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HEC) composite membranes
Journal of Membrane Science 199 (2002) 211–222
Pervaporation dehydration of ethanol–water mixtures with chitosan/hydroxyethylcellulose (CS/HEC) composite membranes II. Analysis of mass transport R. Jiraratananon a,∗ , A. Chanachai a , R.Y.M. Huang b a
Department of Chemical Engineering, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand b Department of Chemical Engineering, University of Waterloo, Waterloo, Ont., Canada N2L 3G1 Received 1 March 2001; accepted 4 October 2001
Abstract This work investigates mass transport in pervaporation dehydration of ethanol–water mixture with CS/HEC composite membrane. The analysis employed the pervaporation data obtained over a wide range of experimental conditions together with the resistance-in-series model, and the concentration dependent diffusion equations. The results reported are transport resistances for components, plasticizing and coupling coefficients. Transport resistances for the top membrane layer were much higher than other resistances which implied that transport in the dense membrane layer was the controlling step. Resistance for transport of water in the top layer was relatively low compared with that of ethanol. Plasticizing coefficients for water-membrane (kii ) were positive and those of ethanol-membrane (kjj ) were negative indicating that water plasticized CS/HEC membrane but ethanol did not. The coupling coefficients obtained confirmed that ethanol reduced diffusivity of water in the membrane and the presence of water enhanced ethanol diffusion. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Coupling coefficient; Pervaporation; Plasticizing coefficient; Resistance-in-series model; Transport resistance; Water–ethanol mixture
1. Introduction The performance of pervaporation is usually assessed from the permeation flux and selectivity which are affected by the transport mechanisms and by the operating conditions. A full description of the transport mechanism of the pervaporation system usually includes mass transfer in the liquid feed boundary layer, the membrane, and the permeate vapor boundary, respectively [1]. To account for all the ∗ Corresponding author. E-mail address: [email protected] (R. Jiraratananon).
mass transfer resistances, a resistance-in-series model has been used by several researchers [1,2]. Apart from its simplicity, the model allows for the contribution of the boundary layer and the membrane resistances to be separated and analyzed. The liquid boundary layer effect due to concentration polarization is often assumed to be insignificant for most pervaporation processes because the permeation fluxes are usually low [3,4]. However, there are reports indicating that fluxes were strongly affected by the operating conditions on the feed side. For example, in removal of trichloroethylene from aqueous solution, solute transfer through the membrane was
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Nomenclature ai ai ,X ai ,XY ci ,X ci ,XY cL dp Di ,X Di o,M Ep Ji kii
kij kL Ksi Mi pi pi ,X pi ,XY psat,i R Ri ,L Ri ,M Ri ,S Ri ,T
activity of component i activity of component i in X bulk activity of component i in X at X/Y interface molar concentration of component i in X (kmol/m3 ) molar concentration of component i in X at X/Y interface (kmol/m3 ) molar density of liquid feed (kmol/m3 ) pore diameter (m) diffusion coefficient of component i in X (m2 /s) diffusion coefficient of component i in the membrane at infinite dilution (m2 /s) apparent activation energy of permeation (J/mol) molar flux of component i (kmol/m2 s) plasticizing coefficient of component i for two-component permeation (m3 /kmol) coupling coefficient of component i with j (m3 /kmol) mass transfer coefficient in liquid boundary layer (m/s) sorption coefficient of component i (kmol/m3 ) molecular weight of component i (kg/kmol) partial vapor pressure of component i (kg/m s2 ) partial vapor pressure of component i in X (kg/m s2 ) partial vapor pressure of component i in X at X/Y interface (kg/m s2 ) saturated vapor pressure of component i (kg/m s2 ) ideal gas constant liquid boundary layer resistance of component i (m2 s/kmol) membrane top layer resistance of component i (m2 s/kmol) support layer resistance of component i (m2 s/kmol) total resistance of component i (m2 s/kmol)
TS vL vP V xi xi ,X xi ,XY
temperature in porous support (K) average bulk liquid velocity (m/s) permeate molar average velocity (m/s) molar volume (m3 /kmol) mole fraction of component i mole fraction of component i in X mole fraction of component i in X at X/Y interface
Greek letters α separation factor βi enrichment factor β i ,M enhancement factor χ porous support porosity δM membrane thickness (m) δS porous support thickness (m) ε porous support tortuosity γ activity coefficient λi mean free path of vapor of component i in support layer (m) ρ density (kg/m3 ) Subscripts L liquid M membrane P permeate S support X liquid (L), membrane (M), permeate (P), or support (S) Y liquid (L), membrane (M), permeate (P), or support (S) primarily governed by the hydrodynamic conditions on the feed side when Reynolds numbers ranged from 1 to 60 [5]. Raghunath and Hwang [6,7] showed that for pervaporation of dilute aromatic organic solutions, liquid boundary layer resistance contributed significantly to total transport resistance. The fact that liquid boundary resistance can be a limiting factor in the dehydration of isopropanol by pervaporation was also reported [8]. Analysis of Feng and Huang [9], based on the film theory showed that the significance of concentration polarization was determined not only by the membrane permeability but also by hydrodynamic conditions and it should not always be overlooked even for the membranes with moderate permeability.
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Concentration polarization should be more significant when the preferentially permeable target component is present at low concentration. The primary transport resistance of pervaporation system is often assumed to be in the membrane itself [3,4]. Pervaporation membrane are usually dense (non-porous) or composite. Transport through a dense membrane or an active layer of a composite membrane can be described by the widely accepted solution–diffusion model [3,4]. A number of mathematical equations have been formulated based on Fick’s law using different empirical expressions for concentration dependence of solubility and/or diffusivity, i.e. coupling and plasticizing between components and the membrane are accounted for. Several studies showed that the properties of porous supports of composite membranes such as porosity affected pervaporation flux and selectivity [10–12] and porous support resistance may not be neglected. The selectivity attainable for the composite membrane was shown to be controlled by the relative resistance of the active layer and the support. There have been limited works which reported detailed analysis of transport resistances of the pervaporation dehydration systems. This paper is part II of our study on pervaporation dehydration of ethanol–water mixtures by composite CS/HEC-cellulose acetate (CA) membrane. In this paper we apply resistance-in-series model to calculate the transport resistance of liquid boundary layer and those of the composite membrane using the experimental data of part I [13]. The objectives of this work are to systematically analyze the transport resistances and to elucidate the transport mechanisms in the composite membrane. Coupling and plasticizing between components and membrane are discussed and presented in terms of related coefficients. The results are expected to enhance the fundamental understanding and contribute to further development of efficient pervaporation systems.
2. Theory 2.1. Mass transport model for pervaporation system Based on the resistance-in-series model transport of a component from the feed solution through the com-
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posite membrane occurs by the following steps: (1) transport through a liquid boundary layer, (2) sorption into the membrane top (active) layer, (3) diffusion of liquid through the membrane top layer, (4) desorption from the top layer, (5) transport of vapors through the porous support, and (6) transport in vapor boundary layer. The concentration profiles of the components for a binary system are depicted in Fig. 1. The transport equations describing mass transfer of each step can be written in terms of permeation flux of i, the more preferentially permeable component (in this case, i = water) and its corresponding driving forces. 2.1.1. Step 1: Transport through the liquid boundary layer The diffusive flux of i through a liquid boundary layer is expressed as Ji = kL (ci,L − ci,LM )
(1)
For dehydration, xi,LM < xi,L , and xj,LM > xj,L , therefore, back diffusion of the components to the bulk solution and convective flux cannot be neglected. To incorporate the contribution of convective transport the concentration polarization equation [9] is substituted into Eq. (1) and rearrange to give Ji =
VP cL (xi,L −xi,LM ) (2) (1 − (1/βi ))[exp(VP /kL ) − 1]
where ai pi xi = = γi γi psat,i
(3)
and βi = enrichment factor for i = xi,P /xi,L By assuming that γi,L = γi,LM , Eq. (2) can be written as Ji =
V P cL (ai,L −ai,LM ) (1 − (1/βi ))[exp(VP /kL )−1]γi,L (4)
2.1.2. Step 2: Sorption of the components into the membrane top layer By assuming equilibrium at the liquid/membrane interface, the concentration of a component in the membrane at the interface, ci ,ML , is proportional to its activity, i.e. ci,ML = Ksi ai,LM
(5)
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Fig. 1. Concentration profiles of components across the liquid boundary layer, a composite membrane and the vapor phase.
