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Ethanol mass transfer during pervaporation with PDMS membrane based on solution-diffusion model considering concentration polarization
Separation and Purification Technology 220 (2019) 276–282
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Separation and Purification Technology journal homepage: www.elsevier.com/locate/seppur
Ethanol mass transfer during pervaporation with PDMS membrane based on solution-diffusion model considering concentration polarization
T
⁎
Boya Qiua, Yuyang Wanga, Senqing Fana, , Jingyun Liua, Shizhao Jiana, Yangmei Qina, ⁎ Zeyi Xiaoa, , Xiaoyu Tangb, Wenguo Wangb a b
School of Chemical Engineering, Sichuan University, 610065 Chengdu, China Biogas Institute of Ministry of Agriculture, 610041 Chengdu, China
A R T I C LE I N FO
A B S T R A C T
Keywords: PDMS membrane pervaporation Ethanol mass transfer Solution-diffusion Concentration polarization
A mass transfer model of ethanol recovery by pervaporation with polydimethylsiloxane (PDMS) membrane was developed based on solution-diffusion theory considering concentration polarization. The water/polymer interaction parameter, ethanol/polymer interaction parameter, the limiting diffusivity of ethanol and plasticization coefficient of ethanol were determined. The concentration polarization coefficient was calculated based on the convective mass transfer on the upstream of the membrane. The effect of convective mass transfer coefficient, partition coefficient and ethanol diffusion mass transfer in membrane on ethanol flux and concentration polarization coefficient were explored. Partition coefficient of 2.98 and ethanol diffusion mass transfer in membrane of 7.05 × 10−7 m2 s−1 were determined. The concentration polarization coefficient of 0.15 and the ethanol flux of 318 g m−2 h−1 were obtained under the condition of 5 wt% of ethanol feed concentration and convective mass transfer coefficient being 1.23 × 10−5 m2 s−1. Higher convective mass transfer coefficient, higher partition coefficient and higher ethanol diffusion mass transfer in membrane could improve the membrane flux. However, the bad effect of concentration polarization coefficient on ethanol flux was severe if the partition coefficient and ethanol diffusion mass transfer in membrane are higher. The developed model could accurately predict membrane separation, especially under the condition of higher concentration polarization coefficient.
1. Introduction Ethanol production from biomass could be a tempting applications for biomass energy systems [1]. Fermentation is one of the most immediate and important process for ethanol production from renewable biomass [2,3]. Ethanol productivity could be effectively enhanced with an approach to remove ethanol from the broth constantly, since the product inhibition due to high ethanol concentration can be eliminated. Pervaporation with a hydrophobic membrane is one of the most promising approaches for ethanol in situ removal during the fermentation process, since it can not cause any harmful effect on the microorganisms and has good separation performance [4–8]. Due to its nice tolerance to the organic solvent and the excellent stability, polydimethylsiloxane (PDMS) is currently the benchmark hydrophobic material for ethanol recovery by pervaporation [9]. Solution-diffusion theory is mostly used to describe mass transfer across membrane during pervaporation process [10,11]. According to this mechanism, three consecutive steps are consisted in pervaporation:
⁎
(i) sorption of ethanol from the feed liquid to the membrane, (ii) diffusion of ethanol in the membrane, and (iii) desorption on the downstream side of the membrane under a low-pressure [12,13]. The sorption step and diffusion step are the most important issues during pervaporation process and the mass transfer rates of components are determined by the two processes [14,15]. Various thermodynamic models have been used to describe the sorption step during pervaporation, including Flory-Huggins, Universal Osuasichemical (UNIQUAC), UNIQUAC Function-Group Activity Coefficient (UNIFAC), Activity Specific Operating Guideliness-Free Volume (ASOG-FV), Entropic-FV, and modified Non-Random Two-Liquid (M-NRTL) [16–22]. In general, three different descriptions of multicomponent diffusion are normally employed: (i) generalized Fick’s law, where the flux is written as a linear combination of driving forces; (ii) the generalized MaxwellStefan theory, where the driving force is given as a linear combination of the flux, and (iii) via the irreversible thermodynamics [23]. Mulder and Smolder proposed a predictive mass transfer model of the aqueous ethanol solution through the polyamide (PA) membrane with the
Corresponding authors at: Sichuan University, No. 24 South Section 1, Yihuan Road, 610065 Chengdu, China. E-mail addresses: [email protected] (S. Fan), [email protected] (Z. Xiao).
https://doi.org/10.1016/j.seppur.2019.03.021 Received 17 December 2018; Received in revised form 6 March 2019; Accepted 6 March 2019 Available online 07 March 2019 1383-5866/ © 2019 Elsevier B.V. All rights reserved.
Separation and Purification Technology 220 (2019) 276–282
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Nomenclature
aim Vi Dsi ue
ce x Di Di0 Dim kl km K cb cbm
cm1 cm2
zb Je S
The activity of component i in the membrane Molar volume Single penetrant swelling capacity Ethanol volume fraction in the ethanol/water mixtures in the polymer Ethanol concentration in membrane (wt%) Direction of mass diffusion (m) Diffusion coefficient of component i into the membrane (m2 s−1) Limiting diffusivity considering concentration polarization (m2 s−1) Mean diffusivity in the membrane (m2 s−1) Convective mass transfer coefficient (m2 s−1) Membrane mass transfer coefficient (m2 s−1) Partition coefficient Ethanol concentration in bulk feed solution (wt%) Ethanol concentration in liquid at interface of liquid boundary layer/membrane (wt%) Ethanol concentration in membrane at interface of liquid boundary layer/membrane (wt%) Ethanol concentration on the downstream side of the membrane (wt%)
Thickness of the membrane cell (m) Ethanol flux (gm−2 h−1) Effective membrane surface area (m2)
Greek letters
ϕ
φ χwe χim η ρ μ τ
Volume fraction of components and membrane in the ternary system Volume fraction of component obtained from the experiments of pure component sorption in the membrane Solvent/solvent interaction parameter Solvent/polymer interaction parameter Concentration polarization coefficient Density (kg m−2) Dynamic viscosity (Pa s) Time duration of experiment (h)
Subscripts and superscripts w e m u d
Water Ethanol PDMS membrane Membrane upstream side Membrane downstream side
permeating component. Concentration polarization usually results in a lower productivity and a lesser extent of separation [12]. The boundary layer effect is expected to be significant for highly permselectivity even though the permeation flux is usually low for some of the current pervaporation membranes [14]. It has been reported that the effect of concentration polarization is depended on both the fluid dynamics conditions and the membrane permeability. Moreover, boundary layer resistance during pervaporation for the transfer of organic solutes across membranes with high selectivity and/or permeability was of great importance [27]. According to the resistance-in-series theory, pervaporation process is composed of two successive mass transfer steps: convective mass transfer on the upstream of the membrane and diffusion mass transfer across membrane [28–30]. Besides, ethanol concentration is kept being equilibrium at the interface of liquid boundary layer/membrane. Membrane separation performance and concentration polarization would be affected by convective mass transfer, phase equilibrium and
activity of the components in the membrane calculated by Flory-Huggins theory [24]. Based on the solution-diffusion model, Raisi used Flory-Huggins theory to describe the transfer of ethanol/water mixture in PDMS membrane [25]. The diffusion step could be simplified using generalized Fick’s law, if ethanol diffusion coefficient was assumed to be only dependent on the total volume fraction of all the solvent species in the membrane [26]. In these researches, ethanol concentration in liquid boundary layer at interface of liquid boundary layer/membrane was assumed being equal to that in liquid bulk. In other words, solution-diffusion models were developed without considering concentration polarization. Concentration polarization is inherent to all membrane processes, since the permeation rates of different permeating components are different during membrane separation. The concentration of the fast permeating component on the membrane surface is lower than that in the liquid bulk because of retention of the slow permeating component on the membrane surface, while the opposite is true for the slow
Fig. 1. Scheme of ethanol mass transfer during pervaporation. 277
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V
diffusion mass transfer. The aim of this study is to develop a mass transfer model based on the solution-diffusion theory with the consideration of concentration polarization to describe ethanol recovery by pervaporation with PDMS membrane. The effects of convective mass transfer coefficient, partition coefficient and diffusion mass transfer coefficient in membrane on membrane separation including ethanol flux and concentration polarization coefficient would be reported.
