, is one of Flue Gas Desulfurization (FGD) methods. The sodium sulfite solution is used in this process.4 One common solution for reducing SO2 is to absorb into liquid solvents. The sulfur is then further stripped from the sulfur-rich solvent in a regenerator. There are several types of absorbers for SO2 capture in industrial 2
applications. The use of scrubbers is a common method for the separation of SO2.5 However, it results in solvent losses and emissions to the atmosphere, because of liquid evaporation and droplets commingling with the gas phase. Likewise, there are drawbacks to removing SO2 from gas mixtures using conventional technologies, such as entrainment, foaming, liquid channeling issues, and the large required space. But using membrane technology, the liquid and gaseous phases are operated independently as two separate streams to avoid the above issues.6 To overcome these shortcomings, membrane gas absorption (MGA) technology is of interest because it has a low investment cost and energy consumption, small volume, and flexibility of operation when compared to the traditional separation methods.7 The membrane is non-selective and just forms a gas-permeable barrier between the absorbent and the gas stream. In particular, the gas selectivity is mainly controlled by the liquid absorbent. SO2 recovery using a membrane contactor allows solvent losses reduce by droplet dragging compared with the technique based on using traditional absorption towers and scrubbers. The MGA method is a promising approach to apply in the industry for gas pollution control.8 It has been successfully used in a Dutch potato starch production plant. In this application, the SO2 removal percentage was as high as 95% with a capacity of 120 m3 h-1.9 Qi and Cussler10 successfully pioneered the use of hollow fiber gas membranes for removing volatile solutes such as NH3, H2S and SO2. The method is also reported to be very effective for acidic gas purification7 (removal of CO2, H2S, and SO2 from the gaseous mixture). Hollow fiber membrane modules have been widely explored experimentally and theoretically for SO2 removal. The influence of operating variables for this method were extensively investigated for gas-liquid systems11-14. It was proven that the gas and liquid characteristics had a significant impact on SO2 capture. One of the major factors on SO2 capture is selecting the liquid solvent. Important factors in selecting suitable solvents for gas separation are identifying solutions, which have high absorption rate and capacity, and are also easy to regenerate. A number of solvents have been used in 3
experimental studies, such H2O or seawater12,15, monoethanolamine (MEA)16,17 and methyldiethanolamine (MDEA)18. Among them, N,N-dimethylaniline (DMA) is a common organic solvent consisting of a tertiary amine. It has a good affinity with SO2 and straightforward desorption characteristics. Luis et al.19,20 investigated the recovery of SO2 from a gas stream in a membrane contactor using a DMA solution as the absorbent. Zero absorbent emission was achieved and about 40-50% SO2 could be recycled from gas stream. The results also showed that SO2 removal using a hollow fiber contactor was viable and technically feasible. However, it was observed that the membrane contactor dimensions also affect the absorption process. To evaluate the membrane performance numerically, a mathematical model for SO2 absorption was developed and the influence of gas and liquid flow rates were systematically studied by simulation21. In addition, the influence of partial wetting and operating conditions on the mass transfer process was also evaluated. It was found that the mass transfer resistance in the membrane increases when the partial wetting takes place. Goyal et al.22 presented the numerical calculation results of membrane gas absorption for two conditions of non-wetting and partial wetting. The CO2 flux in the non-wetting mode was higher than that in the partial wetting mode with different gas or liquid velocities. Furthermore, El-Naas et al.23 and Zhang et al.24 stated that the CO2 capturing performance reduces as wettability of the membrane increases. Other factors, including the gas and liquid concentrations, were considered in the models using DMA as the liquid solution13,25. Fasihi et al.25 simulated the effects of gas velocity and concentration on SO2 mass transfer through membranes in a contactor. To this day, there are only a few studies concentrating on the factors influencing the performance of membranes in a contactor on SO2 separation. The reported literature focused on the operating conditions like gas and liquid flow rates, temperature, liquid concentration, and SO2 content in gas mixture12,14,26. The investigations on the membrane module geometry parameters are inadequate. On the other hand, the previous studies were mainly experimental14 whereas simulations focused on this issue may yield broader and more general insights. This is 4
the first time to conduct numerical investigations on module geometry properties effects on SO2 removal using MGA method. There are several commercially available membrane contactors like Liqui-Cel® Extra-Flow module27, and Sepuran® module28. However, for the specific applications of membrane modules, the dimensions of the membrane contactor should be adjusted according to the requirements of the gas capture process. The aim of the present study is to establish and solve a 2D mass transfer model for SO2 removal from gaseous mixtures in a membrane contactor. A gas mixture of SO2 and air are considered, and H2O and DMA solutions are used for SO2 absorption as solvents under non-wetting conditions. The partial differential equations defining the model, including the tube, membrane, and shell sides are solved by the finite element method. The absorption of SO2 in a ceramic contactor is comprehensively simulated with different module characteristics. Furthermore, another objective of this study is to consider the effects of the contactor dimensions on gas-liquid systems. The SO2 absorption efficiency, mass transfer rate and coefficient are compared for a range of gas-liquid systems.