It should be noted that for non-ideal sorption of polar molecules (water) into hydrophilic membranes, Ksi is concentration dependent. Ksi can be obtained from the sorption experiments. 2.1.3. Step 3: Diffusion through the membrane top layer Fick’s first law of diffusion is applied to describe the diffusion of a component in top membrane layer. For multicomponent mixtures which are non-ideal such as ethanol–water, the exponential diffusion equations which include the effect of plasticizing and coupling on the diffusivities were proposed by Burn et al. [14]. Di,M = Dio,M exp(kii ci + kij cj )
(6)
Dj,M = Dj o,M exp(kji ci + kjj cj )
(7)
where kii and kjj are plasticizing coefficients of components i and j, respectively, and kij and kj i are
coupling coefficients of component i with j and j with i, respectively. By substitution of Eq. (6), the Fickian-type diffusion becomes dci,M Ji = Dio,M exp(kii ci,M + kij cj,M ) (8) dz Then Eq. (8) can be rewritten as Ji =
Dio,M βi,M (ci,ML − ci,MS ) δM
(9)
where βi,M =
1 ci,ML − ci,MS ci,ML × exp(kii ci,M + kij cj,M ) dci,M ci,MS
(10)
β i ,M is the enhancement factor that represents the effect of concentration of the component in the membrane on component diffusivities. By assuming constant sorption coefficient at location 1 and 2
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(see Fig. 1) and that T1 = T2 = T L , the concentration of i at top layer/support interface, ci ,MS , is as follows: ci,MS = Ksi ai,SM Dio,M βi,M Ksi (ai,LM − ai,SM ) δM
(11)
(12)
Ji =
2.1.4. Step 4: Desorption at the membrane top/support interface By assuming that the pressure in the porous support is near the vacuum as in the permeate side, liquid molecules desorped at top membrane layer/support will simultaneously evaporate and there activities can be expressed as in Eq. (11). 2.1.5. Step 5: Transport of vapor molecules through the porous support There are three possible mechanisms of the vapor transport if the pores are assumed to be small capillaries, depending upon Knudsen number (Nkn ) [15,16] Nkn =
mean free path λi = pore diameter dp
(13)
If Nkn ≥ 10, only Knudsen flow prevails. If 0.01 < Nkn < 10, molecular transport in a capillary is by transient flow. When Nkn ≤ 0.01, viscous flow is the main transport mechanism. In this work, pore diameter of the support is approximately 10−6 m, and λi of water and ethanol is 10−4 m. The Knudsen number is higher than 10. The transport of vapors is, thus, by Knudsen flow in which the flux equation is [17] 1 dp ε 8RTS 1/2 1 Ji = (pi,SM − pi,P ) (14) 3 δS χ πMi RTS Eq. (14) can be rearranged to give 1 dp ε 8RTS 1/2 psat,i Ji = (ai,SM − ai,P ) 3 δS χ πMi RTS
2.2. Mass transport resistance To illustrate the resistance-in-series model, the flux Eqs. (4), (12) and (15) are combined into a single equation which expresses the component transport as a function of driving force and total transport resistance
Eq. (9) can be rewritten as Ji =
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(15)
2.1.6. Step 6: Transport through the vapor boundary layer For most pervaporation systems, no transport resistance of permeate side is usually assumed since the vacuum is applied. No transport resistance is, therefore, assumed for our analysis.
1 (ai,L − ai,P ) Ri,L + Ri,M + Ri,S
(16)
where Ri,L =
(1 − (1/βi ))[exp(VP /kL ) − 1]γi,L VP c L
(17)
Ri,M =
δM Dio,M βi,M Ksi
(18)
Ri,S = 3
δS χ dp ε
π Mi 8RTS
1/2
RTS psat,i
(19)
and Ri,T =
ai,L − ai,P = Ri,L + Ri,M + Ri,S Ji
(20)
where Ri ,L is the liquid boundary layer resistance (m2 s/kmol), Ri ,M the membrane top layer resistance (m2 s/kmol), Ri ,S the support layer resistance (m2 s/kmol), and Ri ,T is total resistance (m2 s/kmol).
3. Pervaporation and physical property data 3.1. Pervaporation results The experimental data on pervaporation of ethanol–water mixtures by CS/HEC-CA composite membrane of the blend ratio 3/1 reported in the first part [13] were employed in the calculations of the mass transport resistances. 3.2. Physical properties The physical properties required for the calculations were obtained as the followings: • viscosities of aqueous ethanol solutions [18,19]; • densities of aqueous ethanol solutions [19,20]; • diffusion coefficients of ethanol in water were calculated by Stokes–Einstein equation [21];
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• activity and activity coefficients were determined by UNIFAC method [22,23]; • saturated vapor pressure of water and ethanol were calculated from Antoine equation [24]; • viscosities of water and ethanol vapor [16]; • mean free path of water and ethanol [16]. 3.3. Determination of pure component diffusion coefficients in the membrane by desorption method A dense membrane, cut into a piece of 1.5×10 cm2 , was immersed in a liquid (pure water and ethanol) at room temperature until an equilibrium was reached (approximately 7 days). The swollen membrane was then hung on a microbalance exposed to the vacuum. The decrease of the membrane weight due to vapor desorption was recorded until there was no significant weight change. By using the final rate method proposed by Crank [25] the diffusion coefficient at a certain temperature can be calculated. 4. Calculation procedures For each pervaporation experiment the data of feed, permeate compositions, total fluxes and those listed in Section 3.2 were required in the calculation, Ri ,L and Ri ,S were calculated from Eqs. (17) and (19), respectively. Ri ,T and Ri ,M were then calculated from Eq. (20). In order to calculate kii , kjj , kij and kj i , the concentration profile of each component in the membrane is required. For a binary system, the molar flux ratio of components i and j (see Eq. (8)) is Dio,M exp(kii ci,M + kij cj,M ) dci,M Ji = (21) Dj o,M exp(kji ci,M + kjj cj,M ) dcj,M Jj Let φi = kii − kji and φj = kjj − kij . Therefore, exp(φj cj,M )dcj,M =
Dio,M Jj exp(φi ci,M )dci,M Dj o,M Ji (22)
and exp(kij cj,M ) =
Dio,M Jj φj (exp(φi ci,M ) Dj o,M Ji φi
kij /φj −exp(φi ci,ML ))+exp(φj cj,ML ) (23)
Substitution of Eqs. (21)–(23) into (8) yields Dio,M ci,ML exp(kii ci,M ) Ji = δM ci,MS Dio,M Jj φj × (exp(φi ci,M ) − exp(φi ci,ML )) Dj o,M Ji φi kij /φj +exp(φj cj,ML ) dci,M (24) Compare Eqs. (9) and (24), therefore, ci,ML 1 exp(kii ci,M ) βi,M = ci,ML − ci,MS ci,MS Dio,M Jj φj (exp(φi ci,M ) − exp(φi ci,ML )) × Dj o,M Ji φi kij /φj dci,M (25) +exp(φj cj,ML ) From the obtained values of Ri ,M and Ksi , β i ,M can be calculated from Eq. (18). Di o,M was from the desorption experiment. Then kii , kjj , kij and kj i were obtained by using the iterative Levenberg–Marquardt method. The example of calculations is given in an Appendix A.
