Pervaporative Recovery of Acetic Acid from an Acetylation Industrial

Ind. Eng. Chem. Res. 2005, 44, 977-985

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Pervaporative Recovery of Acetic Acid from an Acetylation Industrial Effluent Using Commercial Membranes Daniel Gorri, Ane Urtiaga, and Inmaculada Ortiz* Departamento de Ingenierı´a Quı´mica y Quı´mica Inorga´ nica, Universidad de Cantabria, Avenida Los Castros s/n, 39005 Santander, Spain

This paper reports the comparative behavior of commercial pervaporation membranes in the recovery of acetic acid from acetylation industrial effluents. The main components of the industrial feed mixture are acetic acid and water; the initial content CH2O ) 24-26 wt %. The performances of four commercial membranes were investigated; the results indicate that all of the membranes were highly selective and permeable toward water. Both the selectivity and permeability were strongly feed-composition-dependent. The selectivity decreased and the permeability increased as the water concentration in the feed increased. Calculation of the pervaporation separation index (at 80 °C and 10 wt % water concentration) as the product of flux and the separation factor led to the selection of the Symplex membrane (GKSS) that behaved more successfully. Because the Symplex membrane is not commercially available on and industrial scale, the CMC-CF23 membrane from Celfa was selected in order to make detailed studies. After a careful experimental design, the flux rate of water permeation and the separation selectivity were determined in the range of temperature 50-80 °C and water content 1-25 wt %. Increased temperatures resulted in larger fluxes. For a fixed water concentration value in the feed of 10 wt %, the water flux through the CMC-CF23 membrane increased from 0.38 kg m-2 h-1 (50 °C) to 1.56 kg m-2 h-1 (80 °C). The results were satisfactorily predicted by a semiempirical model based on Fick’s law with concentration-dependent diffusivity parameters. Introduction The acylation process with acetic anhydride results in the generation of acetic acid as a coproduct along with the acylated product. The acylation of aromatic substrates is an industrially important process to obtain aromatic intermediates used for the production of pharmaceuticals, insecticides, plasticizers, dyes, perfumes, and other commercial products. Distillation has been widely used as a primary unit operation for acetic acid recovery in such processes, utilizing one or more towers to process a number of streams with different concentrations of acetic acid with the purpose of recovering it for further use. The products from the distillation tower are a bottom stream of concentrated acetic acid and an overhead stream that ideally would be pure water. Because of the nonideal behavior of the system acetic acid/water and the equilibrium limitation in such a system, it is necessary to utilize a distillation tower with a high number of theoretical stages and a high reflux ratio to be able to obtain reasonably low levels of acetic acid in the distilled water.1 Big efforts have been directed to find suitable alternatives in order to solve the problem. Among them, azeotropic distillation deserves special attention; it involves the addition of a third component to the distillation tower to improve the relative volatility of the separation and reduce the separation requirements. This existing option provides some reduction in the operating costs, but it generates additional operating and environmental problems.1 From an energy savings point of view, pervaporation can be an alternative to the azeotropic distillation. The * To whom correspondence should be addressed. Tel.: +34942201585. Fax: +34942201591. E-mail: [email protected].

dehydration of aqueous acetic acid mixtures has received relatively little attention because of difficulty in the selection of the membrane material. Several membrane materials have been developed for this purpose,2-8 almost all of them of polymeric nature. However, the membranes that have been employed in such a separation often failed.2 The membranes used in pervaporation have to be sufficiently selective and permeable to be economically appealing. Applied to the dehydration of acetic acid at elevated temperatures, the chemical and thermal resistance of the membrane material can be important constraints.3 Although NaA zeolite membranes are very effective in removing water from organic compounds,9-12 they cannot be applied in the dehydration of acetic acid because of their low resistance to acidic media. Because the chemical stability of zeolites increases with increasing Si/Al ratio in the framework while its hydrophilicity decreases, zeolite membranes with a medium Si/Al ratio would be preferred for dehydration in the presence of organic acids. Li et al.13,14 have reported the pervaporation of water from acetic acid using thin mordenite and ZSM-5 zeolite membranes, but at present, these types of membranes are not commercially available. Flux and selectivity data reported in the literature from pervaporation of acetic acid/water mixtures using different polymeric and inorganic membranes are summarized in Table 1. Reported flux and selectivity values are markedly influenced by the temperature and feed composition. As has been mentioned in different membrane separations, water/acetic acid separations by pervaporation exhibit a typical balance between the selectivity and flux. The present study is focused on the recovery of acetic acid contained in an industrial waste stream. This waste