w
w
The scheme of ethanol mass transfer during pervaporation was illustrated in Fig. 1. Where cb and cbm are ethanol concentration in liquid bulk and in liquid boundary layer at interface of liquid boundary layer/ membrane, respectively. cm1 and cm2 are the concentration in membrane at interface of liquid boundary layer/membrane and on the downstream side of the membrane, respectively. It could be seen that ethanol mass transfer from the feed solution to the downstream of the membrane should be followed the orders: (1) Ethanol is transferred across a liquid boundary layer by convective mass transfer. cb decreased to cbm in the liquid boundary layer. The process of ethanol transfer in liquid boundary layer can be described as follows:
φi =
ln(φi ) + (1 − φi ) (1 − φi )2
Dsi ⎛ Dsi 1 − Dsi ⎞ /⎜ + ⎟ ρi ⎝ ρi ρm ⎠
cm1 =
ϕe ρe ϕe ρe + ϕw ρw
Je = −De ρe
where K is partition coefficient. (3) Ethanol is transferred across membrane by diffusion, and ethanol concentration in membrane is decreased from cm1 to cm2 during diffusion process. cm2 is assumed to be equal to zero under high vacuum. The process of ethanol diffused across the membrane can be described as follows:
(10)
dx
De = De0 ψ (ϕ)
(11)
ψ (ϕ) = exp(γe ϕ)
(12)
where De0 is the limit diffusivity of ethanol and γe is the plasticization coefficient of ethanol. Combining Eqs. (10)–(12), ethanol flux during pervaporation can be described as follows: ϕ
(4)
Je = −De ρe
where km is the membrane mass transfer coefficient through the membrane.
dϕe dx
=
De0 ρe zb
(ϕeu − ϕed )
∫ϕd u ψ (ϕ) dϕ ϕu − ϕd
(13)
where z b is the thickness of the membrane; ϕu and ϕd are the total volume fraction of water and ethanol on membrane upstream and downstream, respectively; ϕeu and ϕed are the volume fraction of ethanol on membrane upstream and downstream, respectively. It is assumed that the permeate side of the membrane is dry during pervaporation under high vacuum condition. Therefore ϕd and ϕed are equal to zero. According to the total solvent volume fraction theory, the mean diffusion coefficient of ethanol can be described as follows:
2.2. Sorption into membrane The activities of ethanol and water in solution are equal to those in the membrane, since equilibrium at interface of liquid boundary layer/ membrane is assumed. The activity of ethanol and water in solution can be calculated according to the Wilson function [17]. The activity of ethanol and water in the ternary system (ethanol, water and membrane) can be obtained according to the Flory-Huggins thermodynamics theory, described as follows:
ϕ
Dem = De0
V
ln a wm = ln ϕw + (1 − ϕw ) − ϕe Vw − ϕm Vw + (χwe ϕe + χwm ϕm)
∫ϕd u ψ (ϕ) dϕ ϕu − ϕd
= De0
e γe ϕu − 1 γe ϕu
(14)
where Dem is the mean diffusivity of ethanol in the membrane. Combining Eqs. (13) and (14), a simple relationship between the flux and the volume fraction in the membrane can be described as
m
Vw ϕϕ Ve e m
dϕe
where De is ethanol diffusion coefficient; ρe is ethanol density and x is the direction of mass diffusion. During pervaporation process, the relationship between ethanol diffusion coefficient and ethanol concentration is often described in exponential form:
(3)
e
(9)
The diffusion process of ethanol in the membrane can be expressed by the Fick’s law, described as follows:
(2) Ethanol is sorpted into the surface of the membrane. Ethanol concentration is increased to cm1 after passing across the interface of liquid boundary layer/membrane. It is assumed that equilibrium of ethanol concentration is achieved at the interface, described as follows:
(ϕe + ϕm) − χem
(8)
2.3. Diffusion across the membrane
(2)
V
(7)
where Dsi is the weight fraction of the component i in the swollen membrane. ρi and ρm are densities of component and PDMS membrane respectively. cm1 is related to density and volume fraction of components in membrane, described as follows:
where kl is the convective mass transfer coefficient. It’s value can be obtained according to our previous work [31]. The concentration polarization coefficient (η ) during pervaporation is related to ethanol concentration in liquid bulk and the concentration in liquid boundary layer at interface of liquid boundary layer/membrane, described as follows:
Je = km (cm1 − cm2)
(6)
where φi is the volume fraction of the component i obtained from the experiments with pure water and pure ethanol sorption in the membrane, described as follows:
(1)
cm1 = K ·cbm
w
where ϕ and V represents volume fraction and molar volume; w, e, m represents water, ethanol and PDMS membrane, respectively; χem , χwm , χwe are ethanol/polymer, water/polymer and water/ethanol interaction parameters, respectively. χwe is determined according to the FloryHuggins thermodynamics. χem and χwm can be expressed using the Flory-Rehner theory, described as follows:
χim = −
(cb − cbm ) × 100% cb
V
V
2.1. Mass transfer steps
η=
m
(ϕw + ϕm) − χwm Ve ϕw ϕm
2. Theory
Je = kl (cb − cbm)
V
ln aem = ln ϕe + (1 − ϕe ) − ϕw Ve − ϕm V e + (χwe ϕw Ve + χem ϕm )
(5) 278
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membrane was increased with the increase of ethanol concentration in feed. This result implied that a higher feed concentration will promote ethanol sorption uptake in the membrane. During the process of sorption equilibrium, the activity of ethanol could be increased linearly with its concentration, if the ethanol concentration in feed is lower than 10 wt%. The increased activity could enhance the sorption of ethanol in the membrane, leading to the higher swelling capacity of the membrane. Swelling of the membrane could weaken the interaction forces between the components in the membrane, with the free volume in the membrane increase, which was favorable to mass transfer during pervaporation. From Fig. 2, it could be also seen that the volume fraction of water showed a slightly decreasing tendency with the ethanol fraction in feed, since the mole fraction of water in feed could decrease slightly with ethanol fraction increase. As a result, the activity of water in feed could be decreased, leading to lower sorption amount in membrane. Ethanol mean diffusivity could be calculated based on the ethanol volume fraction obtained from Fig. 2. The relationship between ethanol mean diffusivity and the total volume fraction was illustrated in Fig. 3. It could be seen that the mean diffusivity of ethanol was exponentially increased with the increase of total volume fraction. The limiting diffusivity of ethanol considering concentration polarization and plasticization coefficient of ethanol would be kept as constants, if the feed temperature and membrane material were determined. The values of these two parameters were induced from Fig. 3. The key parameters of the mathematical models developed in the study for ethanol pervaporation with PDMS-PA composite membrane were illustrated in Table 1.
