Effect of pH, CO2, and High Glucose Concentrations on

Article pubs.acs.org/IECR

Effect of pH, CO2, and High Glucose Concentrations on Polydimethylsiloxane Pervaporation Membranes for Ethanol Removal Diana María Aguilar-Valencia, Miguel Á ngel Gómez-García, and Javier Fontalvo* Grupo de Investigación en Aplicación de Nuevas Tecnologías, Laboratorio de Intensificación de Procesos y Sistemas Híbridos, Departamento de Ingeniería Química, Facultad de Ingeniería y Arquitectura, Universidad Nacional de Colombia―Sede Manizales, Cra 27 No. 64-60, Manizales, Apartado Aéreo 127, Colombia ABSTRACT: Previous studies have shown that hybrid fermentation−pervaporation systems can be attractive for ethanol production. Simultaneous removal of the ethanol produced promises to improve yield and to reduce operation time and the energy required for ethanol purification. This paper experimentally explores the effect of pH (3−5.7), CO2 (at saturated conditions), and high glucose concentrations (50−400 g/L) on the flux and selectivity of PDMS (polydimethylsiloxane) pervaporation membranes at several ethanol concentrations (50−100 g/L) and temperatures (278−313 K). Membrane performance has been simulated using a Henry solution model combined with a Maxwell−Stefan description of mass transport through the membrane. By adjusting the model to the water−ethanol experimental data, it was possible to calculate the relative solubility and diffusion between ethanol and water in the polymeric membrane. Experimental results showed that the higher the glucose concentration is, the higher the membrane selectivity to ethanol will be due to a reduction on water flux. However, at a glucose concentration of 400 g/L a strong drop of total flux was measured. CO2 permeates through the PDMS membrane, but it does not have any effect on ethanol or water flux and, consequently, on selectivity. On the contrary, as pH is reduced so does selectivity while the total flux increases. Low pH values produce a decrease in membrane hydrophobicity, increasing water transport. The results presented in this paper contribute to the design of hybrid fermentation and pervaporation units, especially those that can operate at high glucose concentrations.

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INTRODUCTION Fossil fuel energy represents nearly 80% of the energy consumed in the world, and almost 60% of this amount is used by the transportation sector.1 High demand and low reserves of fossil fuels and negative environmental impacts have generated an important effort to search for new energy sources. Bioethanol, produced from renewable feedstock, has been used in several countries in the Americas and Europe as a fuel, mainly mixed with gas oil. Conventional processes produce ethanol by fermentation followed by distillation and dehydration. The energy consumption in this process is high due to the low ethanol concentration of the stream obtained from the fermentation process which is subsequently purified by distillation. Ethanol concentrations higher than 13 wt % produce yeast inhibition and low ethanol productivity.2 An alternative process to reduce yeast inhibition by ethanol involves simultaneous ethanol removal by pervaporation during the fermentation process.2,3 A hybrid pervaporation−fermentation process reduces ethanol concentration in the fermentation broth and increases ethanol productivity and concentration. A higher ethanol concentration is obtained in the permeate stream than in conventional fermentation. Consequently, energy consumption is reduced in the subsequent distillation stages of the process. Pervaporation is considered to be the most promising separation operation for bioethanol production from other techniques4 such as adsorption,5 perstraction,6 and membrane distillation.7 Pervaporation is simple, compatible with the fermentative microorganisms at the mild and rather © XXXX American Chemical Society

ambient temperature of the fermentation process, and reduces energy consumption compared to distillation.8 In a pervaporation process, ethanol can be selectively removed by a membrane from a liquid feed typically using a vacuum. The difference in ethanol partial pressure between retentate and permeate is the driving force for ethanol removal of this membrane operation. The economic and technical viability of a hybrid fermentation−pervaporation process for ethanol production strongly depends on membrane flux and selectivity. Fermentation broths are complex mixtures with several compounds that influence membrane performance. Lipnizki et al.,9 for PDMS (polydimethylsiloxane) and PDMS−zeolite membranes, and Chovau et al.,10 for two commercial PDMS membranes, determined that sugars or salts dissolved in the fermentation broth can reduce water vapor pressure, while ethanol vapor pressure rises, increasing selectivity. However, Aroujalian et al.11 observed a reduction in selectivity using glucose due to an increase of concentration polarization. Also, selectivity can improve from 16 to 34% on average, due to an increase in mass transfer coefficient, compared to fermentation broths without microorganisms.8 Acids can modify selectivity and flux. Formic acid and succinic acid increase flux while membrane selectivity decreases on PDMS membranes.12 This behavior is similar to Received: January 31, 2012 Revised: June 6, 2012 Accepted: June 15, 2012