10.1021/ie0493560 CCC: $30.25 © 2005 American Chemical Society Published on Web 01/21/2005

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Table 1. Comparative Performance of Polymeric Pervaporation Membranes for Acetic Acid Dehydration mass % of water in the feed

temp (°C)

total flux (kg m-2 h-1)

17.8 13.7 9.3 6 2

30 30 30 30 30

5.0 0.23 0.19 0.18 0.012

30 30 30 70 60 25 25 25 25 25

PVA cross-linked catalytic membrane

10 10 10 15 15 10 10 10 10 10 10 10 10 10 40 20 10

PVA/PAA blend catalytic membrane

10

50 40 40 70 80 90 70 80 90

0.0239 0.0425 0.0739 0.262 0.068 0.180 0.05 0.50 0.35 0.80 0.30 0.14 0.80 0.088 0.035 0.030 0.323 0.352 0.384 0.334 0.380 0.420

40.3 21.0 10.6 161 46 243 7.0 4.5 4.0 2.4 6.6 7.9 2.4 163 2600 3548 10.8 9.9 9.0 7.9 6.7 5.6

80 80 80 80 25 25 75 75 80 80 80 80 80 70 80 80 80 80

0.742 0.153 0.364 0.126 0.55 0.50 5 2.5 0.625 0.51 0.39 0.145 0.030 0.785 2.33 1.76 2.33 1.05

182 206 180 318 3.6 3.8 90 150 265 220 298 234 53 381 105 61 43 48

membrane agarose

modified sodium alginate membranes NaAlg + 5% PVA + 10% PEG NaAlg + 10% PVA + 10% PEG NaAlg + 15% PVA + 10% PEG sodium alginate cross-linked with HDM sodium alginate cross-linked with PVA modified Nafion PVA with 100% hydroxyl content PVA with 96% hydroxyl content PVA with 88% hydroxyl content PVA/PEI PVA/PAA PVA/PHC PVA/PVC PVA cross-linked with glutaraldehyde PVA modified with PAA

PVC/PAN composite membranes top layer thickness of 0.3 µm top layer thickness of 1 µm PAA/TPX silica mordenite (zeolite)

ZSM-5 zeolite membranes Symplex (GKSS) CF23 (Celfa) VP43 (Celfa) Pervap 1005 (Sulzer) a

selectivity Rw/a 1.5 6 6 5 17.5

ref 15

16

17 18 19

2 8 20

3 20.4 2 20.6 1.5 50 30 10 5 52 41 30 18 8.5 50 10 10 10 10

7 21 13

14 this worka

Experiments with industrial acetic acid/water mixtures.

mixture proceeds from an acetylation process of an aromatic compound in a pharmaceutical industry. The acetylated product is recovered by crystallization, and the remaining mother liquor contains acetic acid in approximately 20 wt %; 2400 L/day of this waste are obtained in one production unit. Furthermore, the final mother liquor is fed to a batch distillation process that leads to a quasi-binary mixture of acetic acid (74-76 wt %) and water, with traces of other organic compounds. In this paper, the permeation behavior of water/acetic acid industrial mixtures through commercial hydrophilic membranes has been investigated. Most existing reports on acetic acid dehydration have been based on the results obtained with membranes manufactured or modified individually in the laboratory, and they cannot be applied in process design. Therefore, the purpose of this study has been to investigate acetic acid dehydration by using commercial polymeric membranes and to check the dehydration kinetics and separation performance as a function of the membrane materials, feed composition, and operating temperature.

Theoretical Background The mass transport in nonporous homogeneous polymer membranes is assumed to occur by a solution diffusion-desorption mechanism.22 In a polymer/binary mixture system, the two components will mutually interact with the membrane material. The partial fluxes can be described by Fick’s first law:

Ji ) -FmDi

dWm i dz

(1)

with the diffusion coefficients being concentration dependent and represented by exponential relationships23 m Di ) Di,0 exp(τiiWm i + τijWj )

(2)

m Dj ) Dj,0 exp(τjiWm i + τjjWj )

(3)

and

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where the constants τii, τij, τji, and τjj take into account the interactions referred to above. In this paper, the membranes are preferentially permeated by water because of strong interactions between the hydrophilic polymers and water. The water flux can be considered to be independent of the presence of the organic component in the membrane. If w represents water and a represents acetic acid, the constant τwa of eq 2 is equal to zero because of the mentioned negligible coupling effect. Incorporating eq 2 in eq 1 and then integratiing result in