5. Results 5.1. Transport resistances Table 1 summarizes the transport resistances calculated over the range of experimental conditions studied. All resistances were positive except for Re,L (liquid boundary layer resistance for ethanol) which were negative indicating that transport of ethanol was in opposite direction to water. The top layer resistance to transport of water (Rw,M ) were only 0.008–1.48% of that of ethanol (Re,M ). This indicated that water transported much easier than ethanol due to higher sorption and diffusion of water in the hydrophilic membrane. Rw,M were 95–98% of total transport resistance of water (Rw,T ) while Re,M were as high as Re,T . It suggested that transport in the membrane top layer was the transport controlling step. Compared to other resistances, Ri ,L were low (<4%) and Ri ,S were negligible (<1.4%). For pervaporation of trichloroethylene–water mixtures with silicone rubber
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Table 1 Transport resistances in pervaporation of ethanol–water mixtures calculated from the experimental data Ri (m2 s/kmol)
Ri /Ri ,T (%)
Rw,L Re,L Rw,M Re,M Rw,S Re,S Rw,T Re,T
Rw,L /Rw,T Re,L /Re,T Rw,M /Rw,T Re,M /Re,T Rw,S /Rw,T Re,S /Re,T
770.17–3936.41 −4.62 × 104 to −4.89 × 106 2.46 × 104 to 1.85 × 105 1.89 × 106 to 1.64 × 109 179.12–439.66 123.51–293.84 2.56 × 104 to 1.89 × 105 1.83 × 106 to 1.64 × 109
(hydrophobic) composite membrane [1], porous support layer resistance was also found to be negligible. However, liquid boundary layer resistance was higher than membrane top layer resistance. It might be due to the difference in membranes and transport components. There were reports [5–7] that liquid boundary resistance was significant in pervaporation with hydrophobic membranes. For those cases the resistances were not separately calculated for each component and liquid boundary resistance was calculated directly from inversion of mass transfer coefficient which is true only for the components that are depleted in the boundary layer. It can be seen from Table 1 that Rw,S is higher than Re,S (Rw,S /Re,S = 145.02 − 149.63%) which was unexpected because water molecule is smaller than ethanol molecule. Ri ,S proposed in this model includes the dependence of desorption on the transport of vapor in porous support. The saturated vapor pressure of water is 2.4 times lower than that of ethanol, e.g. psat,w and psat,e are 149.5 and 351.9 mmHg, respectively at 60 ◦ C. This enables the evaporation of ethanol at membrane/support interface to be easier so that the activity of ethanol in the porous support was higher, resulting in a higher driving force for ethanol, i.e. Re,S was lower than Rw,S . 5.1.1. Effect of water content in feed The results are given in Fig. 2. A decrease of Rw,L and absolute Re,L with increasing water content can be observed. According to Eq. (17), Rw,L and absolute Re,L increased with increasing γ i /cL , separation factor and permeate velocity (v P ) and with decreasing kL . In the case of increasing feed water content, a reduction of γ i /cL and separation factor but an increase
Rw /Re (%) 1.14–3.93 0.05–4.19 95.43–98.56 100.05–104.19 0.15–1.38 1.69 × 10−5 to 0.014
Rw,L /Re,L
115.6–222.9
Rw,M /Re,M
0.008–1.45
Rw,S /Re,S
145.02–149.63
Rw,T /Re,T
0.008–1.48
of flux was noticeable. Thus, a decrease of Rw,L and absolute Re,L with water content was attributed to a decrease of γ i /cL and separation factor. This leads to the conclusion that separation factor affected Ri ,L more than flux. A decrease of separation factor (a decrease of β w and an increase of β e ) implied that there was a decrease of ethanol retention at membrane surface. This corresponds to a reduction of component concentration difference between bulk and membrane surface or a decrease of driving force such that Rw,L and absolute Re,L decreased. Both Rw,M and Re,M decreased exponentially with water content in feed which reflected the exponential relationship between diffusion coefficient and concentration in the membrane. An increase of water and ethanol sorption in the membrane caused an increase
Fig. 2. Effect of feed concentration on transport resistances. Operating conditions: ethanol solution, 60 ◦ C; flow rate, 542 ml/min; and permeate pressure, 3 mmHg.
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Fig. 3. Effect of feed flow rate on transport resistances. Operating conditions: 90 wt.% ethanol solution, 60 ◦ C and permeate pressure, 3 mmHg.
of water and ethanol concentration in the membrane top layer, resulted in higher membrane swelling. This behavior enhanced water and ethanol diffusion due to an increase of plasticizing and coupling effects such that β i ,M increased and Ri ,M decreased. Ri ,S was independent upon feed concentration. 5.1.2. Effect of feed flow rate Except Ri ,S which was constant, Rw,L , absolute Re,L , Ri ,M and Ri ,T decreased with increasing feed flow rate as shown in Fig. 3. When feed flow rate was increased for a given feed composition, γ i /cL was constant, separation factor decreased while flux and kL increased. Thus, a reduction of Rw,L and absolute Re,L was due to a decrease of separation factor and an increase of kL (Eq. (17)). Since an increase of flux with feed flow rate caused an increase of Ri ,L , it implied that Ri ,L was more affected by separation factor than by flux. An increase of kL enhanced both transport of water from bulk to the membrane interface and transport of ethanol from the membrane interface to bulk such that Rw,L and absolute Re,L decreased. Concentration polarization effect was expected to be maximum at lowest feed flow rate. As mention earlier that transport in the liquid boundary is not the rate determining step, the question is raised why flux changed with feed flow rate. It was probably because a change of feed flow rate
Fig. 4. Effect of feed temperature on transport resistances. Operating conditions: 90 wt.% ethanol solution; flow rate, 542 ml/min; and permeate pressure, 3 mmHg.
indirectly affected the transport of components in the membrane. A decrease of Rw,L with increasing feed flow rate referred to an increase of water concentration on the membrane surface which induced high water sorption as well as high membrane swelling. Swelling of membrane enhanced water and ethanol diffusion through the membrane and thus both Rw,M and Re,M decreased with increasing feed flow rate. 5.1.3. Effect of feed temperature From Fig. 4, all resistances decreased with feed temperature. Note that the analysis proposed assumes the temperature drop of feed and across the membrane is negligible. An increase of feed temperature caused an increase of kL and a decrease of separation factor, consequently, a decrease of Rw,L and absolute Re,L . Both water and ethanol sorption in the membrane also increased with temperature (higher Ksi ), accordingly, Ri ,M decreased (Eq. (18)). In addition, an increase of sorption caused membrane swelling which resulted in an increase of β i ,M and a decrease of Ri ,M . 5.1.4. Effect of permeate pressure As shown in Fig. 5, raising permeate pressure did not significantly affect Rw,L while Re,L decreased. Since separation factor decreased with increasing permeate pressure the retention of ethanol by membrane was low, which means that the concentration polarization effect was minimized at high permeate pressure.
R. Jiraratananon et al. / Journal of Membrane Science 199 (2002) 211–222
Fig. 5. Effect of permeate pressure on transport resistances. Operating conditions: 90 wt.% ethanol solution, 60 ◦ C and flow rate, 542 ml/min.
By increasing permeate pressure, Ri ,M was increased because of the reduced driving force. Ri ,S was found to be independent of permeate pressure which was also reported by Liu et al. [1]. 5.2. Plasticizing and coupling coefficients Plasticizing coefficients (kii , kjj ) and coupling coefficients (kij , kj i ) for each temperature and composition are displayed in Table 2. Positive kii indicated positive plasticization effect of water on CS/HEC membranes. In other words, the
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presence of water in the membrane caused membrane swelling. On the contrary, ethanol did not plasticize CS/HEC membranes owing to negative kjj . However, kjj were positive for 30 wt.% water content feed at 60 and 70 ◦ C. This may be due to large sorption of ethanol in the membrane at those conditions. Both kii and kjj were often reported to be positive [1,26] for pervaporation of water–organic and organic–organic mixtures with hydrophobic membranes of low sorption selectivity, i.e. sorption of components in the membranes did not significantly different. Negative kij also implied that ethanol had negative effect on diffusion of water. In others words, ethanol reduced diffusivity of water. Ethanol molecules are larger than water molecules and there was a possibility that ethanol molecules blocked the interaction between water molecules and hydrophilic sites of the membrane and then reduced diffusion of water. A positive kj i means that the presence of water enhanced diffusion of ethanol through the CS/HEC membrane. Negative coupling coefficients were also reported [26]. Plasticizing coefficients of water (kii ) increased with feed temperature and water content in feed. However, feed temperature had lower effect. These agreed with the sorption data [13] in which sorption of water increased with temperature and water content. An increase of plasticization effect (or membrane swelling) caused an increase of diffusion of water–ethanol coupled molecules so that kj i increased with feed temperature and water content in feed. Similar results were reported by Sun et al. [26].