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dx.doi.org/10.1021/ie3002765 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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solution. Preparation details of the boehmite coating solution and the dip-coating process are described by Peters et al.17 PDMS and γ-Al2O3 layers were dip-coated within a special cabin to minimize dust contamination. A single hollow fiber membrane was placed in a stainless steel tubular module, resulting in an effective membrane area of 0.0025 m2. The liquid feed was supplied by a continuous recycle in contact with the external face of the tubular membrane. The annular lumen for the retentate stream has an external diameter and an internal diameter (hollow fiber diameter) of 8 and 3 mm, respectively. The liquid feed flow was 15 L/min, which produces a Reynolds number in the turbulent regime and a superficial velocity close to 6 m/s. Aqueous solutions of ethanol (pro analysi, Merck) at several concentrations (50, 70, and 100 g/L) were prepared and fed to the pervaporation module. A typical setup was used for pervaporation.18 On the permeate side, a vacuum was maintained (10 mbar) by a cascade of liquid nitrogen cold traps and a vacuum pump. The feed vessel was loaded with a total liquid volume of 4 L and was vigorously mixed by the pervaporator feed pump itself. Retentate (0.5 g, approximately) and permeate (1 g, approximately) samples were removed every 10−80 min (depending on water and ethanol driving forces), and samples were collected until the total calculated flux through the membrane was constant for at least four permeate samples. The feed temperature was controlled (±0.1 K) using a thermostatic bath at levels of 278, 298, 303, 308, and 313 K. Activity coefficients for water−ethanol mixtures were evaluated with the NRTL model.19 Vapor pressures were calculated using the Antoine equation.19 The recommended values from the Dechema Data Series were used. The total flux was calculated as the ratio of the collected permeate mass, in a period of time, to the membrane area (eq 1a). The membrane selectivity (α) was calculated as the ratio of the molar fractions in the permeate to their molar fractions in the retentate,20 as shown in eq 1b. The flux for every permeable component was calculated as the product of total flux and permeate mass fraction. Driving forces for ethanol and water were calculated according to eq 1c, where activity coefficients and vapor pressure are evaluated at the retentate temperature.

that of silicalite membranes where an irreversible change in the membrane structure that induces a hydrophilic surface and limits its use in industrial fermentations systems was observed.13 Chovau et al.10 found that if the solution pH is higher than the acid dissociation constant, there is no change in the membrane properties. Thus, a higher concentration of ions increases the membrane hydrophilic nature. Using PDMS− zeolite membranes, Bowen et al.14 measured a strong reduction of both flux and selectivity with ethanol aqueous solutions containing acetic acid, but there were no important effects for PDMS membranes. The previously reported studies have been carried out mainly on PDMS−silicalite membranes which present an irreversible decrease in their performance when exposed to the fermentation broth. Also, CO2 is produced in the fermentation process, but there are no reported studies of the effect of this gas on ethanol or water fluxes in PDMS pervaporation membranes. Hybrid fermentation−pervaporation systems for ethanol production have been usually designed by combining a conventional continuous fermentation with a pervaporation unit.2,13,15 Consequently, the sugar concentration in the system is low and, considering an ethanol product concentration between 70 and 100 g/L,16 an average of 11 L of waste is produced for every liter of ethanol. This waste includes mainly water, metabolites, and salts. If a pervaporation membrane, complemented with other separation techniques, is able to remove inhibitors and ethanol, it will be possible to develop hybrid fermentation−pervaporation systems operating with high glucose concentrations. Other separation techniques will be necessary in order to remove nonvolatile metabolites. In this case, there is no bleeding from the fermentation reactor and the only liquid product stream is the condensed permeate from the pervaporation unit. Therefore, an increased productivity and a lower amount of waste will be expected compared to hybrid fermentation−pervaporation systems conventionally studied. In a future publication experimental and theoretical results will be presented of such hybrid systems. This study presents experimental results of the influence of pH, glucose at high concentrations (>40 g/L), and CO2, at several ethanol concentrations and temperatures, on ethanol selectivity and flux with PDMS membranes. A theoretical model based on a solution-diffusion model using the Maxwell− Stefan theory was fitted with the ethanol−water experimental data. This model can be used for designing, optimizing, and controlling hybrid fermentation and pervaporation systems for ethanol production.