Dw0 Jw ) Fm [exp(τwwWm(z)0) ) - exp(τwwWm(z)δ) )] (4) w w δτww A linear relationship between the solubility and activity with no interactions among penetrants is usually assumed for solubility modeling in diluted solutions. Assuming thermodynamic equilibrium between the fluid phase and the membrane phase for each component of the mixture results for the feed side in

Wm(z)0) ) kwafw w Wm(z)0) a

)

kaafa

q)

Dw0τaa{exp[(τww - τaw)kwafw] - 1} Da0(τww - τaw)[exp(τaakaafa) - 1]

The dependence of the water flux and of the ratio of water to acetic acid fluxes on the feed component activities is described by eqs 9 and 12. Similar approaches were used by other authors in previous works24,25 for the description of the pervaporation flux through hydrophilic membranes. To evaluate the model parameters, these can be grouped in a smaller number of independent parameters. Because it is known that the concentration of acetic acid in the phase membrane is negligible, its plasticization effect on its own diffusion coefficient can be ignored (τaa ) 0). Thus, integration of eq 10 leads to the simplified expression

q)

Dw0{exp[(τww - τaw)kwafw] - 1} Da0(τww - τaw)kaafa

(5)

Wm(z)δ) ) kaapa a

(8)

Substitution of eqs 5 and 7 in eq 4 allows for the description of the variation of the water flux with the composition of the fluid phases. For low values of the permeate pressure, exp(τwwkwapw) is very small and the water flux can be expressed as a function of the feed composition:

Dw0 [exp(τwwkwafw) - 1] Jw ) Fm δτww

(9)

The ratio of the two partial fluxes, q ) Jw/Ja, after substitution of eqs 2 and 3 with τwa ) 0, can be written in the following form:

q)

m Dw0 exp[(τww - τaw)Wm w ] dWw m Da0 exp(τaaWm a ) dWa

(10)

This ratio remains constant across the membrane and, after integration of eq 10 with the boundaries Wm(z)0) , w m(z)δ) m(z)δ) Wm(z)0) , and W , W , leads to a w a q) Dw0τaa{exp[(τww - τaw)Wm(z)0) ] - exp[(τww - τaw)Wm(z)δ) ]} w w Da0(τww - τaw)[exp(τaaWm(z)0) ) - exp(τaaWm(z)δ) )] a a (11)

Substitution of eqs 5-8 in eq 11, combined with the fact that for low permeate pressures the exponents involving Wm(z)δ) and Wm(z)δ) can approach zero, yields w a

FmDw0 δτww

(14)

A2 ) τwwkw

(15)

A1 )

(6)

(7)

(13)

which can be used instead of eq 12. Equations 9 and 13 contain four parameters:

and for the permeate side in

Wm(z)δ) ) kwapw w

(12)

A3 )

Dw0 Da0(τww - τaw)ka

A4 ) (τww - τaw)kw

(16) (17)

Experimental Section Industrial effluents coming from distillation of acetylation processes were used in all of the experiments. The initial water content was in the range 24-26 wt %. The main components of the feed were acetic acid and water, with traces of other organic components. Pervaporation Membranes. The Symplex membrane was kindly supplied by GKSS (Geesthacht, Germany). It is a composite membrane formed by polyelectrolytes on a microporous poly(vinylidine fluoride) support.26 Polyelectrolytes based on cellulosic materials are well-known for their affinity to water. In the membrane manufacturing process, the polyelectrolyte complex is formed in situ from aqueous solutions of the polyanion (cellulose sulfate) and polycation [poly(dimethylallylammonium chloride)]. The active layer of the composite membrane has a thickness of about 2 µm. The membrane Pervap 1005 was purchased from Sulzer Chemtech (Neunkirchen, Germany). This membrane is made of poly(vinyl alcohol) (PVA) cross-linked by special agents to provide chemical resistance in acidic media. They can be used up to temperatures of 100 °C. The major chemical constraints are a maximum content of water of 80% and 1% mineral acids in the feed.27,28 Domingues et al.29 reported the kinetics and equilibrium shift of a batch esterification of benzyl alcohol with acetic acid using a pervaporation reactor with a Pervap 1005 membrane. In addition, Krupiczka and Koszorz30 studied the hybrid process of the esterification of acetic acid with ethanol, coupled to a pervaporation unit also using a Pervap 1005 membrane.