follows:
Dem ρe
Je =
zb
(ϕeu − ϕed )
(15)
Combining Eqs. (15) and (4), km could be calculated as follows:
km =
Dem zb
(16)
The developed models with the set of nonlinear equations could be solved by the MATLAB software. 3. Materials and method 3.1. Experiments The preparation of the composite PDMS-PA membrane has been fully described in our previous work [31]. In order to determine the amount of pure components absorbed in the PDMS layer of the composite membrane, swelling measurements of the membrane were performed by the well-known gravimetric analysis method. Before the sorption experiment, a piece of round pristine PDMS-PA membrane (diameter 100 mm) and a piece of round pristine PA membrane (diameter 100 mm) were dried in an oven at 60 °C for 5 h to obtain a dry sample and were weighted. After that, the PA membrane and PDMS-PA membrane were fixed at the bottom of petri dishes (inner diameter 130 mm, height 30 mm and wall thickness 5 mm, maximum volume around 400 mL). The ethanol and water (200 mL) were then poured into the dishes, with dishes kept at 45 °C for more than 24 h. The membranes were then removed from the liquid, blotted carefully by filter papers to remove the adherent liquid and weighed in a closed bottle (accuracy 1 mg) as fast as possible. Repeat the above process until constant weight is reached. The membrane sorption experiment of ethanol and water has been conducted more than 50 times to reduce the standard deviation. The detailed pervaporation experimental procedure could be referred from our previous work [31].
4.2. Effect of convective mass transfer coefficient on pervaporation The convective mass transfer coefficient was one of the direct factors that affect ethanol mass transfer behavior during pervaporation. The effect of convective mass transfer coefficient on ethanol separation by PDMS membrane pervaporation was illustrated in Fig. 4. It could be seen that ethanol flux could be increased with the increase of convective mass transfer coefficient. Moreover, the effect of the convective mass transfer on membrane flux was gradually weakened, with the increase of convective mass transfer coefficient. For example, the ethanol flux could be increased 2.63%, if the convective mass transfer coefficient was increased from 8.8 × 10−6 m2 s−1 to 10.0 × 10−6 m2 s−1. The corresponding value was 1.82%, if the convective mass transfer coefficient was increased from 10.0 × 10−6 m2 s−1 to 11.2 × 10−6 m2 s−1. This phenomenon implied that the convective mass transfer would be the controlling step during
3.2. Analytical methods The swelling capacity of the PDMS layer is calculated according to the swelling capacity difference between the PA membrane and the composite membrane, described as follows:
Dsi =
(wi′, PDMS − PA − wi, PDMS − PA) − (wi′, PA − wi, PA ) wi, PDMS − PA − wi, PA
(17)
where w′ and w denote the weight of swollen and dry membranes, respectively. The weight fraction of ethanol and water in the swelled membrane is calculated by integrating Eqs. (5)–(8) and Eq. (17). The flux of membrane is described as follows:
J=
W S·τ
(18)
where W is the mass of ethanol; S is effective membrane surface area and τ is time duration of pervaporation experiment. The measurement for permeate mass and ethanol concentration have also been described in detail in our previous work [31]. 4. Results and discussion 4.1. Determination of parameters Preferential sorption is a prerequisite for preferential diffusion during pervaporation [17,24]. The sorption behavior of ethanol and water in PDMS-PA composite membrane could be determined based on the swelling experiments and corresponding models, as illustrated in Fig. 2. It could be seen that the volume fraction of ethanol in the
Fig. 2. Relationship between ethanol feed concentration and volume fraction of ethanol and water in PDMS-PA composite membrane. feed temperature: 45 °C. 279
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Fig. 5. Effect of partition coefficient on ethanol pervaporation, ethanol concentration: 5 wt%; temperature: 45 °C.
Fig. 3. Effect of total volume fraction on ethanol mean diffusivity coefficient (PDMS-PA membrane, ethanol-water mixture at 45 °C). Table 1 The key parameters of the models for ethanol pervaporation with PDMS membrane. ethanol concentration: 5 wt%; temperature: 45 °C; Reynolds number: 1300. Parameters
Values
Water/polymer interaction parameter χwm Ethanol/polymer interaction parameter χem Water/ethanol interaction parameter χew Limiting diffusivity of ethanol De0 (m2 s−1) Plasticization coefficient of ethanol γe Convective mass transfer coefficient kl (m2 s−1) Diffusion mass transfer coefficient km (m2 s−1) Partition coefficient K
0.78 1.91 2.29 1.85 × 10−5 43.03 1.23 × 10−5 7.05 × 10−7 2.98
Fig. 6. Effect of diffusion mass transfer coefficient on ethanol pervaporation, ethanol concentration: 5 wt%; temperature: 45 °C. Table 2 The decreased ethanol flux caused by concentration polarization under the condition of different convective mass transfer coefficient and diffusion coefficient of ethanol in membrane. km (m2 s−1)
1.0 × 10−6 2.0 × 10−6 3.0 × 10−6
Fig. 4. Effect of convective mass transfer coefficient on ethanol pervaporation with PDMS membrane, ethanol concentration: 5 wt%; temperature: 45 °C.
Decreased ethanol flux caused by concentration polarization (gm−2 h−1) kl = 6.0 × 10−6
kl = 9.0 × 10−6
kl = 12.0 × 10−6
479.02 785.81 998.51
453.35 718.61 892.42
448.04 581.52 690.59
concentration polarization coefficient was illustrated in Fig. 4. It could be seen that the concentration polarization coefficient was decreased with the increase of the convective mass transfer coefficient. This implied that increase of the convective mass transfer could weaken the concentration polarization and improve the membrane separation performance. Moreover, the liquid boundary layer could become thinner with the convective mass transfer resistance decreased, according to the convective mass transfer theory. From Fig. 4, it could be also seen that the concentration polarization coefficient was decreased asymptotically, since the boundary layer could gradually became thinner and tended to be stable with the increase of the convective mass transfer coefficient. The similar phenomenon could also be deduced from our previous work with resistance-in-series model for the description of ethanol pervaporation [31]. From Fig. 4, it could be deduced that ethanol flux could be increased gradually with the decrease
pervaporation, if the convective mass transfer coefficient was lower. In this case, enhancing the convective mass transfer on the upstream of membrane could effectively improve ethanol pervaporation. The reason why ethanol flux was changed with the convective mass transfer coefficient was that the concentration polarization was changed with the convective mass transfer coefficient. Concentration polarization caused ethanol, which was enriched in the permeate to be depleted in the boundary layer, and water which was depleted in the permeate to be enriched in the boundary layer [32]. In this case, there would be a difference of ethanol concentration between in liquid bulk and in liquid boundary layer at interface of liquid boundary layer/ membrane. The effect of convective mass transfer coefficient on the 280
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of the concentration polarization coefficient. The ethanol flux was 292 gm−2 h−1, if the concentration polarization coefficient was 0.23. The corresponding value would be about 380 gm−2 h−1, if there the concentration polarization coefficient was zero (the flowrate was infinite and the convective mass transfer resistance was zero). This value should be the maximum flux at ethanol concentration in liquid bulk being 5 wt% under the condition of feed temperature being 45 °C. In order to minimize concentration polarization caused by convective mass transfer, the most straightforward way was to enhance the flowing performance on the upstream of the membrane, such as developing highly turbulent membrane modules.