Table 2 Plasticizing coefficients of water (kii ) and of water (kjj ) and coupling coefficients of water (kij ) and ethanol (kj i ) Feed temperature (◦ C)
kii (m3 /kmol)
kjj (m3 /kmol)
kij (m3 /kmol)
kj i (m3 /kmol)
5
50 60 70
0.0096 0.0103 0.0105
−7.2023 −4.5972 −2.9762
−3.1085 −2.0429 −1.2837
0.0048 0.0075 0.0079
10
50 60 70
0.0097 0.0112 0.0126
−1.8835 −1.2458 −1.0293
−1.8680 −1.6627 −1.259
0.0085 0.0103 0.0116
20
50 60 70
0.0257 0.0261 0.0277
−1.5521 −1.0810 −0.3670
−1.0075 −1.2783 −0.8303
0.0193 0.0218 0.0231
30
50 60 70
0.0452 0.0491 0.0683
−0.6398 0.6114 0.4506
−1.2678 −1.6126 −1.4903
0.0226 0.0451 0.0626
Water (wt.%)
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6. Conclusions
Flux: J w = 273.05362 g/m2 h (4.21 × 10−6 kmol/ 2 −9 kmol/m2 s), e = 0.35152 g/m h (2.119×10 −6 2 J = 4.2124 × 10 kmol/m s. Sorption data: xw,ML = 0.97553, xe,ML = 0.02447.
m2 s), J Application of resistance-in-series model allows for transport resistances and parameters to be calculated separately but permits overall analysis of the pervaporation system. For pervaporation dehydration of ethanol–water mixture with composite CS/HEC membrane, mass transport of the system was controlled by the transport resistance of components in the top membrane layer (Rw,M , Re,M ). On the other hand, transport resistances in the liquid boundary layer and in the porous support were negligible. All transport resistances for water were relatively low compared to those of ethanol. Therefore, for dehydration purpose the operating conditions selected and the membrane used should be such that transport resistance in the membrane top layer is minimized to obtain the optimal flux, i.e. the system be operated at higher feed flow rate and temperature but at lower permeate pressure. Analysis of plasticizing and coupling coefficients together with transport resistances has enhanced an insight of transport mechanism in pervaporation by hydrophilic membrane in which we expect that the concepts and analysis employed in this work be further applied usefully to analyze pervaporation data of different mixtures and membranes.
Acknowledgements The authors would like to gratefully acknowledge the research funds supported by the National Science and Technology Development Agency of Thailand (NSTDA), and by Natural Sciences and Engineering Research Council of Canada (NSERC).
Appendix A. Example of calculations For pervaporation of 90 wt.% ethanol solution at 60 ◦ C, flow rate 73.925 ml/min and permeate pressure = 3 mmHg. Feed: xw,L = 0.22127, xe,L = 0.77813, ρ L = 785.02 kg/m3 , µL = 7.1 × 10−4 kg/m s, cL = 19.7317 kmol/m3 . Permeate: xw,P = 0.9995, xe,P = 0.0005.
A.1. Mass transport resistance in liquid boundary layer, Ri,L βi = xi,P /xi,L ; β w = 4.51711, β e = 1.6514 × 10−3 , vP = J /cL = 2.139 × 10−7 m/s. Mass transfer coefficient (kL ): for laminar flow in thin channels the mass transfer correlation is as in the following equation [27,28].
vL Di,L kL = 1.18 hL
1/3
where v L is the average bulk velocity the 0.0123 m/s, Di ,L the diffusion coefficient of water in ethanol the 3.498 × 10−9 m2 /s, h the channel half-width the 0.0015/2 m, L the membrane radius 0.02125 m, k L = 2.49445 × 10−5 m/s, γw,L = 1.97317, γe,L = 1.0393. By Eq. (17), Rw,L = 3.14093 × 103 m2 s/kmol, Re,L = −3.28638 × 103 m2 s/kmol. A.2. Mass transport resistance in porous support, Ri,S δ S = 116 × 10−6 m, d p = 1.4 × 10−6 m. Assume ε = 0.6, χ = 3, R = 8.3144 × 103 Pa m3 /kmol K, TS ∼ = feed temperature = 333.15 K, psat,w = 1.99212 × 104 kg/m s2 , psat,e = 4.69017 × 104 kg/m s2 . From Eq. (19), Rw,S = 276.17441 m2 s/kmol, Re,S = 187.58928 m2 s/kmol. A.3. Total transport resistance, Ri,T aw,L = 0.43661, ae,L = 0.80933, ai,P = pi,P / psat,i .Therefore, aw,P = 0.02007, ae,P = 4.29072 × 10−6 . From Eq. (20), Rw,T = 9.89343 × 104 m2 s/kmol, Re,T = 3.81851 × 108 m2 s/kmol. A.4. Mass transport resistance in membrane top layer, Ri,M Ri,M = Ri,T − Ri,L − Ri,S .
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Therefore, Rw,M = 9.55712 × 104 m2 s/kmol, Re,M = 3.85137 × 108 m2 s/kmol. From Eq. (18) δM βi,M = Dio,M Ri,M Ksi where δ M = 4 × 10−6 m, Dwo,M = 20.138 × 10−13 m2 /s, Deo,M = 13.071 × 10−13 m2 /s, K sw = 1.19525 × 102 kmol/m3 , K se = 1.55518 kmol/m3 , Thus, βw,M = 0.17398, βe,M = 0.00511. A.5. Determination of plasticizing and coupling coefficients The ci ,ML was calculated from sorption data, ci ,MS was calculated by Eq. (11); cw,ML = 50.60507 kmol/ m3 , ce,ML = 1.26949 kmol/m3 , cw,MS = 2.53752 kmol/m3 , ce,MS = 7.29119 × 10−6 kmol/m3 . The ci ,ML , ci ,MS and β i ,M were substituted into Eq. (25). Integration of Eq. (25) were carried out by Mathcad program which is based on the iterative Levenberg–Marquardt method. The kii , kjj , kij and kj i were first assumed to obtain the calculated values and the procedures were repeated until there was no difference between the previous and present values.
References [1] M.G. Liu, J.M. Dickson, P. Cote, Simulation of a pervaporation system on the industrial scale for water treatment. Part I. Extended resistance-in-series model, J. Membr. Sci. 111 (1996) 227–241. [2] W. Ji, S.K. Sikdar, S.-T. Hwang, Modeling of multicomponent pervaporation for removal of volatile organic compounds from water, J. Membr. Sci. 93 (1994) 1–19. [3] M.N. De Pinho, R. Rautenbech, C. Herion, Mass transfer in radiation grafted pervaporation membranes, J. Membr. Sci. 54 (1990) 131–143. [4] R.A. Sferrazza, R. Escobosa, C.H. Gooding, Estimation of parameters in a sorption–diffusion model of pervaporation, J. Membr. Sci. 35 (1988) 125–136. [5] R. Psaume, P. Aptel, Y. Aurelle, J.C. Mora, J.L. Bersillon, Pervaporation: importance of concentration polarization in the extraction of trace organics from water, J. Membr. Sci. 36 (1988) 373–384. [6] B. Raghunath, S.-T. Hwang, Effect of boundary layer mass transfer resistance in the pervaporation of dilute organics, J. Membr. Sci. 65 (1992) 147–161.