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The membranes CMC-CF23 and CMC-VP43 were purchased from CM-Celfa (Seewen-Schwyz, Switzerland). The type CMC-CF23 membrane is a so-called integral-asymmetric membrane of an acrylic copolymer; the membrane layer in the lower part (permeate side) has a highly porous structure, and the top side shows a granular, dense structure that is modified through additional physical and chemical treatment in order to obtain the desired selectivity. The membrane is additionally provided with a thin and resistant protective coating based on a cross-linked polymer blend that is responsible for the good properties in use, especially a long service. Because integral-asymmetric membranes with a very thin dense skin layer never are completely free of π holes, the protective layer also provides efficient clogging of pores. A polyester fabric as additional reinforcement forms an integral part of the membrane. The CMC-CF23 is designed for the removal of water from organic liquids (solvents). It is applicable to a large number of different solvents and a wide range of water content from 500 ppm up to 50%.31 The CMC-VP43 membrane is a composite membrane made of an especially hydrophilic polymer blend that is coated onto a porous polyacrylonitrile membrane by a multistage process. The active membrane layer is hereby anchored partially in the pores of the substrate, thus providing high mechanical strength. The membrane is provided with an additional nonwoven support of polypropylene, which serves as a reinforcement. This membrane is designed for the removal of high amounts of water at low temperatures (40-60 °C). On the other hand, at water contents below 5%, the permeate flux drops considerably.31 Pervaporation Unit. The pervaporation experiments were carried out in a laboratory-scale unit supplied by Sulzer Chemtech (Neunkirchen, Germany), previously used by the authors in different pervaporation studies. The experimental setup is described in detail elsewhere.32,33 The systems were operated in batch mode with continuous recirculation of the liquid mixture to the feed tank (volume ) 2 L). The temperature was selected between 50 and 80 °C, and a vacuum on the permeate side was maintained below 15 mbar using a rotary vacuum pump (Telstar 2P-3, Madrid, Spain). The vacuum was monitored using a digital vacuum gauge (Vacuubrand, Wertheim, Germany) installed in the vacuum line connecting the pervaporation module and the condenser unit. The permeate vapor was collected by a cold trap cooled by liquid nitrogen. Two cold traps were set in parallel, allowing the experiment to be carried out in a continuous mode. Flat membranes were inserted in a circular plate and frame pervaporation test cell, providing 0.0178 m2 of membrane area. Feed liquid preheated to a constant temperature was fed to the inside of the pervaporation cell at a flow rate of 5 L/min. Because of the geometry of the pervaporation cell,32 the feed Reynolds number varied along the radial position in the membrane module from a maximum value at the center of the cell (feed inlet position) to a minimum value at the maximum radius (feed exit position). At the maximum radius, the values of the Reynolds number as a function of temperature are in the range 470 (T ) 50 °C) < Re < 630 (T ) 80 °C). Analytical Techniques. Retentate and permeate samples were collected over time. The water concentra-

tion in the retentate was monitored by titration using a Karl Fischer titrator, model DL31 (Mettler Toledo, Beaumont Leys Leicester, U.K.). The permeate weight and volume were measured. The weight fraction of acetic acid in permeate was determined by a titration method using sodium hydroxide. Results and Discussion In a pervaporation membrane process, it is desirable to have a polymer film that combines the characteristics of high permeation through polymer films with good selectivity. To obtain good permeation rates and a high degree of separation for a liquid mixture, it is essential to choose the right membrane as well as the optimum operating conditions. The major purpose of this study is to analyze the behavior of a pervaporation process for dehydration of waste acetic acid; thus, it is important to determine the permselectivity and flux rates of different water permselective membranes for waste acetic acid dehydration and also to investigate the dependence of the permeation behavior on the feed composition as well as the operating temperature. The water flux through the membrane was calculated by the expression

m Jw ) WpwJ ) Wpw ∆tA

(18)

where m is the permeate weight that goes through the effective membrane area, A, and is collected over the ∆t period of sample time, and Wpw is the water content in the permeate mass fraction. The separation factor R is defined by

Rw/a )

Wpw/Wpa Wfw/Wfa

(19)