concentration polarization coefficient was obtained even under the condition of high Reynolds number, owing to the high membrane mass transfer coefficient [31]. The mass transfer resistance in convective layer could become more significant, if the membrane was highly permeable for ethanol. Under this condition, the concentration polarization coefficient may be higher and the mass transfer resistance in convective layer may become comparable to the mass transfer resistance in membrane [33]. It could be deduced from Fig. 6 that the bad effect of concentration polarization on pervaporation was more and more obvious, if the diffusion coefficient of ethanol in membrane was increased. Obvious decreased ethanol flux caused by concentration polarization was performed under the condition of higher diffusion coefficient of ethanol in membrane. Serious effects of concentration polarization on pervaporation have been also reported in the study of water/methylene chloride system at high Reynolds number ranges [33]. It could be calculated that ethanol flux was just decreased by 133 gm−2 h−1 caused by the concentration polarization, under the condition of diffusion coefficient of ethanol in membrane being 1.0 × 10−6 m2 s−1 with the corresponding concentration polarization coefficient being 0.22. However, ethanol flux could be decreased by 824 gm−2 h−1 owing to concentration polarization, under the condition of diffusion coefficient of ethanol in membrane being 3.0 × 10−6 m2 s−1 with the corresponding concentration polarization coefficient being 0.45. Thus, our developed model could more accurately predict the membrane separation than previous ones without considering concentration polarization, under the condition of higher diffusion coefficient of ethanol in membrane. The convective mass transfer coefficient was one order higher than diffusion coefficient of ethanol in membrane during pervaproation with PDMS membrane. In order to improve the flux of the membrane, improvement of the ethanol permeability of membrane would be of great importance during pervaporation for ethanol separation. However, the concentration polarization was severe if the diffusion coefficient of ethanol in membrane was higher. In this case, it was of great importance to minimize the concentration polarization by some approaches, such as enhanced the convective mass transfer on the upstream of the membrane. The decreased ethanol flux caused by concentration polarization under the different convective mass transfer coefficient and diffusion coefficient of ethanol in membrane were illustrated in Table 2. It could be deduced that enhanced convective mass transfer on the upstream of the membrane was more effective to weak the concentration polarization and promote membrane separation, under the condition of using high ethanol permeable membranes [34]. Moreover, accomplish of a microfluidic format could also weak concentration polarization, since it could drastically improve mass transfer in the boundary layer on the upstream of the membrane [35].
4.3. Effect of partition coefficient on pervaporation Pervaporation performance could be affected by the partition coefficient, as illustrated in Fig. 5. It could be seen that ethanol flux was increased with partition coefficient. The partition coefficient represents an equilibrium state of solute ethanol at the interface of membrane phase and solution phase. It is mainly affected by the interaction between solvent and polymer, which could be characterized by χim . Lower χem or higher χwm would lead to stronger interaction and greater affinity between ethanol and membrane than between water and membrane. In this case, higher ethanol volume fraction in PDMS membranes and higher partition coefficient could be obtained. In order to increase the partition coefficient and improve the mass transfer during pervaporation, it is necessary for invention and application for advanced material and modification of existing membrane materials, which should have stronger interaction between ethanol and polymer and weaker interaction between water and polymer. From Fig. 5, it could be also seen that the concentration polarization coefficient was increased with the increase of the partition coefficient. Higher concentration polarization coefficient has a bad effect on the increase flux. It could be deduced that the decreased ethanol flux caused by concentration polarization was more and more obvious, if the concentration polarization coefficient was higher. For example, ethanol flux was just decreased by 19 gm−2 h−1 caused by the concentration polarization, under the condition of partition coefficient being 2.0 with the corresponding concentration polarization coefficient being 0.09. However, ethanol flux could be decreased by 79 gm−2 h−1 owing to concentration polarization, under the condition of partition coefficient being 3.5 with the corresponding concentration polarization coefficient being 0.17. Therefore, the bad effect of concentration polarization on membrane separation should be paid much attention, if the advanced material having stronger interaction between ethanol and polymer and weaker interaction between water and polymer was used as pervaporation membrane. 4.4. Effect of diffusion mass transfer coefficient on pervaporation
5. Conclusions The diffusion mass transfer coefficient was also one of the direct factors affecting the mass transfer behavior. The effect of diffusion mass transfer coefficient on ethanol flux was illustrated in Fig. 6. It could be seen that ethanol flux could be increased with the increase of the membrane mass transfer coefficient. The increase extent of ethanol flux under the condition of higher diffusion mass transfer coefficient was not as obvious as that in the case of lower diffusion mass transfer coefficient. For example, the ethanol flux could be increased 64.7%, if the diffusion mass transfer coefficient was increased from 1.0 × 10−6 m2 s−1 to 2.0 × 10−6 m2 s−1. The corresponding value was just 26.5%, if the diffusion mass transfer coefficient was increased from 2.0 × 10−6 m2 s−1 to 3.0 × 10−6 m2 s−1. The effect of diffusion mass transfer coefficient on concentration polarization was also illustrated in Fig. 6. It could be seen that the concentration polarization coefficient was increased gradually, with diffusion coefficient of ethanol in membrane increased. This similar result has also be reported from the previous study that higher
A mass transfer model of ethanol recovery by pervaporation with PDMS membrane was developed based on solution-diffusion theory considering concentration polarization. Ethanol flux and polarization coefficient were 318 gm−2 h−1 and 0.42, respectively, under the condition of convective mass transfer coefficient being 1.23 × 10−5 m2 s−1, partition coefficient being 2.98 and ethanol diffusion mass transfer in membrane being 7.05 × 10−7 m2 s−1. Higher convective mass transfer coefficient, higher partition coefficient and higher ethanol diffusion mass transfer in membrane could improve the membrane flux. However, the bad effect of concentration polarization coefficient on ethanol flux was severe if the partition coefficient and ethanol diffusion mass transfer in membrane are higher. The developed model could accurately predict membrane separation, especially under the condition of higher concentration polarization coefficient.