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[7] B. Raghunath, S.-T. Hwang, General treatment of liquid-phase boundary layer resistance in dilute aqueous organics, J. Membr. Sci. 75 (1992) 29–64. [8] D.A. Colman, T.D. Naylor, G.K. Pearce, R.D. Whitby, Application of membrane pervaporation to the dehydration of alcohols in chemicals and pharmaceuticals processing, in: A. Green (Ed.), Proceedings of the International Technical Conference on Mem. Sep. Proc., Brighton, UK, 1989, pp. 1–17. [9] X. Feng, R.Y.M. Huang, Concentration polarization in pervaporation separation processes, J. Membr. Sci. 92 (1994) 201–208. [10] H. Ohya, M. Shibata, Y. Negishi, Q.H. Guo, H.S. Choi, The effect of molecular weight cut-off of PAN ultrafiltration support layer on separation of water–ethanol mixtures through pervaporation with PAA–PAN composite membrane, J. Membr. Sci. 90 (1994) 91–100. [11] G.H. Koops, J.A.M. Nolten, M.H.V. Mulder, C.A. Smolders, Poly(vinyl chloride)/polyacrylonitrile composite membranes for the dehydration of acetic, J. Membr. Sci. 81 (1993) 57–70. [12] H.S. Choi, T. Hino, M. Shibata, Y. Negishi, H. Ohya, The characteristics of a PAA–PSf composite membranes for a separation of water–ethanol mixtures through pervaporation, J. Membr. Sci. 72 (1992) 259–266. [13] R. Jiraratananon, A. Chanachai, R.Y.M. Huang, D. Uttapap, Pervaporation dehydration of ethanol–water mixtures with chitosan/hydroxyethylcellulose (CS/HEC) composite membranes: I. Effect of operating conditions, J. Membr. Sci. 195 (2002) 143–151. [14] J.P. Burn, C. Larchet, R. Melet, G. Bulvestre, Modeling of the pervaporation of binary mixtures through moderately swelling non-reacting membranes, J. Membr. Sci. 23 (1985) 257–283. [15] T. Matsura, Synthetic Membranes and Membrane Separation Process, CRC Press, Boca Raton, FL, 1994. [16] R.S. Brodkey, H.C. Hershey, Transport Phenomena, International Editions, McGraw-Hill, Singapore, 1988. [17] R.W. Schofield, A.G. Fane, C.J.D. Fell, Gas and vapor transport through microporous membranes. I. Knudsen– Poiseuille transition, J. Membr. Sci. 53 (1990) 159–171. [18] R.C. Ried, J.M. Prausnitz, T.K. Sherwood, The Properties of Gases and Liquids, 3rd Edition, McGraw-Hill, New York, 1977. [19] R.H. Perry, D. Green, Perry’s Chemical Engineers’ Handbook, 6th Edition, McGraw-Hill, New York, 1977. [20] V.L. Streeter, E.B. Wylie, Fluid Mechanics, McGraw-Hill, Singapore, 1983. [21] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, Wiley, Singapore, 1960. [22] J.M. Smith, H.C. Van Ness, Introduction to Chemical Engineering Thermodynamics, 4th Edition, McGraw-Hill, New York, 1987. [23] J. Gmehling, P. Resmussen, A. Fredenslund, Vapor–liquid equilibria by UNIFAC group contribution. Revision and extension 2, Ind. Chem. Proc. Des. Dev. 21 (1982) 118–127. [24] T. Boublik, V. Fried, E. Hala, The Vapor Pressures of Pure Substances, Elsevier, Amsterdam, 1984.
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[25] J. Crank, The Mathematics of Diffusion, 2nd Edition, Clarendon Press, London, 1975. [26] Y.-M. Sun, Y.-K. Chen, C.-H. Wu, A. Lin, Pervaporation for the mixture of benzene and cyclohexane through PPOP membranes, AIChE J. 45 (1999) 523–534. [27] J. Joseph, S. Shen, R.F. Probstein, On the prediction of the limiting flux in laminar ultrafiltration of macro-
molecule solutions, Ind. Eng. Chem. Fund. 16 (1977) 459– 465. [28] W.F. Blatt, A. Dravid, A.S. Michales, L. Nelsen, Solute polarization and cake formation in membrane ultrafiltration: case, consequences and control techniques, in: J.E. Flinn (Ed.), Membrane Science and Technology, Plenum Press, New York, 1970, pp. 47–49.
Pervaporation dehydration of ethanol–water mixtures with chitosan/hydroxyethylcellulose (CS/HEC) composite membranes II. Analysis of mass transport R. Jiraratananon a,∗ , A. Chanachai a , R.Y.M. Huang b a
Department of Chemical Engineering, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand b Department of Chemical Engineering, University of Waterloo, Waterloo, Ont., Canada N2L 3G1 Received 1 March 2001; accepted 4 October 2001
Abstract This work investigates mass transport in pervaporation dehydration of ethanol–water mixture with CS/HEC composite membrane. The analysis employed the pervaporation data obtained over a wide range of experimental conditions together with the resistance-in-series model, and the concentration dependent diffusion equations. The results reported are transport resistances for components, plasticizing and coupling coefficients. Transport resistances for the top membrane layer were much higher than other resistances which implied that transport in the dense membrane layer was the controlling step. Resistance for transport of water in the top layer was relatively low compared with that of ethanol. Plasticizing coefficients for water-membrane (kii ) were positive and those of ethanol-membrane (kjj ) were negative indicating that water plasticized CS/HEC membrane but ethanol did not. The coupling coefficients obtained confirmed that ethanol reduced diffusivity of water in the membrane and the presence of water enhanced ethanol diffusion. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Coupling coefficient; Pervaporation; Plasticizing coefficient; Resistance-in-series model; Transport resistance; Water–ethanol mixture
1. Introduction The performance of pervaporation is usually assessed from the permeation flux and selectivity which are affected by the transport mechanisms and by the operating conditions. A full description of the transport mechanism of the pervaporation system usually includes mass transfer in the liquid feed boundary layer, the membrane, and the permeate vapor boundary, respectively [1]. To account for all the ∗ Corresponding author. E-mail address: [email protected] (R. Jiraratananon).
mass transfer resistances, a resistance-in-series model has been used by several researchers [1,2]. Apart from its simplicity, the model allows for the contribution of the boundary layer and the membrane resistances to be separated and analyzed. The liquid boundary layer effect due to concentration polarization is often assumed to be insignificant for most pervaporation processes because the permeation fluxes are usually low [3,4]. However, there are reports indicating that fluxes were strongly affected by the operating conditions on the feed side. For example, in removal of trichloroethylene from aqueous solution, solute transfer through the membrane was
0376-7388/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 6 - 7 3 8 8 ( 0 1 ) 0 0 6 9 9 - 8
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Nomenclature ai ai ,X ai ,XY ci ,X ci ,XY cL dp Di ,X Di o,M Ep Ji kii
kij kL Ksi Mi pi pi ,X pi ,XY psat,i R Ri ,L Ri ,M Ri ,S Ri ,T
activity of component i activity of component i in X bulk activity of component i in X at X/Y interface molar concentration of component i in X (kmol/m3 ) molar concentration of component i in X at X/Y interface (kmol/m3 ) molar density of liquid feed (kmol/m3 ) pore diameter (m) diffusion coefficient of component i in X (m2 /s) diffusion coefficient of component i in the membrane at infinite dilution (m2 /s) apparent activation energy of permeation (J/mol) molar flux of component i (kmol/m2 s) plasticizing coefficient of component i for two-component permeation (m3 /kmol) coupling coefficient of component i with j (m3 /kmol) mass transfer coefficient in liquid boundary layer (m/s) sorption coefficient of component i (kmol/m3 ) molecular weight of component i (kg/kmol) partial vapor pressure of component i (kg/m s2 ) partial vapor pressure of component i in X (kg/m s2 ) partial vapor pressure of component i in X at X/Y interface (kg/m s2 ) saturated vapor pressure of component i (kg/m s2 ) ideal gas constant liquid boundary layer resistance of component i (m2 s/kmol) membrane top layer resistance of component i (m2 s/kmol) support layer resistance of component i (m2 s/kmol) total resistance of component i (m2 s/kmol)
TS vL vP V xi xi ,X xi ,XY
temperature in porous support (K) average bulk liquid velocity (m/s) permeate molar average velocity (m/s) molar volume (m3 /kmol) mole fraction of component i mole fraction of component i in X mole fraction of component i in X at X/Y interface
Greek letters α separation factor βi enrichment factor β i ,M enhancement factor χ porous support porosity δM membrane thickness (m) δS porous support thickness (m) ε porous support tortuosity γ activity coefficient λi mean free path of vapor of component i in support layer (m) ρ density (kg/m3 ) Subscripts L liquid M membrane P permeate S support X liquid (L), membrane (M), permeate (P), or support (S) Y liquid (L), membrane (M), permeate (P), or support (S) primarily governed by the hydrodynamic conditions on the feed side when Reynolds numbers ranged from 1 to 60 [5]. Raghunath and Hwang [6,7] showed that for pervaporation of dilute aromatic organic solutions, liquid boundary layer resistance contributed significantly to total transport resistance. The fact that liquid boundary resistance can be a limiting factor in the dehydration of isopropanol by pervaporation was also reported [8]. Analysis of Feng and Huang [9], based on the film theory showed that the significance of concentration polarization was determined not only by the membrane permeability but also by hydrodynamic conditions and it should not always be overlooked even for the membranes with moderate permeability.