2. Model Development To access the absorption performance of the hollow fiber contactors, a comprehensive mass transfer model for SO2 removal is proposed and implemented. A schematic representation of the gas transport process inside the membrane module is shown in Fig. 1. For all the membrane modules, the non-wetted condition is considered (i.e., only gas diffusion in the membrane section). For this case, it can be seen from the diagram that the gas mixture of SO2 and air are fed outside the hollow fibers, and then passes via the membrane pores. Gas and liquid flow countercurrently inside the module. Finally, SO2 is absorbed by the absorbent inside the fibers due to chemical or physico-chemical reactions. At the same time, the mixed gas flows out at the outlet of the 5
shell. In the model, several assumptions are made: (1) the gas phases behave as ideal gases, (2) steady-state and isothermal conditions prevail, (3) laminar parabolic velocity distribution exists inside the fibers, and (4) Henry’s law applies at the gas-liquid contact surface.
2.1. Material balance equations 2.1.1. Governing equations inside the fiber
In this configuration considered here, the absorbent flows through the fibers. Thus, the species continuity equation for the physical/chemical absorption of SO2 may be generally expressed by − ∇ ∙ ∇ + ∇ ∙ =
(1)
where represents the diffusion coefficient of SO2 in the liquid phase; is the SO2 concentration in the liquid phase; denotes the z-velocity inside the tube; denotes the gas-liquid reaction rate. The velocity profile inside the lumen side is assumed to follow a fully-developed laminar flow29 U = 2 1 −
(2)
where and r1 represent the average z-velocity within the tube and the inner fiber radius, respectively. The average velocity can be calculated as =
!
where QL and n are the volumetric flow rate and the number of hollow fibers, respectively. The initial and boundary conditions imposed on the above equation (1) or (2) are as follows
where m is the solubility of SO2 in the solutions. The second boundary condition corresponds to the fact that the SO2 concentration in the tube is determined by its solubility in the liquid absorbent.
2.1.2. Governing equations in the membrane
The material balance equation for SO2 transport inside the membrane region, operating in a non-wetted condition is − & ∇ ∙ ∇ & = 0
(7)
where & and & are the SO2 diffusion coefficient and SO2 concentration in the membrane, respectively. For the non-wetted case, the diffusion coefficient of SO2 passing through the membrane can be represented by30 & = ,- ⁄./
(8)
where ε and τ denote the membrane porosity and the tortuosity factor, respectively. There are three mass transfer resistances for SO2 transport through the membrane pores including gas transfer from the shell side to the membrane section, gas diffusion across the pores to the tube-membrane interface, and SO2 dissolution into the liquid solution. The boundary conditions of the mass transfer equation in the membrane can be written as B.C. 1:
The third boundary condition at both ends of membrane is considered to be insulated. This boundary condition states that SO2 cannot diffuse via the solid wall in the membrane section.