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Acknowledgements [18]
The present work was supported by the Fundamental Research Funds for the Central Universities (No. 20822041B4013).
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Contents lists available at ScienceDirect
Separation and Purification Technology journal homepage: www.elsevier.com/locate/seppur
Ethanol mass transfer during pervaporation with PDMS membrane based on solution-diffusion model considering concentration polarization
T
⁎
Boya Qiua, Yuyang Wanga, Senqing Fana, , Jingyun Liua, Shizhao Jiana, Yangmei Qina, ⁎ Zeyi Xiaoa, , Xiaoyu Tangb, Wenguo Wangb a b
School of Chemical Engineering, Sichuan University, 610065 Chengdu, China Biogas Institute of Ministry of Agriculture, 610041 Chengdu, China
A R T I C LE I N FO
A B S T R A C T
Keywords: PDMS membrane pervaporation Ethanol mass transfer Solution-diffusion Concentration polarization
A mass transfer model of ethanol recovery by pervaporation with polydimethylsiloxane (PDMS) membrane was developed based on solution-diffusion theory considering concentration polarization. The water/polymer interaction parameter, ethanol/polymer interaction parameter, the limiting diffusivity of ethanol and plasticization coefficient of ethanol were determined. The concentration polarization coefficient was calculated based on the convective mass transfer on the upstream of the membrane. The effect of convective mass transfer coefficient, partition coefficient and ethanol diffusion mass transfer in membrane on ethanol flux and concentration polarization coefficient were explored. Partition coefficient of 2.98 and ethanol diffusion mass transfer in membrane of 7.05 × 10−7 m2 s−1 were determined. The concentration polarization coefficient of 0.15 and the ethanol flux of 318 g m−2 h−1 were obtained under the condition of 5 wt% of ethanol feed concentration and convective mass transfer coefficient being 1.23 × 10−5 m2 s−1. Higher convective mass transfer coefficient, higher partition coefficient and higher ethanol diffusion mass transfer in membrane could improve the membrane flux. However, the bad effect of concentration polarization coefficient on ethanol flux was severe if the partition coefficient and ethanol diffusion mass transfer in membrane are higher. The developed model could accurately predict membrane separation, especially under the condition of higher concentration polarization coefficient.
1. Introduction Ethanol production from biomass could be a tempting applications for biomass energy systems [1]. Fermentation is one of the most immediate and important process for ethanol production from renewable biomass [2,3]. Ethanol productivity could be effectively enhanced with an approach to remove ethanol from the broth constantly, since the product inhibition due to high ethanol concentration can be eliminated. Pervaporation with a hydrophobic membrane is one of the most promising approaches for ethanol in situ removal during the fermentation process, since it can not cause any harmful effect on the microorganisms and has good separation performance [4–8]. Due to its nice tolerance to the organic solvent and the excellent stability, polydimethylsiloxane (PDMS) is currently the benchmark hydrophobic material for ethanol recovery by pervaporation [9]. Solution-diffusion theory is mostly used to describe mass transfer across membrane during pervaporation process [10,11]. According to this mechanism, three consecutive steps are consisted in pervaporation:
⁎
(i) sorption of ethanol from the feed liquid to the membrane, (ii) diffusion of ethanol in the membrane, and (iii) desorption on the downstream side of the membrane under a low-pressure [12,13]. The sorption step and diffusion step are the most important issues during pervaporation process and the mass transfer rates of components are determined by the two processes [14,15]. Various thermodynamic models have been used to describe the sorption step during pervaporation, including Flory-Huggins, Universal Osuasichemical (UNIQUAC), UNIQUAC Function-Group Activity Coefficient (UNIFAC), Activity Specific Operating Guideliness-Free Volume (ASOG-FV), Entropic-FV, and modified Non-Random Two-Liquid (M-NRTL) [16–22]. In general, three different descriptions of multicomponent diffusion are normally employed: (i) generalized Fick’s law, where the flux is written as a linear combination of driving forces; (ii) the generalized MaxwellStefan theory, where the driving force is given as a linear combination of the flux, and (iii) via the irreversible thermodynamics [23]. Mulder and Smolder proposed a predictive mass transfer model of the aqueous ethanol solution through the polyamide (PA) membrane with the
Corresponding authors at: Sichuan University, No. 24 South Section 1, Yihuan Road, 610065 Chengdu, China. E-mail addresses: [email protected] (S. Fan), [email protected] (Z. Xiao).
https://doi.org/10.1016/j.seppur.2019.03.021 Received 17 December 2018; Received in revised form 6 March 2019; Accepted 6 March 2019 Available online 07 March 2019 1383-5866/ © 2019 Elsevier B.V. All rights reserved.
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Nomenclature
aim Vi Dsi ue
ce x Di Di0 Dim kl km K cb cbm
cm1 cm2
zb Je S
The activity of component i in the membrane Molar volume Single penetrant swelling capacity Ethanol volume fraction in the ethanol/water mixtures in the polymer Ethanol concentration in membrane (wt%) Direction of mass diffusion (m) Diffusion coefficient of component i into the membrane (m2 s−1) Limiting diffusivity considering concentration polarization (m2 s−1) Mean diffusivity in the membrane (m2 s−1) Convective mass transfer coefficient (m2 s−1) Membrane mass transfer coefficient (m2 s−1) Partition coefficient Ethanol concentration in bulk feed solution (wt%) Ethanol concentration in liquid at interface of liquid boundary layer/membrane (wt%) Ethanol concentration in membrane at interface of liquid boundary layer/membrane (wt%) Ethanol concentration on the downstream side of the membrane (wt%)
Thickness of the membrane cell (m) Ethanol flux (gm−2 h−1) Effective membrane surface area (m2)
Greek letters
ϕ
φ χwe χim η ρ μ τ
Volume fraction of components and membrane in the ternary system Volume fraction of component obtained from the experiments of pure component sorption in the membrane Solvent/solvent interaction parameter Solvent/polymer interaction parameter Concentration polarization coefficient Density (kg m−2) Dynamic viscosity (Pa s) Time duration of experiment (h)
Subscripts and superscripts w e m u d
Water Ethanol PDMS membrane Membrane upstream side Membrane downstream side
permeating component. Concentration polarization usually results in a lower productivity and a lesser extent of separation [12]. The boundary layer effect is expected to be significant for highly permselectivity even though the permeation flux is usually low for some of the current pervaporation membranes [14]. It has been reported that the effect of concentration polarization is depended on both the fluid dynamics conditions and the membrane permeability. Moreover, boundary layer resistance during pervaporation for the transfer of organic solutes across membranes with high selectivity and/or permeability was of great importance [27]. According to the resistance-in-series theory, pervaporation process is composed of two successive mass transfer steps: convective mass transfer on the upstream of the membrane and diffusion mass transfer across membrane [28–30]. Besides, ethanol concentration is kept being equilibrium at the interface of liquid boundary layer/membrane. Membrane separation performance and concentration polarization would be affected by convective mass transfer, phase equilibrium and
activity of the components in the membrane calculated by Flory-Huggins theory [24]. Based on the solution-diffusion model, Raisi used Flory-Huggins theory to describe the transfer of ethanol/water mixture in PDMS membrane [25]. The diffusion step could be simplified using generalized Fick’s law, if ethanol diffusion coefficient was assumed to be only dependent on the total volume fraction of all the solvent species in the membrane [26]. In these researches, ethanol concentration in liquid boundary layer at interface of liquid boundary layer/membrane was assumed being equal to that in liquid bulk. In other words, solution-diffusion models were developed without considering concentration polarization. Concentration polarization is inherent to all membrane processes, since the permeation rates of different permeating components are different during membrane separation. The concentration of the fast permeating component on the membrane surface is lower than that in the liquid bulk because of retention of the slow permeating component on the membrane surface, while the opposite is true for the slow
Fig. 1. Scheme of ethanol mass transfer during pervaporation. 277
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V
diffusion mass transfer. The aim of this study is to develop a mass transfer model based on the solution-diffusion theory with the consideration of concentration polarization to describe ethanol recovery by pervaporation with PDMS membrane. The effects of convective mass transfer coefficient, partition coefficient and diffusion mass transfer coefficient in membrane on membrane separation including ethanol flux and concentration polarization coefficient would be reported.