ÑT =

m TP A m Δt

(1a)

ye

■

α=

MATERIALS AND METHODS PDMS membranes were prepared by sequential dip-coating on top of ceramic hollow fiber supports using a speed of 10 mm/s and ambient temperature. The membrane thickness was approximately 2 μm. The PDMS solution was prepared by adding 10 g of PDMS prepolymer and 2 g of catalyst (SILGARD 184 kit) to 100 g of n-hexane (pro analysi, Merck). After dip-coating of a single layer of PDMS, the membranes were cured at 363 K for 5 h. This protocol was sequentially performed to deposit a total of three layers. The ceramic hollow fiber supports (CEPAration B.V., The Netherlands) have a porosity of ∼30%, pore diameter of 300 nm, length in the range of 20−30 cm, and inner and outer diameters of 2.0 and 3.0 mm, respectively. On top of the substrates, intermediate mesoporous γ-Al2O3 layers were prepared by sequential dip-coating with a boehmite coating

1 − ye xiR 1 − xiR

(1b)

ΔPi = xiR pi° γi

(1c)

Acetic acid (pro analysi, Merck) was added to the aqueous ethanol solution to adjust the pH at values of 3.0, 3.5, and 4.0. Ethanol and acetic acid concentrations were measured by HPLC with a refractive index detector and a ROH-801 column (Transgenomic). A sulfuric acid solution (0.0025 N) was used as a mobile phase. Some mixtures were also prepared by adding D-(+)-glucose (anhydrous for biochemistry reagents, Merck) to the ethanol aqueous solutions at concentrations of 50, 100, 200, and 400 g/L. After every single experiment of pervaporation at various conditions of temperature, pH, and ethanol and glucose concentrations, the membranes were tested by pervaporation using a standard solution of 70 g/L ethanol, with a measured B



Article

layer. This model does not take into account any transport resistance in the ceramic support layer. Components i and j diffuse through a membrane M. The mass transport of component i is due to a difference of chemical potential in the membrane, and it is described by30

pH 5.7, and 308 K in order to evaluate the membrane stability. There were no observed changes in the flux and selectivity of the PDMS membrane using the standard solution. The same membrane was used for experiments at several ethanol concentrations, temperatures, pHs, and glucose concentrations. A second membrane was prepared to evaluate the effect of CO2 on its performance. Thus, experiments were carried out with and without CO2 at several ethanol concentrations and temperatures as described above. For experiments with CO2, the aqueous feed liquid was saturated by continuously injecting this gas into the liquid feed vessel at 0.0102 m3/h(STP). Liquid and CO2 were recycled to the feed vessel, where CO2 was released after passing the pervaporation membrane. Concentration polarization in the liquid was calculated for the pervaporation experiments with ethanol−water−glucose mixtures. The mass transfer in the liquid was evaluated using a multicomponent Fick model21,22 using the matrix of diffusion coefficients measured by van de Ven-Lucassen et al.23,24 at infinite dilution of ethanol and 298.13 K. The matrix of Fick diffusion coefficients was corrected by temperature using the Wilke−Chang equation.21 The main diffusion coefficient of ethanol was corrected to an ethanol concentration of 10 g/L by use of the Vignes equation,21 and the diffusion coefficient of infinite dilution of glucose in ethanol was calculated by the Wilke−Chang equation. Kinematic viscosities of ethanol− water−glucose mixtures were measured by Moreira et al.,25 and densities of ethanol−glucose solutions were measured by Castaldi et al.26 The matrix of mass transfer coefficients21 was calculated using a correlation for tubes in the turbulent regime (Table 5-23, eq Q in Perry’s Chemical Engineers’ Handbook27) and the corresponding Reynolds number for annular channels.22 Mass transfer in the membrane was calculated using the model obtained in this study for pervaporation of binary ethanol−water mixtures and presented below in eqs 6 and 7 with the parameters reported in Table 1. Unfortunately, there are no reported activity models using vapor−liquid equilibrium data or experimental partial pressures for water− ethanol−glucose mixtures. Thus, the excess Gibss energy calculated by Bockstanz et al.,28 from experimental data of glucose solubility in ethanol−water mixtures, was used to calculate water and ethanol activity coefficients,29 which are necessary to evaluate the driving forces of ethanol and water through the membrane (eq 1c). Mass transfer resistance in the permeate was neglected, and the total glucose flux was taken as zero. The multicomponent Fick equation for the liquid and the Maxwell−Stefan mass transfer model through the membrane (eqs 6 and 7) were coupled to calculate water, ethanol, and glucose fluxes and concentrations on the liquid−membrane interface.