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Concentration polarization should be more significant when the preferentially permeable target component is present at low concentration. The primary transport resistance of pervaporation system is often assumed to be in the membrane itself [3,4]. Pervaporation membrane are usually dense (non-porous) or composite. Transport through a dense membrane or an active layer of a composite membrane can be described by the widely accepted solution–diffusion model [3,4]. A number of mathematical equations have been formulated based on Fick’s law using different empirical expressions for concentration dependence of solubility and/or diffusivity, i.e. coupling and plasticizing between components and the membrane are accounted for. Several studies showed that the properties of porous supports of composite membranes such as porosity affected pervaporation flux and selectivity [10–12] and porous support resistance may not be neglected. The selectivity attainable for the composite membrane was shown to be controlled by the relative resistance of the active layer and the support. There have been limited works which reported detailed analysis of transport resistances of the pervaporation dehydration systems. This paper is part II of our study on pervaporation dehydration of ethanol–water mixtures by composite CS/HEC-cellulose acetate (CA) membrane. In this paper we apply resistance-in-series model to calculate the transport resistance of liquid boundary layer and those of the composite membrane using the experimental data of part I [13]. The objectives of this work are to systematically analyze the transport resistances and to elucidate the transport mechanisms in the composite membrane. Coupling and plasticizing between components and membrane are discussed and presented in terms of related coefficients. The results are expected to enhance the fundamental understanding and contribute to further development of efficient pervaporation systems.
2. Theory 2.1. Mass transport model for pervaporation system Based on the resistance-in-series model transport of a component from the feed solution through the com-
213
posite membrane occurs by the following steps: (1) transport through a liquid boundary layer, (2) sorption into the membrane top (active) layer, (3) diffusion of liquid through the membrane top layer, (4) desorption from the top layer, (5) transport of vapors through the porous support, and (6) transport in vapor boundary layer. The concentration profiles of the components for a binary system are depicted in Fig. 1. The transport equations describing mass transfer of each step can be written in terms of permeation flux of i, the more preferentially permeable component (in this case, i = water) and its corresponding driving forces. 2.1.1. Step 1: Transport through the liquid boundary layer The diffusive flux of i through a liquid boundary layer is expressed as Ji = kL (ci,L − ci,LM )
(1)
For dehydration, xi,LM < xi,L , and xj,LM > xj,L , therefore, back diffusion of the components to the bulk solution and convective flux cannot be neglected. To incorporate the contribution of convective transport the concentration polarization equation [9] is substituted into Eq. (1) and rearrange to give Ji =
VP cL (xi,L −xi,LM ) (2) (1 − (1/βi ))[exp(VP /kL ) − 1]
where ai pi xi = = γi γi psat,i
(3)
and βi = enrichment factor for i = xi,P /xi,L By assuming that γi,L = γi,LM , Eq. (2) can be written as Ji =
V P cL (ai,L −ai,LM ) (1 − (1/βi ))[exp(VP /kL )−1]γi,L (4)
2.1.2. Step 2: Sorption of the components into the membrane top layer By assuming equilibrium at the liquid/membrane interface, the concentration of a component in the membrane at the interface, ci ,ML , is proportional to its activity, i.e. ci,ML = Ksi ai,LM
(5)
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Fig. 1. Concentration profiles of components across the liquid boundary layer, a composite membrane and the vapor phase.
It should be noted that for non-ideal sorption of polar molecules (water) into hydrophilic membranes, Ksi is concentration dependent. Ksi can be obtained from the sorption experiments. 2.1.3. Step 3: Diffusion through the membrane top layer Fick’s first law of diffusion is applied to describe the diffusion of a component in top membrane layer. For multicomponent mixtures which are non-ideal such as ethanol–water, the exponential diffusion equations which include the effect of plasticizing and coupling on the diffusivities were proposed by Burn et al. [14]. Di,M = Dio,M exp(kii ci + kij cj )
(6)
Dj,M = Dj o,M exp(kji ci + kjj cj )
(7)
where kii and kjj are plasticizing coefficients of components i and j, respectively, and kij and kj i are
coupling coefficients of component i with j and j with i, respectively. By substitution of Eq. (6), the Fickian-type diffusion becomes dci,M Ji = Dio,M exp(kii ci,M + kij cj,M ) (8) dz Then Eq. (8) can be rewritten as Ji =
Dio,M βi,M (ci,ML − ci,MS ) δM
(9)
where βi,M =
1 ci,ML − ci,MS ci,ML × exp(kii ci,M + kij cj,M ) dci,M ci,MS
(10)
β i ,M is the enhancement factor that represents the effect of concentration of the component in the membrane on component diffusivities. By assuming constant sorption coefficient at location 1 and 2
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(see Fig. 1) and that T1 = T2 = T L , the concentration of i at top layer/support interface, ci ,MS , is as follows: ci,MS = Ksi ai,SM Dio,M βi,M Ksi (ai,LM − ai,SM ) δM
(11)
(12)
Ji =
2.1.4. Step 4: Desorption at the membrane top/support interface By assuming that the pressure in the porous support is near the vacuum as in the permeate side, liquid molecules desorped at top membrane layer/support will simultaneously evaporate and there activities can be expressed as in Eq. (11). 2.1.5. Step 5: Transport of vapor molecules through the porous support There are three possible mechanisms of the vapor transport if the pores are assumed to be small capillaries, depending upon Knudsen number (Nkn ) [15,16] Nkn =
mean free path λi = pore diameter dp
(13)
If Nkn ≥ 10, only Knudsen flow prevails. If 0.01 < Nkn < 10, molecular transport in a capillary is by transient flow. When Nkn ≤ 0.01, viscous flow is the main transport mechanism. In this work, pore diameter of the support is approximately 10−6 m, and λi of water and ethanol is 10−4 m. The Knudsen number is higher than 10. The transport of vapors is, thus, by Knudsen flow in which the flux equation is [17] 1 dp ε 8RTS 1/2 1 Ji = (pi,SM − pi,P ) (14) 3 δS χ πMi RTS Eq. (14) can be rearranged to give 1 dp ε 8RTS 1/2 psat,i Ji = (ai,SM − ai,P ) 3 δS χ πMi RTS
2.2. Mass transport resistance To illustrate the resistance-in-series model, the flux Eqs. (4), (12) and (15) are combined into a single equation which expresses the component transport as a function of driving force and total transport resistance
Eq. (9) can be rewritten as Ji =
215
(15)
2.1.6. Step 6: Transport through the vapor boundary layer For most pervaporation systems, no transport resistance of permeate side is usually assumed since the vacuum is applied. No transport resistance is, therefore, assumed for our analysis.
1 (ai,L − ai,P ) Ri,L + Ri,M + Ri,S
(16)
where Ri,L =
(1 − (1/βi ))[exp(VP /kL ) − 1]γi,L VP c L
(17)
Ri,M =
δM Dio,M βi,M Ksi
(18)
Ri,S = 3
δS χ dp ε
π Mi 8RTS
1/2
RTS psat,i
(19)
and Ri,T =
ai,L − ai,P = Ri,L + Ri,M + Ri,S Ji
(20)
where Ri ,L is the liquid boundary layer resistance (m2 s/kmol), Ri ,M the membrane top layer resistance (m2 s/kmol), Ri ,S the support layer resistance (m2 s/kmol), and Ri ,T is total resistance (m2 s/kmol).