2.1.3. Governing equations outside the fiber
The steady-state conservation equation of SO2 transport in the shell, using Fick’s law for estimating the diffusive flux, is as follows − 1 ∇ ∙ ∇ 1 + ∇ ∙ 1 1 = 0
(12)
where 1 and 1 are SO2 diffusion coefficient and SO2 concentration in the gas phase, respectively. 1 is the z-velocity in the shell side. Assuming Happel’s free surface model (Fig. 2), the radius of free surface can be defined by31 r4 = ,1⁄5/6.8
(13)
where r2 is the outer fiber radius, θ denotes the pack density of the membrane module. The axial velocity inside the shell is expressed as30 ,r⁄r3 /2 -,r2 ⁄r3 /2 +2ln,r2 ⁄r/ r2 2 Uz-G =2z-G 1- r3 3+,r2 ⁄r3 /4 -4,r2 ⁄r3 /2 +4ln,r2 ⁄r3 /
(14)
The corresponding boundary conditions are B.C. 1:
at r = r2
1 = &
(15)
B.C. 2:
at r = re
" 1 ⁄ = 0 (symmetry)
(16)
B.C. 3:
at z = L
1 = 6
(17)
where C0 represents the initial concentration of SO2 in the feed gas.
< Fig. 2 Schematic representation of Happel’s free surface model > 8
The gas mass transfer process into the aqueous solvents is improved by chemical reactions. The following reactions of hydrolysis between SO2 and H2O in the solvent may occur11,32 CD
SO + 2H O ⇔ HF OG + HSO F C
G HSO F + H O ⇔ HF O + SOF
k I = 0.014 mol mF
(18)
k MI = 6.24 × 10P mol mF
(19)
where kE and k MI are the equilibrium constants for the chemical reactions. The formation of SO F can be negligible when the pH of the solution is lower than 4 to 5. Under the + electro-neutrality condition, it is required that the concentrations of HSO F and H3O are the same. Therefore,
the reaction rate expressions are13 −R = R C −
R , V / RI TU
(20)
where the forward rate constant for SO2 ionization of k1 is 3.17×10-2 s-1.
2.2.2. Reaction mechanism between SO2 and DMA Regarding SO2 absorption into DMA solutions, the following reactions may occur in the solvent33 SO + W X ⇔ W G + WYXF
(21)
WYXF ⇔ W G + YXF
(22)
DMA + W G ⇔ ]^W G
(23)
Furthermore, an additional compound is formed during the reaction of SO2-DMA34 SO + _ W8 `, WF / ⇔ _ W8 `, WF / · YX
(24)
The gas-liquid reaction is considered an instantaneous pseudo first-order reversible reaction with a high DMA concentration. The pseudo first order reaction rate constant can be obtained from the literature33. 9
2.3. Numerical solution of simulations The governing equations are solved numerically using the finite element method in COMSOL. It is noticed that this software creates triangular meshes, which are isotropic in size and 24156 elements are created in this model. The specifications of modules 1 and 2 are listed in Table 1. In addition, the physico-chemical parameters and the reaction kinetics between SO2 and absorbent liquids are listed in Table 2. A set of the partial differential equations containing the tube, membrane, and shell sections is solved subject to the boundary conditions. A numerical solver UMFPACK is used for meshing and error control that is an implicit time-stepping scheme and well-suited to solve non-stiff and stiff non-linear boundaries and preferable for a 2D model. The computer was equipped with a 64-bit operating system, RAM 4.00 GB and Intel CoreTM i5 4200U CPU. In order to minimize the difference between r and z directions, a scaling factor of 160 was employed in the axial direction.