The performance of pervaporation is dependent not only on the membranes but also on the operating parameters such as the feed composition, temperature, and other factors. Because the sorption and diffusion of each component are strongly concentration dependent, changing of the feed composition will affect the flux and selectivity in pervaporation. On the other hand, changing the operating temperature may cause a change of the membrane structure and mutual interaction between components, which consequently contributes to a change of their mass transport coefficients.34 Influence of the Feed Concentration. The performance of a pervaporation membrane can be characterized in terms of the permeation flux and separation factor. For the pervaporation of a binary liquid mixture, there is usually a nonlinear relationship between the permeation flux and its concentration in the feed mixture because of complex interactions between the membrane material and the permeating components.35 A comparison was made in terms of the water flux and selectivity obtained with the investigated membranes. The feed temperature of 80 °C was used for comparison. Figure 1 shows the evolution of the water flux corresponding to the dehydration experiments versus the water content in the feed calculated as the average concentration between samples. As shown in Figure 1, the largest flux values were obtained using the Symplex polyelectrolyte membrane, closely followed by those obtained with the VP43 membrane.

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Figure 1. Water flux vs water content in the feed solution at 80 °C.

Figure 3. Separation factor as a function of the feedwater concentration at 80 °C.

factors in the separation process. A pervaporation separation index (PSI) can be defined as a new measure of the separation ability of a membrane36

PSI ) JR

Figure 2. Permeate water content vs feedwater content for operation at 80 °C.

In Figure 2, the pervaporation selectivity expressed as the water mass fraction (%) in the permeate is shown as a function of the water mass fraction (%) in the feed mixture for each membrane at 80 °C. As can be observed, pervaporation through the investigated membranes ensures acetic acid enrichment in the feed phase by preferential water transfer. All of the membranes were highly selective toward water, but the Symplex membrane shows the highest water concentration in the permeate, followed by the CMC-CF23 membrane. For a feedwater concentration from 5 to 25 wt %, the water concentration in the permeate fraction slowly decreases with a decrease in the feed concentration, while it significantly decreases at a feedwater concentration below 5 wt %. Figure 3 shows the effect of the composition of the feed mixture on the separation factor of the investigated membranes. It appears from this figure that selectivity increases with a decrease in the water content in the feed. This phenomenon can be explained in terms of the plasticizing effect of water on the membrane.36 The plasticization action of water enhances the acetic acid permeation by decreasing the energy required for diffusive transport of acetic acid through the membrane, but the plasticizing effect of acetic acid to enhance water permeation is not remarkable as that of water, resulting in a reduction of selectivity. Comparison of Pervaporation Membranes. The separation ability of a membrane can be expressed in terms of permeation and selectivity, which usually take place in the opposite way, that is, when one factor increases, the other decreases, but both are important

(20)

where PSI is the pervaporation separation index (kg m-2 h-1) and J is the total permeate flux (kg m-2 h-1). In Figures 1-5, the investigated membrane performances are compared using the results obtained at constant temperature (80 °C). From this comparison, it is obvious that the separation capability of the Symplex membrane was higher than the separation capability obtained with the other membranes. Because the Symplex membrane is not commercially available on an industrial scale, the CMC-CF23 membrane was selected in order to make detailed studies. The higher separation factor of the CMC-CF23 membrane (see Figure 3) led to the higher value of the PSI (Figure 5) of CMC-CF23 compared to the other two commercial membranes (CMC-VP43 and Pervap 1005). The flux obtained with the CMC-VP43 membrane is higher than the flux obtained with the CMC-CF23 membrane, but the selectivity and PSI index are lower. The experimental results show that the higher the water concentration in the feed, the higher the flux of acetic acid (Figure 6). Similar observations were reported by Yeom and Lee2 and Kusumocahyo et al.37 using cross-linked PVA membranes for a water concentration in the liquid mixture of below 16 and 30 wt %, respectively. Also, similar dependences were obtained by Semenova et al.38 when they investigated pervaporation separation of the water/2-propanol mixtures by polyelectrolyte complexes. The increase in the acetic acid flux from a very low value (for pure acid permeation), when the acetic acid content in the feed mixture decreases, i.e., when its driving force for permeation decreases, indicates that the permeation of acetic acid is facilitated by the presence of water. Because all of the employed membranes lead to permeates with significant acetic acid contents (∼10 wt %), it would be necessary to use another complementary technique to recover this acid. The relative volatility between water and acetic acid is close to unity. To recover acetic acid from diluted aqueous streams, several authors propose to use hydrophobic membranes.39-42 Another alternative, from Gualy et al.,1 proposes the use of liquid-liquid extraction as a way to recover acetic acid from streams containing 0.1-20 wt % acetic acid. The preferred solvents are of the Cyanex type and

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Figure 4. Comparison of membrane performances for a 10 wt % feedwater content at 80 °C.