3. Pervaporation and physical property data 3.1. Pervaporation results The experimental data on pervaporation of ethanol–water mixtures by CS/HEC-CA composite membrane of the blend ratio 3/1 reported in the first part [13] were employed in the calculations of the mass transport resistances. 3.2. Physical properties The physical properties required for the calculations were obtained as the followings: • viscosities of aqueous ethanol solutions [18,19]; • densities of aqueous ethanol solutions [19,20]; • diffusion coefficients of ethanol in water were calculated by Stokes–Einstein equation [21];
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• activity and activity coefficients were determined by UNIFAC method [22,23]; • saturated vapor pressure of water and ethanol were calculated from Antoine equation [24]; • viscosities of water and ethanol vapor [16]; • mean free path of water and ethanol [16]. 3.3. Determination of pure component diffusion coefficients in the membrane by desorption method A dense membrane, cut into a piece of 1.5×10 cm2 , was immersed in a liquid (pure water and ethanol) at room temperature until an equilibrium was reached (approximately 7 days). The swollen membrane was then hung on a microbalance exposed to the vacuum. The decrease of the membrane weight due to vapor desorption was recorded until there was no significant weight change. By using the final rate method proposed by Crank [25] the diffusion coefficient at a certain temperature can be calculated. 4. Calculation procedures For each pervaporation experiment the data of feed, permeate compositions, total fluxes and those listed in Section 3.2 were required in the calculation, Ri ,L and Ri ,S were calculated from Eqs. (17) and (19), respectively. Ri ,T and Ri ,M were then calculated from Eq. (20). In order to calculate kii , kjj , kij and kj i , the concentration profile of each component in the membrane is required. For a binary system, the molar flux ratio of components i and j (see Eq. (8)) is Dio,M exp(kii ci,M + kij cj,M ) dci,M Ji = (21) Dj o,M exp(kji ci,M + kjj cj,M ) dcj,M Jj Let φi = kii − kji and φj = kjj − kij . Therefore, exp(φj cj,M )dcj,M =
Dio,M Jj exp(φi ci,M )dci,M Dj o,M Ji (22)
and exp(kij cj,M ) =
Dio,M Jj φj (exp(φi ci,M ) Dj o,M Ji φi
kij /φj −exp(φi ci,ML ))+exp(φj cj,ML ) (23)
Substitution of Eqs. (21)–(23) into (8) yields Dio,M ci,ML exp(kii ci,M ) Ji = δM ci,MS Dio,M Jj φj × (exp(φi ci,M ) − exp(φi ci,ML )) Dj o,M Ji φi kij /φj +exp(φj cj,ML ) dci,M (24) Compare Eqs. (9) and (24), therefore, ci,ML 1 exp(kii ci,M ) βi,M = ci,ML − ci,MS ci,MS Dio,M Jj φj (exp(φi ci,M ) − exp(φi ci,ML )) × Dj o,M Ji φi kij /φj dci,M (25) +exp(φj cj,ML ) From the obtained values of Ri ,M and Ksi , β i ,M can be calculated from Eq. (18). Di o,M was from the desorption experiment. Then kii , kjj , kij and kj i were obtained by using the iterative Levenberg–Marquardt method. The example of calculations is given in an Appendix A.
5. Results 5.1. Transport resistances Table 1 summarizes the transport resistances calculated over the range of experimental conditions studied. All resistances were positive except for Re,L (liquid boundary layer resistance for ethanol) which were negative indicating that transport of ethanol was in opposite direction to water. The top layer resistance to transport of water (Rw,M ) were only 0.008–1.48% of that of ethanol (Re,M ). This indicated that water transported much easier than ethanol due to higher sorption and diffusion of water in the hydrophilic membrane. Rw,M were 95–98% of total transport resistance of water (Rw,T ) while Re,M were as high as Re,T . It suggested that transport in the membrane top layer was the transport controlling step. Compared to other resistances, Ri ,L were low (<4%) and Ri ,S were negligible (<1.4%). For pervaporation of trichloroethylene–water mixtures with silicone rubber
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Table 1 Transport resistances in pervaporation of ethanol–water mixtures calculated from the experimental data Ri (m2 s/kmol)
Ri /Ri ,T (%)
Rw,L Re,L Rw,M Re,M Rw,S Re,S Rw,T Re,T
Rw,L /Rw,T Re,L /Re,T Rw,M /Rw,T Re,M /Re,T Rw,S /Rw,T Re,S /Re,T
770.17–3936.41 −4.62 × 104 to −4.89 × 106 2.46 × 104 to 1.85 × 105 1.89 × 106 to 1.64 × 109 179.12–439.66 123.51–293.84 2.56 × 104 to 1.89 × 105 1.83 × 106 to 1.64 × 109
(hydrophobic) composite membrane [1], porous support layer resistance was also found to be negligible. However, liquid boundary layer resistance was higher than membrane top layer resistance. It might be due to the difference in membranes and transport components. There were reports [5–7] that liquid boundary resistance was significant in pervaporation with hydrophobic membranes. For those cases the resistances were not separately calculated for each component and liquid boundary resistance was calculated directly from inversion of mass transfer coefficient which is true only for the components that are depleted in the boundary layer. It can be seen from Table 1 that Rw,S is higher than Re,S (Rw,S /Re,S = 145.02 − 149.63%) which was unexpected because water molecule is smaller than ethanol molecule. Ri ,S proposed in this model includes the dependence of desorption on the transport of vapor in porous support. The saturated vapor pressure of water is 2.4 times lower than that of ethanol, e.g. psat,w and psat,e are 149.5 and 351.9 mmHg, respectively at 60 ◦ C. This enables the evaporation of ethanol at membrane/support interface to be easier so that the activity of ethanol in the porous support was higher, resulting in a higher driving force for ethanol, i.e. Re,S was lower than Rw,S . 5.1.1. Effect of water content in feed The results are given in Fig. 2. A decrease of Rw,L and absolute Re,L with increasing water content can be observed. According to Eq. (17), Rw,L and absolute Re,L increased with increasing γ i /cL , separation factor and permeate velocity (v P ) and with decreasing kL . In the case of increasing feed water content, a reduction of γ i /cL and separation factor but an increase
Rw /Re (%) 1.14–3.93 0.05–4.19 95.43–98.56 100.05–104.19 0.15–1.38 1.69 × 10−5 to 0.014
Rw,L /Re,L
115.6–222.9
Rw,M /Re,M
0.008–1.45
Rw,S /Re,S
145.02–149.63
Rw,T /Re,T
0.008–1.48
of flux was noticeable. Thus, a decrease of Rw,L and absolute Re,L with water content was attributed to a decrease of γ i /cL and separation factor. This leads to the conclusion that separation factor affected Ri ,L more than flux. A decrease of separation factor (a decrease of β w and an increase of β e ) implied that there was a decrease of ethanol retention at membrane surface. This corresponds to a reduction of component concentration difference between bulk and membrane surface or a decrease of driving force such that Rw,L and absolute Re,L decreased. Both Rw,M and Re,M decreased exponentially with water content in feed which reflected the exponential relationship between diffusion coefficient and concentration in the membrane. An increase of water and ethanol sorption in the membrane caused an increase
Fig. 2. Effect of feed concentration on transport resistances. Operating conditions: ethanol solution, 60 ◦ C; flow rate, 542 ml/min; and permeate pressure, 3 mmHg.
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Fig. 3. Effect of feed flow rate on transport resistances. Operating conditions: 90 wt.% ethanol solution, 60 ◦ C and permeate pressure, 3 mmHg.
of water and ethanol concentration in the membrane top layer, resulted in higher membrane swelling. This behavior enhanced water and ethanol diffusion due to an increase of plasticizing and coupling effects such that β i ,M increased and Ri ,M decreased. Ri ,S was independent upon feed concentration. 5.1.2. Effect of feed flow rate Except Ri ,S which was constant, Rw,L , absolute Re,L , Ri ,M and Ri ,T decreased with increasing feed flow rate as shown in Fig. 3. When feed flow rate was increased for a given feed composition, γ i /cL was constant, separation factor decreased while flux and kL increased. Thus, a reduction of Rw,L and absolute Re,L was due to a decrease of separation factor and an increase of kL (Eq. (17)). Since an increase of flux with feed flow rate caused an increase of Ri ,L , it implied that Ri ,L was more affected by separation factor than by flux. An increase of kL enhanced both transport of water from bulk to the membrane interface and transport of ethanol from the membrane interface to bulk such that Rw,L and absolute Re,L decreased. Concentration polarization effect was expected to be maximum at lowest feed flow rate. As mention earlier that transport in the liquid boundary is not the rate determining step, the question is raised why flux changed with feed flow rate. It was probably because a change of feed flow rate
Fig. 4. Effect of feed temperature on transport resistances. Operating conditions: 90 wt.% ethanol solution; flow rate, 542 ml/min; and permeate pressure, 3 mmHg.
indirectly affected the transport of components in the membrane. A decrease of Rw,L with increasing feed flow rate referred to an increase of water concentration on the membrane surface which induced high water sorption as well as high membrane swelling. Swelling of membrane enhanced water and ethanol diffusion through the membrane and thus both Rw,M and Re,M decreased with increasing feed flow rate. 5.1.3. Effect of feed temperature From Fig. 4, all resistances decreased with feed temperature. Note that the analysis proposed assumes the temperature drop of feed and across the membrane is negligible. An increase of feed temperature caused an increase of kL and a decrease of separation factor, consequently, a decrease of Rw,L and absolute Re,L . Both water and ethanol sorption in the membrane also increased with temperature (higher Ksi ), accordingly, Ri ,M decreased (Eq. (18)). In addition, an increase of sorption caused membrane swelling which resulted in an increase of β i ,M and a decrease of Ri ,M . 5.1.4. Effect of permeate pressure As shown in Fig. 5, raising permeate pressure did not significantly affect Rw,L while Re,L decreased. Since separation factor decreased with increasing permeate pressure the retention of ethanol by membrane was low, which means that the concentration polarization effect was minimized at high permeate pressure.