xi dμi = RT dz

n

∑ j=1

xiNj − xjNi ctD̵ ij

−

xMNi ctD̵ iM

(2) 18

If xM/D̵ iM is replaced by 1/ D̵ iM , eq 2 can be written as xi dμi = RT dz

n

∑ j=1

xiNj − xjNi ctD̵ ij

−

Ni ct D̵ iM

(3)

Using a Henry equation, ci = HiPi, to relate the partial pressure of component i in the liquid, Pi , to the membrane concentration, ci, and inserting μi = μio + RT ln(Pi) in eq 3, for ethanol (e) and water (w), leads to He

dPe H P N − H wPwNe Ne = ee w − dz ctD̵ ew D̵ eM

(4)

Hw

H P N − HePeNw dPw Nw = w w e − dz ctD̵ ew D̵ wM

(5)

Integrating eqs 4 and 5 by assuming that ethanol and water compositions are linear within the membrane and Maxwell− Stefan diffusivities are constants (“method of Krishna”)21,31,32 produces ΔPe = −(K1Pw + K 2)Ne + K3PeNw

(6)

ΔPw = −(K4Pe + K5)Nw + K3PwNe

(7)

Pi in eqs 6 and 7 is the average partial pressure (between permeate and retentate) of component i through the membrane. The five parameters obtained from this model are ΔzH w Δz Δz K2 = K3 = HectD̵ ew He D̵ eM ctD̵ ew ΔzHe Δz K4 = K5 = H wctD̵ ew H w D̵ wM

K1 =

These parameters were fitted using experimental data, presented in Figure 2, of pervaporation for ethanol/water mixtures at several ethanol concentrations (50, 70, and 100 g/ L) and temperatures (298, 303, 308, and 313 K). Fitted values are presented in Table 1. A parity plot is shown in Figure 1, where the predictions of this model have a maximum error of 2%.

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RESULTS AND DISCUSSION Ethanol and water fluxes through the PDMS membrane at several ethanol concentrations and temperatures are presented in Figure 2 as a function of the driving force. For each

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SOLUTION-DIFFUSION MODEL OF THE PDMS MEMBRANE A solution-diffusion model is used to describe water and ethanol fluxes through the PDMS membranes. In this model the solubility in the polymer is predicted using a Henry equation due to the small range of ethanol concentrations. Solubility experiments, carried out in this study and not shown in this paper, of ethanol/water mixtures in the PDMS polymer proved that a Henry type of behavior is suitable at ethanol concentrations lower than 100 g/L. The Henry equation was coupled to a Maxwell−Stefan model for predicting the mass transport of water and ethanol through the polymeric PDMS

Table 1. Fitted Parameters of a Solution-Diffusion Model (eqs 6 and 7) for Pervaporation of Ethanol−Water Mixtures in PDMS Membrane at Several Ethanol Concentrations (50, 70, and 100 g/L) and Temperatures (298, 303, 308, and 313 K)

C

membrane

K1 (m2 h/kmol)

K2 (m2 h bar/kmol)

K3 (m2 h/kmol)

K4 (m2 h/kmol)

K5 (m2 h bar/kmol)

PDMS

97.18

3.30

60.81

26.34

0.82



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curve. Consequently, ethanol permeability is not constant as a function of the driving force. This behavior could show a small coupling between the ethanol and water fluxes, which is more marked for ethanol due to its low fluxes compared to those for water. Thus, a solution-diffusion model, presented above, has been fitted to the experimental data with a maximum error of 2%. The experimental results and the solution-diffusion model show that water transport slightly contributes to ethanol transport by, perhaps, dragging it due to a molecular friction mechanism described by the Maxwell−Stefan model. The ratio between parameters K4 and K1 represents the ratio between the Henry constants in the PDMS membrane for ethanol and water, respectively (eq 8a). From the adjusted parameters it was found that, on a molar basis, the solubility of ethanol is lower than that of water. In eq 8b, from the ratio of K5 to K2, it can be observed that the PDMS membrane offers a higher resistance to the transport of ethanol than that of water.