Figure 7. Influence of the feed concentration on the water flux through the CMC-CF23 membrane. Figure 5. PSI as a function of the feedwater concentration at 80 °C.

Figure 6. Acetic acid flux vs feedwater content for operation at 80 °C.

amines. Once the extraction step is completed, a series of distillation steps are required to recover the acid and to recirculate the extractive agent back to the extraction stage. Analysis of the CMC-CF23 Membrane Performance. Figure 7 shows the evolution of the water flux corresponding to the dehydration experiments with the CMC-CF23 membrane versus the water content in the feed. For each operating temperature, the permeation flux rises when the water content of the feed increases. For example, at 80 °C, between 10 and 20 wt % water, the total flux and water flux increase from 1.76 to 4.9

kg m-2 h-1 and from 1.56 to 4.3 kg m-2 h-1, respectively. This increase is due to the superposition of two different phenomena, i.e., (i) the exponential dependence of the diffusion coefficients on the concentration of permeants sorbed by the membrane and (ii) the increase of the sorbed component concentration with the concentration of the preferential solvent in the feed. The chemical interactions between the membrane and water are stronger than those between acetic acid and the membrane. Therefore, when the water weight percentage in the feed increases, the interactions between water and the membrane become more significant and the water sorption and diffusion capacity is enhanced. For a water concentration in the retentate of 10 wt %, the water flux through the membrane reached the values of 0.38, 0.82, and 1.56 kg m-2 h-1 at the working temperatures of 50, 65, and 80 °C, respectively. It was observed that the overall permeation flux increases progressively with an increase in the temperature. That is, as the temperature increases, the thermal motion of the polymer chains is intensified, facilitating diffusion of the permeants. As a result, the transport of both permeating species is enhanced, leading to an increase in the total permeation rate. Because the experiments were run batchwise, the permeation of water through the pervaporation membrane makes the concentration of water in the recirculation tank diminish with time. The feed composition reported is the average value of the feed compositions at the beginning and at the end of the time interval of the permeate sample collection (normally half an hour). In the experiment performed at 80 °C with an initial water concentration of 25.4 wt %, the final concentration

Ind. Eng. Chem. Res., Vol. 44, No. 4, 2005 983 Table 2. Computed Coefficients of the Model and 95% Confidence Intervals T ) 80 °C A1 ) 0.3794 ( 0.067 kg m-2 h-1 A2 ) 4.285 ( 0.246 A3 ) 280.83 ( 17.4 A4 ) 0.0874 ( 0.0054 Apparent Activation Energy for Individual Flux Ea,water ) 47.2 kJ mol-1 Ea,acetic ) 57.8 kJ mol-1

Figure 9. Influence of the feed temperature on the water flux through the CMC-CF23 membrane for various water weight percentages in the feed.

Figure 8. Water flux and permeate concentration during pervaporation through the CMC-CF23 membrane at 80 °C. The solid lines represent the predictions of the model.

of water in the organic mixture was reduced to a value of 0.57 wt %. This value confirms the viability of the pervaporation process to achieve a high degree of dryness. Usually, characterization of pervaporation membranes is carried out under steady-state conditions, resulting in a single datapoint. However, an experimental study of the dynamic mass-transfer effects in pervaporation from Rautenbach and Ho¨mmerich43 concludes that the conditioning behavior of commercial dehydration membranes during operation is clearly overrated, and the mass transfer through PVA membranes can be regarded as “pseudo-steady-state” with sufficient precision when looking at the dynamics of processes for solvent dehydration. In this work, each experiment in batch mode allows one to obtain a data set Ji vs Ci in a most time-efficient manner. Sorption experiments could not be conducted with the investigated membranes (composite structure) because of difficulty in differentiating between skin and support layers. The thickness of the CF23 membrane in dry conditions is 7 µm (scanning electron microscopy). The activity coefficients in the liquid feed have been calculated for a range of experimental conditions using the nonrandom two-liquid method (with coefficients from Okasinski and Doherty44). The values of the model parameters were calculated by comparing the experimental results with the simulated results to provide a minimum standard deviation, using the gEST parameter estimation package in combination with the gPROMS solver. The best-fit values are listed in Table 2. Figure 8 compares the experimental values of the water flux and permeate concentration with the corresponding computed values (which are represented by solid lines) at 80 °C. The experimental results are in good agreement with the prediction of the semiempirical model and, hence, support the validity of the basic assumptions underlying the model. In other words, water permeation rates are not affected by the presence