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Fig. 5. Effect of permeate pressure on transport resistances. Operating conditions: 90 wt.% ethanol solution, 60 ◦ C and flow rate, 542 ml/min.
By increasing permeate pressure, Ri ,M was increased because of the reduced driving force. Ri ,S was found to be independent of permeate pressure which was also reported by Liu et al. [1]. 5.2. Plasticizing and coupling coefficients Plasticizing coefficients (kii , kjj ) and coupling coefficients (kij , kj i ) for each temperature and composition are displayed in Table 2. Positive kii indicated positive plasticization effect of water on CS/HEC membranes. In other words, the
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presence of water in the membrane caused membrane swelling. On the contrary, ethanol did not plasticize CS/HEC membranes owing to negative kjj . However, kjj were positive for 30 wt.% water content feed at 60 and 70 ◦ C. This may be due to large sorption of ethanol in the membrane at those conditions. Both kii and kjj were often reported to be positive [1,26] for pervaporation of water–organic and organic–organic mixtures with hydrophobic membranes of low sorption selectivity, i.e. sorption of components in the membranes did not significantly different. Negative kij also implied that ethanol had negative effect on diffusion of water. In others words, ethanol reduced diffusivity of water. Ethanol molecules are larger than water molecules and there was a possibility that ethanol molecules blocked the interaction between water molecules and hydrophilic sites of the membrane and then reduced diffusion of water. A positive kj i means that the presence of water enhanced diffusion of ethanol through the CS/HEC membrane. Negative coupling coefficients were also reported [26]. Plasticizing coefficients of water (kii ) increased with feed temperature and water content in feed. However, feed temperature had lower effect. These agreed with the sorption data [13] in which sorption of water increased with temperature and water content. An increase of plasticization effect (or membrane swelling) caused an increase of diffusion of water–ethanol coupled molecules so that kj i increased with feed temperature and water content in feed. Similar results were reported by Sun et al. [26].
Table 2 Plasticizing coefficients of water (kii ) and of water (kjj ) and coupling coefficients of water (kij ) and ethanol (kj i ) Feed temperature (◦ C)
kii (m3 /kmol)
kjj (m3 /kmol)
kij (m3 /kmol)
kj i (m3 /kmol)
5
50 60 70
0.0096 0.0103 0.0105
−7.2023 −4.5972 −2.9762
−3.1085 −2.0429 −1.2837
0.0048 0.0075 0.0079
10
50 60 70
0.0097 0.0112 0.0126
−1.8835 −1.2458 −1.0293
−1.8680 −1.6627 −1.259
0.0085 0.0103 0.0116
20
50 60 70
0.0257 0.0261 0.0277
−1.5521 −1.0810 −0.3670
−1.0075 −1.2783 −0.8303
0.0193 0.0218 0.0231
30
50 60 70
0.0452 0.0491 0.0683
−0.6398 0.6114 0.4506
−1.2678 −1.6126 −1.4903
0.0226 0.0451 0.0626
Water (wt.%)
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6. Conclusions
Flux: J w = 273.05362 g/m2 h (4.21 × 10−6 kmol/ 2 −9 kmol/m2 s), e = 0.35152 g/m h (2.119×10 −6 2 J = 4.2124 × 10 kmol/m s. Sorption data: xw,ML = 0.97553, xe,ML = 0.02447.
m2 s), J Application of resistance-in-series model allows for transport resistances and parameters to be calculated separately but permits overall analysis of the pervaporation system. For pervaporation dehydration of ethanol–water mixture with composite CS/HEC membrane, mass transport of the system was controlled by the transport resistance of components in the top membrane layer (Rw,M , Re,M ). On the other hand, transport resistances in the liquid boundary layer and in the porous support were negligible. All transport resistances for water were relatively low compared to those of ethanol. Therefore, for dehydration purpose the operating conditions selected and the membrane used should be such that transport resistance in the membrane top layer is minimized to obtain the optimal flux, i.e. the system be operated at higher feed flow rate and temperature but at lower permeate pressure. Analysis of plasticizing and coupling coefficients together with transport resistances has enhanced an insight of transport mechanism in pervaporation by hydrophilic membrane in which we expect that the concepts and analysis employed in this work be further applied usefully to analyze pervaporation data of different mixtures and membranes.
Acknowledgements The authors would like to gratefully acknowledge the research funds supported by the National Science and Technology Development Agency of Thailand (NSTDA), and by Natural Sciences and Engineering Research Council of Canada (NSERC).
Appendix A. Example of calculations For pervaporation of 90 wt.% ethanol solution at 60 ◦ C, flow rate 73.925 ml/min and permeate pressure = 3 mmHg. Feed: xw,L = 0.22127, xe,L = 0.77813, ρ L = 785.02 kg/m3 , µL = 7.1 × 10−4 kg/m s, cL = 19.7317 kmol/m3 . Permeate: xw,P = 0.9995, xe,P = 0.0005.
A.1. Mass transport resistance in liquid boundary layer, Ri,L βi = xi,P /xi,L ; β w = 4.51711, β e = 1.6514 × 10−3 , vP = J /cL = 2.139 × 10−7 m/s. Mass transfer coefficient (kL ): for laminar flow in thin channels the mass transfer correlation is as in the following equation [27,28].
vL Di,L kL = 1.18 hL
1/3
where v L is the average bulk velocity the 0.0123 m/s, Di ,L the diffusion coefficient of water in ethanol the 3.498 × 10−9 m2 /s, h the channel half-width the 0.0015/2 m, L the membrane radius 0.02125 m, k L = 2.49445 × 10−5 m/s, γw,L = 1.97317, γe,L = 1.0393. By Eq. (17), Rw,L = 3.14093 × 103 m2 s/kmol, Re,L = −3.28638 × 103 m2 s/kmol. A.2. Mass transport resistance in porous support, Ri,S δ S = 116 × 10−6 m, d p = 1.4 × 10−6 m. Assume ε = 0.6, χ = 3, R = 8.3144 × 103 Pa m3 /kmol K, TS ∼ = feed temperature = 333.15 K, psat,w = 1.99212 × 104 kg/m s2 , psat,e = 4.69017 × 104 kg/m s2 . From Eq. (19), Rw,S = 276.17441 m2 s/kmol, Re,S = 187.58928 m2 s/kmol. A.3. Total transport resistance, Ri,T aw,L = 0.43661, ae,L = 0.80933, ai,P = pi,P / psat,i .Therefore, aw,P = 0.02007, ae,P = 4.29072 × 10−6 . From Eq. (20), Rw,T = 9.89343 × 104 m2 s/kmol, Re,T = 3.81851 × 108 m2 s/kmol. A.4. Mass transport resistance in membrane top layer, Ri,M Ri,M = Ri,T − Ri,L − Ri,S .
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Therefore, Rw,M = 9.55712 × 104 m2 s/kmol, Re,M = 3.85137 × 108 m2 s/kmol. From Eq. (18) δM βi,M = Dio,M Ri,M Ksi where δ M = 4 × 10−6 m, Dwo,M = 20.138 × 10−13 m2 /s, Deo,M = 13.071 × 10−13 m2 /s, K sw = 1.19525 × 102 kmol/m3 , K se = 1.55518 kmol/m3 , Thus, βw,M = 0.17398, βe,M = 0.00511. A.5. Determination of plasticizing and coupling coefficients The ci ,ML was calculated from sorption data, ci ,MS was calculated by Eq. (11); cw,ML = 50.60507 kmol/ m3 , ce,ML = 1.26949 kmol/m3 , cw,MS = 2.53752 kmol/m3 , ce,MS = 7.29119 × 10−6 kmol/m3 . The ci ,ML , ci ,MS and β i ,M were substituted into Eq. (25). Integration of Eq. (25) were carried out by Mathcad program which is based on the iterative Levenberg–Marquardt method. The kii , kjj , kij and kj i were first assumed to obtain the calculated values and the procedures were repeated until there was no difference between the previous and present values.
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