Figure 1. Parity plot of water and ethanol fluxes measured and calculated using a solution-diffusion model (eqs 6 and 7) at several ethanol concentrations of 50, 70, and 100 g/L; temperatures of 298, 303, 308, and 313 K; and pH 5.7.

K4 H = e = 0.5 K1 Hw K H D̵ eM = 5 w = 0.48 D̵ wM K 2 He

(8a)

(8b)

Figure 2 also shows that the water flux is higher than the ethanol flux. Nevertheless, membrane selectivity is higher than in a liquid−vapor equilibrium or simple evaporation process. Selectivity and flux are comparable to those measured for Pervatech PDMS membranes.10 Experimental results at several pHs (Figure 3) show that membrane selectivity rises as pH increases, while total flux decreases. Also, the ethanol flux slightly rises with pH. Although the water flux contributes to ethanol transport, the hydrophilicity of the membrane rises as pH decreases, reducing slightly the solubility of ethanol in the polymer but increasing it for water. Selectivity increases more rapidly at low pHs (4). Chovau et al.10 have shown an increase in hydrophilicity in PDMS membranes when pH is lower than the dissociation constant of the acid used in the solution. Specifically, for acetic acid it corresponds to pH 4.7, which seems to agree with the results presented in Figure 3. Also, acetic acid permeated through the membrane and the measured acid concentrations in the permeate are shown, except for pH 5.7, which corresponds to an ethanol−water solution of 70 g/L without acetic acid addition. Acetic acid concentrations remain constant for pHs higher than 3.5. Because the membrane is swollen by water also acetic acid permeates, which confirms the hydrophilic character of the membrane at low pHs. This behavior is important for ethanolic fermentation processes because acetic acid and perhaps other fermentation byproducts can be removed through the membrane as they are produced. After every single experiment the membrane was tested with the standard solution. No change in membrane selectivity and flux was found, suggesting that the loss in selectivity is a reversible process. On the contrary, the negative effect of acids on membrane performance is irreversible for PDMS−silicalite membranes9,13 and PDMS−zeolite membranes,14 which limits the application of these membranes for fermentation processes. The influence of glucose on membrane flux and selectivity is presented in Figure 4. At glucose concentrations below 200 g/ L, an increase of glucose concentration raises membrane selectivity. The main reason for this improved selectivity is due to a reduction of the water flux while the ethanol flux remains

Figure 2. Water and ethanol fluxes as a function of their driving forces evaluated at several ethanol concentrations of 50, 70, and 100 g/L; temperatures of 298, 303, 308, and 313 K; and pH 5.7. The lines are a guide to the eye.

temperature the fluxes at several ethanol concentrations are shown. The water flux is approximately constant at the same temperature and several ethanol concentrations. Due to the low concentration of ethanol in the retentate, the water driving force is nearly constant and so is the water flux. Also, the water flux is directly proportional to its driving force. However, the ethanol flux does not fit on a straight line but fits on a slight D



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Figure 3. Influence of pH on membrane selectivity and flux for PDMS pervaporation membrane. At 308 K and ethanol concentration of 70 g/L.

Figure 4. Influence of glucose concentration on membrane selectivity and flux. Ethanol concentration 70 g/L and 308 K.

approximately constant. An increase of 5% in ethanol vapor pressure, in the presence of 24.6 g/L sucrose, was found by Aroujalian et al.11 in a 38 wt % ethanol/water solution at 293 K, while the water vapor pressure was reduced in 18%. However, the results presented in this study indicate a reduction of water vapor pressure but not an increase of ethanol vapor pressure for glucose concentrations higher than 50 g/L. Nevertheless, the ethanol concentration is lower and the glucose concentration is much higher in this study (50−400 g/L) than those used by Aroujalian et al.11 For a high glucose concentration of 400 g/L, experimental results show that selectivity and water and ethanol fluxes strongly drop (Figure 4). The concentration polarization was calculated for this experiment, using the membrane model presented above, and the calculated ethanol flux was 0.28 kg/ m2 h, which is close to the measured ethanol flux of 0.27 kg/m2 h. The calculated values of concentration on the membrane surface showed that the concentration polarization of glucose, water, or ethanol is very small. Thus, the ethanol flux through the membrane can be explained based on its retentate partial pressure, diffusion, and transport in the membrane. On the other hand, the water flux was overpredicted by 13%. It seems that water partial pressures are overpredicted using the activity model presented in this work. This activity model was derived from an excess Gibss energy function obtained from solubility data for glucose in ethanol−water mixtures.28 Unfortunately, there are no published data, at atmospheric pressure, of ethanol and water partial pressures in glucose solutions or activity models obtained from the liquid−vapor equilibrium.