w
w
The scheme of ethanol mass transfer during pervaporation was illustrated in Fig. 1. Where cb and cbm are ethanol concentration in liquid bulk and in liquid boundary layer at interface of liquid boundary layer/ membrane, respectively. cm1 and cm2 are the concentration in membrane at interface of liquid boundary layer/membrane and on the downstream side of the membrane, respectively. It could be seen that ethanol mass transfer from the feed solution to the downstream of the membrane should be followed the orders: (1) Ethanol is transferred across a liquid boundary layer by convective mass transfer. cb decreased to cbm in the liquid boundary layer. The process of ethanol transfer in liquid boundary layer can be described as follows:
φi =
ln(φi ) + (1 − φi ) (1 − φi )2
Dsi ⎛ Dsi 1 − Dsi ⎞ /⎜ + ⎟ ρi ⎝ ρi ρm ⎠
cm1 =
ϕe ρe ϕe ρe + ϕw ρw
Je = −De ρe
where K is partition coefficient. (3) Ethanol is transferred across membrane by diffusion, and ethanol concentration in membrane is decreased from cm1 to cm2 during diffusion process. cm2 is assumed to be equal to zero under high vacuum. The process of ethanol diffused across the membrane can be described as follows:
(10)
dx
De = De0 ψ (ϕ)
(11)
ψ (ϕ) = exp(γe ϕ)
(12)
where De0 is the limit diffusivity of ethanol and γe is the plasticization coefficient of ethanol. Combining Eqs. (10)–(12), ethanol flux during pervaporation can be described as follows: ϕ
(4)
Je = −De ρe
where km is the membrane mass transfer coefficient through the membrane.
dϕe dx
=
De0 ρe zb
(ϕeu − ϕed )
∫ϕd u ψ (ϕ) dϕ ϕu − ϕd
(13)
where z b is the thickness of the membrane; ϕu and ϕd are the total volume fraction of water and ethanol on membrane upstream and downstream, respectively; ϕeu and ϕed are the volume fraction of ethanol on membrane upstream and downstream, respectively. It is assumed that the permeate side of the membrane is dry during pervaporation under high vacuum condition. Therefore ϕd and ϕed are equal to zero. According to the total solvent volume fraction theory, the mean diffusion coefficient of ethanol can be described as follows:
2.2. Sorption into membrane The activities of ethanol and water in solution are equal to those in the membrane, since equilibrium at interface of liquid boundary layer/ membrane is assumed. The activity of ethanol and water in solution can be calculated according to the Wilson function [17]. The activity of ethanol and water in the ternary system (ethanol, water and membrane) can be obtained according to the Flory-Huggins thermodynamics theory, described as follows:
ϕ
Dem = De0
V
ln a wm = ln ϕw + (1 − ϕw ) − ϕe Vw − ϕm Vw + (χwe ϕe + χwm ϕm)
∫ϕd u ψ (ϕ) dϕ ϕu − ϕd
= De0
e γe ϕu − 1 γe ϕu
(14)
where Dem is the mean diffusivity of ethanol in the membrane. Combining Eqs. (13) and (14), a simple relationship between the flux and the volume fraction in the membrane can be described as
m
Vw ϕϕ Ve e m
dϕe
where De is ethanol diffusion coefficient; ρe is ethanol density and x is the direction of mass diffusion. During pervaporation process, the relationship between ethanol diffusion coefficient and ethanol concentration is often described in exponential form:
(3)
e
(9)
The diffusion process of ethanol in the membrane can be expressed by the Fick’s law, described as follows:
(2) Ethanol is sorpted into the surface of the membrane. Ethanol concentration is increased to cm1 after passing across the interface of liquid boundary layer/membrane. It is assumed that equilibrium of ethanol concentration is achieved at the interface, described as follows:
(ϕe + ϕm) − χem
(8)
2.3. Diffusion across the membrane
(2)
V
(7)
where Dsi is the weight fraction of the component i in the swollen membrane. ρi and ρm are densities of component and PDMS membrane respectively. cm1 is related to density and volume fraction of components in membrane, described as follows:
where kl is the convective mass transfer coefficient. It’s value can be obtained according to our previous work [31]. The concentration polarization coefficient (η ) during pervaporation is related to ethanol concentration in liquid bulk and the concentration in liquid boundary layer at interface of liquid boundary layer/membrane, described as follows:
Je = km (cm1 − cm2)
(6)
where φi is the volume fraction of the component i obtained from the experiments with pure water and pure ethanol sorption in the membrane, described as follows:
(1)
cm1 = K ·cbm
w
where ϕ and V represents volume fraction and molar volume; w, e, m represents water, ethanol and PDMS membrane, respectively; χem , χwm , χwe are ethanol/polymer, water/polymer and water/ethanol interaction parameters, respectively. χwe is determined according to the FloryHuggins thermodynamics. χem and χwm can be expressed using the Flory-Rehner theory, described as follows:
χim = −
(cb − cbm ) × 100% cb
V
V
2.1. Mass transfer steps
η=
m
(ϕw + ϕm) − χwm Ve ϕw ϕm
2. Theory
Je = kl (cb − cbm)
V
ln aem = ln ϕe + (1 − ϕe ) − ϕw Ve − ϕm V e + (χwe ϕw Ve + χem ϕm )
(5) 278
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membrane was increased with the increase of ethanol concentration in feed. This result implied that a higher feed concentration will promote ethanol sorption uptake in the membrane. During the process of sorption equilibrium, the activity of ethanol could be increased linearly with its concentration, if the ethanol concentration in feed is lower than 10 wt%. The increased activity could enhance the sorption of ethanol in the membrane, leading to the higher swelling capacity of the membrane. Swelling of the membrane could weaken the interaction forces between the components in the membrane, with the free volume in the membrane increase, which was favorable to mass transfer during pervaporation. From Fig. 2, it could be also seen that the volume fraction of water showed a slightly decreasing tendency with the ethanol fraction in feed, since the mole fraction of water in feed could decrease slightly with ethanol fraction increase. As a result, the activity of water in feed could be decreased, leading to lower sorption amount in membrane. Ethanol mean diffusivity could be calculated based on the ethanol volume fraction obtained from Fig. 2. The relationship between ethanol mean diffusivity and the total volume fraction was illustrated in Fig. 3. It could be seen that the mean diffusivity of ethanol was exponentially increased with the increase of total volume fraction. The limiting diffusivity of ethanol considering concentration polarization and plasticization coefficient of ethanol would be kept as constants, if the feed temperature and membrane material were determined. The values of these two parameters were induced from Fig. 3. The key parameters of the mathematical models developed in the study for ethanol pervaporation with PDMS-PA composite membrane were illustrated in Table 1.