In the MGA method, the main driving force for SO2 transport is SO2 concentration gradient between the tube side and the shell side. Thus, in order to analyze the process of SO2 absorption in the hollow fiber membrane module, the SO2 removal efficiency and flux can be expressed by the following formulas η = c1 − de* ⁄ 6 f × 100%
h =
1000 × 273.15 × , 6 6 − de* de* / 22.4 × k × Y
(25) (26)
where η and h are the SO2 absorption efficiency and flux, respectively. Q0 denotes the initial gas flow rate in shell. de* and de* represent the concentration and flow rate of SO2 at the outlet of the shell side, respectively. T denotes the operating temperature and S represents the gas and liquid contact area. 10
H2O was used as the liquid solvent for the membrane gas absorption process to verify the accuracy of the simulations. The relationship between the outlet SO2 concentration and the absorbent flow rate is plotted in Fig. 3. This figure indicates that the proposed model is more accurate than that of Karoor and Sirkar (KS)11 for the prediction of SO2 absorption. With the increase of absorbent flow rate from 1 to 23.6 ml min-1, the experimental SO2 concentration in the outlet gas stream decreases from 0.58 to 0.08% at a 200 ml min-1 gas flow. This can be explained by the enhancement in gas concentration gradient inside and outside the lumen side and in the following, reduction of the thickness of liquid boundary layer with increasing the liquid flow rate. In addition, the significant reduction in the outlet SO2 concentration is enhanced by the adequate supply of fresh absorbents in the tube, which accelerates the chemical reaction with SO239. The corresponding value in the current model varies from 0.59 to 0.07%, while it changes from 0.69 to 0.03% in the simulation of Karoor and Sirkar. Moreover, the error between KS’s experiment and modeling results is in range from 0.04 to 0.11%, however, the value between KS’s experimental data and our simulation results is within 0.01%. This good agreement demonstrates that the model is feasible and valid to simulate the membrane gas absorption process. As shown in Fig. 4, the effect of the gas concentration on the SO2 absorption flux is compared between the experimental data19 and numerical calculation results when DMA is used as the absorbent. The SO2 volume fractions considered here are 0.15, 0.3, 0.6, 2.4, 3.3, and 4.8%. It is noted that the SO2 flux depends on the inlet
gas composition. The absorption flux of SO2 considerably increases from 0.003 to 0.083 mol m-2 h-1 when the SO2 content increases from 0.15 to 4.8 % in the feed gas mixture. This can be explained by the enhancement of the gas mass transfer process. Similar results were reported elsewhere40. Furthermore, as demonstrated in Fig. 3, it can be seen that the absorption performance is better in the calculated results than in the experiments. This is due to the long operational time, which entails potential problems with membrane wettability and stability. In these conditions, not all assumptions for the theoretical calculations are still valid.
Figs. 5a and 5b illustrate the dimensionless concentration distribution of SO2 in the hollow fiber membrane contactor calculated by the model. It can be concluded from Fig. 5a that the concentration of SO2 considerably increases from z = 0 to z = L in the tube side due to more absorbed SO2 in the liquid solvent. The SO2 concentration close to the tube-membrane interface is higher than that in the center of the tube along the membrane radius. Futhermore, Fig. 5b indicates that the SO2 concentration ratio decreases significantly to 0.53 at the outlet of the shell along the membrane length. This phenomenon is caused by more SO2 reacting with the absorbent in the liquid phase.
3.2. Influence of the fiber radius Fig. 6 compares the contactor performance with various inner fiber radius. It is noted that both the SO2 removal efficiency and flux increase and then decrease with an increase in inner fiber radius at a constant 12
thickness of the membrane. On one hand, the mass transfer is affected by the increase of the gas and liquid contact area. On the other hand, it is also caused by the reduction in liquid velocity due to the increment in the cross section area at a constant inlet liquid flow rate. It can be seen that the original dimension of hollow fiber provides the better absorption performance of SO2 than other dimensions. When the radius of the inner fiber is 1500 µm, the SO2 removal efficiency and flux are 47.6% and 0.0046 mol m-2 h-1, respectively. An increase in the inner tube radius results in a reduction of the absorbent velocity and a reduction of the gas-liquid residence time when maintaining the same liquid flow rate. It is also shown in this figure that the two values yield only negative changes under these conditions. A similar phenomenon has been reported in the literature41.
3.3. Influence of the membrane thickness Fig. 7 shows the effect of a variation of the membrane thickness (100, 200, 300, 400, 500, and 600 µm) on the SO2 removal. It was observed that SO2 removal efficiency and SO2 flux are decreased by 23.3% and 0.0023 mol m-2 h-1, respectively, as the membrane thickness increases. A six-fold increase of membrane thickness decreases SO2 removal efficiency and flux by only 1.5 times. So, the rate limiting step for SO2 removal should not be the diffusion inside membrane. This occurs because both the gas residence time and the on-way resistance in the membrane pores increase as the membrane thickness increases. Furthermore, the gas flow in the membrane becomes more complex with an increase of the membrane thickness, which may have a negative impact on the separation performance40.