The presence of CO2 during an ethanolic fermentation could influence water and ethanol fluxes in a pervaporation process. Figure 5 presents experimental results using aqueous solutions without CO2 and with a saturated solution of this gas. During the experiments it was observed that CO2 permeated through the membrane and the gas was collected in the cold traps but it was not possible to accurately measure its flux. In the pressurization stage to atmospheric pressure also air is condensed in the cold traps, where the permeate sample is collected. With the experimental technique used, it was not possible to effectively control the amount of air that is condensed in order to calculate the amount of CO2 permeated. However, Figure 5 shows that CO2 does not have any influence on either the water or the ethanol flux, and consequently it does not affect selectivity. Although CO2 will change the pH of the solution, its effect is small, at saturated conditions, giving a slightly acid solution. Due to this effect, there is no influence of pH on membrane hydrophilicity using CO2 compared to solutions without CO2. Nevertheless, CO2 permeation could hinder ethanol recovery by condensation in the permeate stream for industrial applications where liquid nitrogen is not used as a refrigerant. Although, the membrane used to produce Figure 2 is different from the one used for Figure 5, both figures show comparable values of flux. Also, in Figures 2 and 5, the relation between the water flux and its driving force is linear while for ethanol it is slightly curved. E



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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support from COLCIENCIAS under Project No. 1119-405-20248 and Contract No. CT-018-2007 is gratefully acknowledged. We would like to thank Mario Andrés Noriega Valencia for his measurements of pervaporation using CO2.

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Figure 5. Influence of CO2 in the aqueous solution on water and ethanol fluxes as a function of their driving forces evaluated at several ethanol concentrations of 50, 70, and 100 g/L and temperatures of 278, 298, 303, 308, and 313 K. The lines are a guide to the eye.

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CONCLUSIONS

This work experimentally explores the effect of pH (3−5.7), CO2 (at saturated conditions), and high glucose concentrations (50−400 g/L) on the flux and selectivity of PDMS pervaporation membranes at several ethanol concentrations (50−100 g/L) and temperatures (278−313 K). The water flux through the PDMS membrane slightly contributes to the ethanol flux due to a dragging effect predicted by a Maxwell− Stefan mass transport model. Also, experimental results showed that the higher the glucose concentration is the higher the membrane selectivity to ethanol will be due to a reduction of water flux. However, at a glucose concentration of 400 g/L a strong drop of total flux was detected which is related to a decrease of ethanol and water partial pressures in the retentate. CO2 permeates through the PDMS membrane, but it does not have any effect on the ethanol or water flux and, consequently, on selectivity. On the contrary, as pH is reduced so is selectivity, while the total flux increases. Low pHs produce a decrease of membrane hydrophobicity, increasing water transport. The results presented in this study show that a hybrid fermentation−pervaporation system using PDMS membranes operating at high glucose concentrations (>40 g/ L) can improve ethanol selectivity while acetic acid is removed from the system. Such hybrid systems need more attention and research.

NOMENCLATURE Am = membrane area (m2) ci = molar concentration of component i (kmol/m3) D̵ ij = Maxwell−Stefan diffusivity for pair i−j (m2/h) D̵ iM = Maxwell−Stefan diffusivity of component i in membrane (m2/h) Hi = Henry solubility constant of component i (kmol/m3 bar) mPT = total mass collected in permeate in a period of time Δt (kg) Ni = molar flux of component i through membrane (kmol/ m2 h) Ñ T = total mass flux through membrane (kg/m2 h) Pi = partial pressure of i in liquid (bar) p°i = vapor pressure of pure component i (bar) R = constant of ideal gas (kJ/kmol K) xi = mole fraction of component i in membrane xRe = mole fraction of ethanol in retentate ye = mole fraction of ethanol in permeate z = coordinate perpendicular to membrane surface (m) μi = chemical potential of component i (kJ/kmol) ΔPi = driving force of component i through membrane (bar) Δt = elapsed time for permeate sampling (h) Δz = membrane thickness (m) α = membrane selectivity

Subscripts

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e = ethanol w = water M = membrane t = total

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