follows:
Dem ρe
Je =
zb
(ϕeu − ϕed )
(15)
Combining Eqs. (15) and (4), km could be calculated as follows:
km =
Dem zb
(16)
The developed models with the set of nonlinear equations could be solved by the MATLAB software. 3. Materials and method 3.1. Experiments The preparation of the composite PDMS-PA membrane has been fully described in our previous work [31]. In order to determine the amount of pure components absorbed in the PDMS layer of the composite membrane, swelling measurements of the membrane were performed by the well-known gravimetric analysis method. Before the sorption experiment, a piece of round pristine PDMS-PA membrane (diameter 100 mm) and a piece of round pristine PA membrane (diameter 100 mm) were dried in an oven at 60 °C for 5 h to obtain a dry sample and were weighted. After that, the PA membrane and PDMS-PA membrane were fixed at the bottom of petri dishes (inner diameter 130 mm, height 30 mm and wall thickness 5 mm, maximum volume around 400 mL). The ethanol and water (200 mL) were then poured into the dishes, with dishes kept at 45 °C for more than 24 h. The membranes were then removed from the liquid, blotted carefully by filter papers to remove the adherent liquid and weighed in a closed bottle (accuracy 1 mg) as fast as possible. Repeat the above process until constant weight is reached. The membrane sorption experiment of ethanol and water has been conducted more than 50 times to reduce the standard deviation. The detailed pervaporation experimental procedure could be referred from our previous work [31].
4.2. Effect of convective mass transfer coefficient on pervaporation The convective mass transfer coefficient was one of the direct factors that affect ethanol mass transfer behavior during pervaporation. The effect of convective mass transfer coefficient on ethanol separation by PDMS membrane pervaporation was illustrated in Fig. 4. It could be seen that ethanol flux could be increased with the increase of convective mass transfer coefficient. Moreover, the effect of the convective mass transfer on membrane flux was gradually weakened, with the increase of convective mass transfer coefficient. For example, the ethanol flux could be increased 2.63%, if the convective mass transfer coefficient was increased from 8.8 × 10−6 m2 s−1 to 10.0 × 10−6 m2 s−1. The corresponding value was 1.82%, if the convective mass transfer coefficient was increased from 10.0 × 10−6 m2 s−1 to 11.2 × 10−6 m2 s−1. This phenomenon implied that the convective mass transfer would be the controlling step during
3.2. Analytical methods The swelling capacity of the PDMS layer is calculated according to the swelling capacity difference between the PA membrane and the composite membrane, described as follows:
Dsi =
(wi′, PDMS − PA − wi, PDMS − PA) − (wi′, PA − wi, PA ) wi, PDMS − PA − wi, PA
(17)
where w′ and w denote the weight of swollen and dry membranes, respectively. The weight fraction of ethanol and water in the swelled membrane is calculated by integrating Eqs. (5)–(8) and Eq. (17). The flux of membrane is described as follows:
J=
W S·τ
(18)
where W is the mass of ethanol; S is effective membrane surface area and τ is time duration of pervaporation experiment. The measurement for permeate mass and ethanol concentration have also been described in detail in our previous work [31]. 4. Results and discussion 4.1. Determination of parameters Preferential sorption is a prerequisite for preferential diffusion during pervaporation [17,24]. The sorption behavior of ethanol and water in PDMS-PA composite membrane could be determined based on the swelling experiments and corresponding models, as illustrated in Fig. 2. It could be seen that the volume fraction of ethanol in the
Fig. 2. Relationship between ethanol feed concentration and volume fraction of ethanol and water in PDMS-PA composite membrane. feed temperature: 45 °C. 279
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Fig. 5. Effect of partition coefficient on ethanol pervaporation, ethanol concentration: 5 wt%; temperature: 45 °C.
Fig. 3. Effect of total volume fraction on ethanol mean diffusivity coefficient (PDMS-PA membrane, ethanol-water mixture at 45 °C). Table 1 The key parameters of the models for ethanol pervaporation with PDMS membrane. ethanol concentration: 5 wt%; temperature: 45 °C; Reynolds number: 1300. Parameters
Values
Water/polymer interaction parameter χwm Ethanol/polymer interaction parameter χem Water/ethanol interaction parameter χew Limiting diffusivity of ethanol De0 (m2 s−1) Plasticization coefficient of ethanol γe Convective mass transfer coefficient kl (m2 s−1) Diffusion mass transfer coefficient km (m2 s−1) Partition coefficient K
0.78 1.91 2.29 1.85 × 10−5 43.03 1.23 × 10−5 7.05 × 10−7 2.98
Fig. 6. Effect of diffusion mass transfer coefficient on ethanol pervaporation, ethanol concentration: 5 wt%; temperature: 45 °C. Table 2 The decreased ethanol flux caused by concentration polarization under the condition of different convective mass transfer coefficient and diffusion coefficient of ethanol in membrane. km (m2 s−1)
1.0 × 10−6 2.0 × 10−6 3.0 × 10−6
Fig. 4. Effect of convective mass transfer coefficient on ethanol pervaporation with PDMS membrane, ethanol concentration: 5 wt%; temperature: 45 °C.
Decreased ethanol flux caused by concentration polarization (gm−2 h−1) kl = 6.0 × 10−6
kl = 9.0 × 10−6
kl = 12.0 × 10−6
479.02 785.81 998.51
453.35 718.61 892.42
448.04 581.52 690.59
concentration polarization coefficient was illustrated in Fig. 4. It could be seen that the concentration polarization coefficient was decreased with the increase of the convective mass transfer coefficient. This implied that increase of the convective mass transfer could weaken the concentration polarization and improve the membrane separation performance. Moreover, the liquid boundary layer could become thinner with the convective mass transfer resistance decreased, according to the convective mass transfer theory. From Fig. 4, it could be also seen that the concentration polarization coefficient was decreased asymptotically, since the boundary layer could gradually became thinner and tended to be stable with the increase of the convective mass transfer coefficient. The similar phenomenon could also be deduced from our previous work with resistance-in-series model for the description of ethanol pervaporation [31]. From Fig. 4, it could be deduced that ethanol flux could be increased gradually with the decrease
pervaporation, if the convective mass transfer coefficient was lower. In this case, enhancing the convective mass transfer on the upstream of membrane could effectively improve ethanol pervaporation. The reason why ethanol flux was changed with the convective mass transfer coefficient was that the concentration polarization was changed with the convective mass transfer coefficient. Concentration polarization caused ethanol, which was enriched in the permeate to be depleted in the boundary layer, and water which was depleted in the permeate to be enriched in the boundary layer [32]. In this case, there would be a difference of ethanol concentration between in liquid bulk and in liquid boundary layer at interface of liquid boundary layer/ membrane. The effect of convective mass transfer coefficient on the 280
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of the concentration polarization coefficient. The ethanol flux was 292 gm−2 h−1, if the concentration polarization coefficient was 0.23. The corresponding value would be about 380 gm−2 h−1, if there the concentration polarization coefficient was zero (the flowrate was infinite and the convective mass transfer resistance was zero). This value should be the maximum flux at ethanol concentration in liquid bulk being 5 wt% under the condition of feed temperature being 45 °C. In order to minimize concentration polarization caused by convective mass transfer, the most straightforward way was to enhance the flowing performance on the upstream of the membrane, such as developing highly turbulent membrane modules.