3.4. Influence of the fiber length Fig. 8 represents the influence of the membrane length (0.2 – 1.0 m) on the absorption of SO2 in the hollow fiber module. A long length of fiber promotes SO2 capture, and the removal efficiency of SO2 significantly increases from 34.7 to 55.6% with increasing membrane length. This is due to the increase of the gas and liquid contact area and residence time with a longer fiber. The gas and liquid contacting area is significantly increased from 0.528 to 2.638 m2 with the increase in fiber length considered here. However, a longer fiber length has an adverse effect on the SO2 absorption flux. The flux of SO2 at outlet of the membrane contactor drops from 0.0074 to 0.0024 mol m-2 h-1 in the fiber range of 0.2-1.0 m. The decline in SO2 flux is mainly due to increasing the mass transfer area S in eq. (26). A longer membrane module also provides a smaller driving force per unit area than the shorter one42,43.
3.5. Influence of the number of fibers The effect of the number of fibers on the absorption of SO2 from the gas mixture is plotted in Fig. 9. The SO2 removal efficiency increases dramatically from 10.22 to 100% when the number of fibers increases from 100 to 500. The SO2 absorption process achieves complete removal with 500 fibers. This is because that the gas and liquid residence time and interface area inside the module is increased. In addition, there is a peak in SO2 flux due to simultaneous impacts of the changes of the gas-liquid contacting area and the absorbed amount of SO2 in the solutions. In the meantime, the fiber packing density considerably increases with increasing the number of hollow fibers. The decline in SO2 flux when the fibers number is higher than 400 is caused by the 14
limited spaces among fibers, which could impede the gas-liquid mass transfer process. Naim and Ismail44 found that high packing density of fibers may result in dead zones inside the shell side which weakens the SO2 absorption flux. The highest flux achieved is 0.0064 mol m-2 h-1 suggesting that the optimum number of fibers is 400 for the module configuration in this study. Zhang et al.45 and Razavi et al.46 reported a similar membrane performance of CO2 absorption with various numbers of tubes.
3.6. Influence of the module radius Fig. 10 shows the SO2 removal as a function of the module radius. The SO2 removal performance decreases when the module radius increases from 0.0035 to 0.006 m. In this case, the number of fibers is kept constant at 280 in module 2. The decreasing performance is explained by the increase in the packing density of large-radius modules. Fig. 9 also shows that the SO2 removal efficiency and flux are considerably decreased from 86.64% and 0.0082 mol m-2 h-1 to 23.9% and 0.0023 mol m-2 h-1, respectively. Those considerable declines in SO2 absorption efficiency and SO2 flux are due to more gas mixture passing through the shell section with an increase of the module radius when the fiber properties are constant. Similar observations have been reported for CO2 capture45.
3.7. Influence of the membrane porosity For the gas-liquid absorption process, the value of the mass transfer coefficient is an important indicator of 15
the reaction rate. The overall mass transfer coefficient for SO2 capture is calculated by the driving force of the logarithmic mean concentration 47: K 1 = , 1 ⁄Y/m 6 ⁄ de*
(27)
An increase in membrane porosity from 0.15 to 0.55 was considered. As shown in Fig. 11, the outlet SO2 concentration shows a downward trend with increasing membrane porosity in non-wetting conditions. The SO2 concentration at the outlet decreases slightly from 2.673 to 2.653% . However, a high porosity of the membrane enhances the gas mass transfer process because more SO2 can pass via the membrane pores from the shell to the tube. The mass transfer coefficient for SO2 removal changes from 8.996×10-7 to 9.103×10-7 m s-1 as the membrane porosity increases. Similar observations have been reported in an experimental study48. The rate of change of outlet SO2 concentration is greater at lower membrane porosities because of the longer distances between the adjacent membrane pores in such conditions49. However, a high porosity of the membrane may cause membrane wetting issues and deteriorate the SO2 absorption performance.