concentration polarization coefficient was obtained even under the condition of high Reynolds number, owing to the high membrane mass transfer coefficient [31]. The mass transfer resistance in convective layer could become more significant, if the membrane was highly permeable for ethanol. Under this condition, the concentration polarization coefficient may be higher and the mass transfer resistance in convective layer may become comparable to the mass transfer resistance in membrane [33]. It could be deduced from Fig. 6 that the bad effect of concentration polarization on pervaporation was more and more obvious, if the diffusion coefficient of ethanol in membrane was increased. Obvious decreased ethanol flux caused by concentration polarization was performed under the condition of higher diffusion coefficient of ethanol in membrane. Serious effects of concentration polarization on pervaporation have been also reported in the study of water/methylene chloride system at high Reynolds number ranges [33]. It could be calculated that ethanol flux was just decreased by 133 gm−2 h−1 caused by the concentration polarization, under the condition of diffusion coefficient of ethanol in membrane being 1.0 × 10−6 m2 s−1 with the corresponding concentration polarization coefficient being 0.22. However, ethanol flux could be decreased by 824 gm−2 h−1 owing to concentration polarization, under the condition of diffusion coefficient of ethanol in membrane being 3.0 × 10−6 m2 s−1 with the corresponding concentration polarization coefficient being 0.45. Thus, our developed model could more accurately predict the membrane separation than previous ones without considering concentration polarization, under the condition of higher diffusion coefficient of ethanol in membrane. The convective mass transfer coefficient was one order higher than diffusion coefficient of ethanol in membrane during pervaproation with PDMS membrane. In order to improve the flux of the membrane, improvement of the ethanol permeability of membrane would be of great importance during pervaporation for ethanol separation. However, the concentration polarization was severe if the diffusion coefficient of ethanol in membrane was higher. In this case, it was of great importance to minimize the concentration polarization by some approaches, such as enhanced the convective mass transfer on the upstream of the membrane. The decreased ethanol flux caused by concentration polarization under the different convective mass transfer coefficient and diffusion coefficient of ethanol in membrane were illustrated in Table 2. It could be deduced that enhanced convective mass transfer on the upstream of the membrane was more effective to weak the concentration polarization and promote membrane separation, under the condition of using high ethanol permeable membranes [34]. Moreover, accomplish of a microfluidic format could also weak concentration polarization, since it could drastically improve mass transfer in the boundary layer on the upstream of the membrane [35].
4.3. Effect of partition coefficient on pervaporation Pervaporation performance could be affected by the partition coefficient, as illustrated in Fig. 5. It could be seen that ethanol flux was increased with partition coefficient. The partition coefficient represents an equilibrium state of solute ethanol at the interface of membrane phase and solution phase. It is mainly affected by the interaction between solvent and polymer, which could be characterized by χim . Lower χem or higher χwm would lead to stronger interaction and greater affinity between ethanol and membrane than between water and membrane. In this case, higher ethanol volume fraction in PDMS membranes and higher partition coefficient could be obtained. In order to increase the partition coefficient and improve the mass transfer during pervaporation, it is necessary for invention and application for advanced material and modification of existing membrane materials, which should have stronger interaction between ethanol and polymer and weaker interaction between water and polymer. From Fig. 5, it could be also seen that the concentration polarization coefficient was increased with the increase of the partition coefficient. Higher concentration polarization coefficient has a bad effect on the increase flux. It could be deduced that the decreased ethanol flux caused by concentration polarization was more and more obvious, if the concentration polarization coefficient was higher. For example, ethanol flux was just decreased by 19 gm−2 h−1 caused by the concentration polarization, under the condition of partition coefficient being 2.0 with the corresponding concentration polarization coefficient being 0.09. However, ethanol flux could be decreased by 79 gm−2 h−1 owing to concentration polarization, under the condition of partition coefficient being 3.5 with the corresponding concentration polarization coefficient being 0.17. Therefore, the bad effect of concentration polarization on membrane separation should be paid much attention, if the advanced material having stronger interaction between ethanol and polymer and weaker interaction between water and polymer was used as pervaporation membrane. 4.4. Effect of diffusion mass transfer coefficient on pervaporation
5. Conclusions The diffusion mass transfer coefficient was also one of the direct factors affecting the mass transfer behavior. The effect of diffusion mass transfer coefficient on ethanol flux was illustrated in Fig. 6. It could be seen that ethanol flux could be increased with the increase of the membrane mass transfer coefficient. The increase extent of ethanol flux under the condition of higher diffusion mass transfer coefficient was not as obvious as that in the case of lower diffusion mass transfer coefficient. For example, the ethanol flux could be increased 64.7%, if the diffusion mass transfer coefficient was increased from 1.0 × 10−6 m2 s−1 to 2.0 × 10−6 m2 s−1. The corresponding value was just 26.5%, if the diffusion mass transfer coefficient was increased from 2.0 × 10−6 m2 s−1 to 3.0 × 10−6 m2 s−1. The effect of diffusion mass transfer coefficient on concentration polarization was also illustrated in Fig. 6. It could be seen that the concentration polarization coefficient was increased gradually, with diffusion coefficient of ethanol in membrane increased. This similar result has also be reported from the previous study that higher
A mass transfer model of ethanol recovery by pervaporation with PDMS membrane was developed based on solution-diffusion theory considering concentration polarization. Ethanol flux and polarization coefficient were 318 gm−2 h−1 and 0.42, respectively, under the condition of convective mass transfer coefficient being 1.23 × 10−5 m2 s−1, partition coefficient being 2.98 and ethanol diffusion mass transfer in membrane being 7.05 × 10−7 m2 s−1. Higher convective mass transfer coefficient, higher partition coefficient and higher ethanol diffusion mass transfer in membrane could improve the membrane flux. However, the bad effect of concentration polarization coefficient on ethanol flux was severe if the partition coefficient and ethanol diffusion mass transfer in membrane are higher. The developed model could accurately predict membrane separation, especially under the condition of higher concentration polarization coefficient.
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Acknowledgements [18]
The present work was supported by the Fundamental Research Funds for the Central Universities (No. 20822041B4013).
[19]
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