4. Conclusions This study investigates the impact of module parameters on SO2 removal using DMA as the absorbent liquids inside a hollow fiber membrane module. The 2D mathematical model for SO2 transport has been proposed under non-wetting conditions. The governing equations for three regions of the membrane contactor were solved. For modeling validation, the comparison between experimental data and simulated results were in excellent agreement considering various values of the gas and liquid flow rates. After the proposed model was 16
verified, the influences of membrane diameter, thickness, length, and porosity were simulated. The 3D SO2 concentration distributions within and outside the fibers are illustrated for modules using DMA as the absorbent. The simulated results identify the original dimensions of the module that provide the best SO2 absorption performance. Particularly, decreasing membrane thickness and inside module radius to 100 µm and 0.035 m, and increasing number of fibers to 400 can further enhance SO2 removal. In addition, under the given conditions, it is observed that the contactor performance is improved by increasing the fiber numbers and the membrane porosity, and decreasing the membrane thickness and the module radius. The SO2 removal process is enhanced and the SO2 flux decreases as the effective membrane length is increased. The established model provides the theoretical basis for determining the optimum region of the module parameters. Overall, the developed model shows a good prediction of gas absorption using the membrane technology. It is a good tool for optimization of the gas-liquid membrane system before its practical applications. Moreover, it is possible to absorb two acidic gases simultaneously using the simulated method such as CO2 and SO2, CO2 and H2S in the following studies. The model should be optimized further with a complex flow; in this work, a laminar flow condition was considered. In addition, the influences of the flow pattern, the membrane wettability and properties of gas and liquid phases could be taken into consideration.
Acknowledgments
The
authors
gratefully
acknowledge
the
financial
support
from
China National Tobacco
Corporation Chongqing Branch (No. NY20130501010010) and the Fundamental Research Funds for the Central Universities (No. CDJZR12140034). Zhien Zhang would like to acknowledge the Chinese Scholarship Council for the full scholarship of his two years studying as a Joint PhD student in the Ohio State University 17
θ packing density δ membrane thickness (µm) η removal efficiency (%) Subscripts av
average
G
gas phase
L
liquid phase
M
membrane
0
module inlet
out module outlet T
tube
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Figures Fig. 1 Schematics of (a) a gas-liquid membrane contactor and (b) gas and liquid flows inside the membrane module. Fig. 2 Schematic of the Happel’s free surface model (HFSM). Fig. 3 Comparison of the influence of absorbent flow rate on SO2 removal11 (1% SO2-air mixture, QG=200 ml min-1, T=298 K, module 1). Fig. 4 Influence of the gas concentration on SO2 absorption flux19 (0.15 to 4.8% SO2-air mixture, QG=1 L min-1, QL=1 L min-1, T=290 K, module 2). Fig. 5 SO2 concentration distributions in (a) tube and (b) shell (5% SO2-air mixture, QG=0.1 L min-1, QL=1 L min-1, T=290 K, module 2). Fig. 6 Influence of the inner fiber radius on SO2 removal (5% SO2-air mixture, QG=0.1 L min-1, QL=1 L min-1, T=290 K, module 2). Fig. 7 Influence of the membrane thickness on SO2 removal (5% SO2-air mixture, QG=0.1 L min-1, QL=1 L min-1, T=290 K, module 2). Fig. 8 Influence of the fiber length on SO2 removal (5% SO2-air mixture, QG=0.1 L min-1, QL=1 L min-1, T=290 K, module 2). Fig. 9 Influence of the number of fibers on SO2 removal (5% SO2-air mixture, QG=0.1 L min-1, QL=1 L min-1, T=290 K, module 2). Fig. 10 Influence of the module radius on SO2 removal (5% SO2-air mixture, QG=0.1 L min-1, QL=1 L min-1, T=290 K, module 2). Fig. 11 Influence of the membrane porosity on SO2 removal (5% SO2-air mixture, QG=0.1 L min-1, QL=1 L min-1, T=290 K, module 2). 26