of small amounts of acetic acid in the membrane. On the contrary, acetic acid permeation through the membrane is directly proportional to the water content in the liquid mixture. Empirically, the temperature dependence of the permeation flux follows an exponential function, as shown by the semilogarithmic plot depicted in Figure 9. The water flux at three different temperatures is plotted in logarithmic form as a function of the reciprocal temperature for four different compositions. Qualitatively, the lines show that the flux rate increases with an increase in the water concentration in the feed and decreases with a decrease in the temperature. The same tendency has been observed for the temperature dependence of the acetic acid flux (Ja increases with Wfw in the range of concentrations investigated). An Arrhenius-type equation has been adopted to describe the temperature dependence of the partial fluxes

Ji,T ) Ji,T0 exp(Ea,i/RT)

(21)

The apparent activation energies Ea,i of the water and acetic acid fluxes have been estimated from experimental data at different temperatures. In Figure 9, the change in the water permeation rate due to the temperature influence is almost the same for all weight percentages in the feed. The apparent activation energy for water permeation is in the range of 43.9-50.5 kJ mol-1 and that for acetic acid permeation in the range of 54.6-60.9 kJ mol-1. The water mass fraction in the permeate decreases with a temperature rise. This can be described by eq 22, which relates the water concentration in the permeate to the apparent water and acetic acid activation energies. p ) Ww,T 2

1 Ea,acetic - Ea,water 1 1 1+ exp Jw,T1 R T1 T2 Ja,T1

[

(

)]

(22)

with Ea,water being lower than Ea,acetic, as was noticed previously; an increase in the temperature therefore implies a decrease in the water mass fraction in the permeate.

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Figure 10. Enrichment factor as a function of the feedwater concentration for the CMC-CF23 membrane.

For process design, some authors45 propose to use the enrichment factor β ) Wpw/Wfw in order to describe the process selectivity. Figure 10 shows the experimental enrichment factor as a function of the feedwater concentration for the CMC-CF23 membrane. It is observed that the enrichment factor is almost independent of the temperature, which simplifies its use in design calculations.

ai ) activity of component i (mole fraction) Di ) diffusion coefficient of species i in the membrane (m2 s-1) Di,0 ) intrinsic diffusion coefficient of species i in the membrane (m2 s-1) Ea,i ) apparent activation energy for permeation of species i (kJ mol-1) J ) total flux (kg m2 h-1) Ji ) flux of component i through the membrane (kg m2 h-1) ki ) sorption coefficient of component i m ) mass of the permeate collected in the condensers (kg) R ) ideal gas constant T ) feed temperature (K) W ) weight fraction z ) distance coordinate in the direction of flux (m) Greek Symbols R ) separation factor β ) enrichment factor δ ) membrane thickness (m) Fm ) density of the swollen membrane (kg m-3) τii ) plasticizing coefficient reflecting the ability of a penetrant to increase its own diffusion τij ) plasticizing coefficient reflecting the ability of a penetrant j to increase the diffusion of species i Subscripts

Conclusions Pervaporative recovery of acetic acid from industrial waste mixtures coming from acetylation processes was studied. The obtained results show that the industrial acetic acid can be efficiently dehydrated with the membranes under study, although the dehydration process is more efficient using the polyelectrolyte Symplex membrane because it provides a higher water flux and higher selectivity. The corresponding permeates need to be processed in order to recover the permeated acid (∼10 wt %). Also, this study is a useful reference in the membrane selection for esterification membrane reactors. Because the Symplex membrane is not commercially available on an industrial scale, the CMC-CF23 membrane from Celfa was selected in order to make detailed studies. Increasing the temperature from 50 to 80 °C will give an additional increase in both the total mass flux and obviously the water flux, whereas the enrichment factor is almost independent of the temperature. Thus, this work reports the mathematical model and parameters needed for the design of a pervaporation process for dehydration of waste acetic acid using the selected CMC-CF23 membrane. Acknowledgment Financial support of the Spanish Ministry for Science and Technology under Projects BQU2002-03357 and PPQ2003-0934 is gratefully acknowledged. D.G. also thanks the Ministry of Science and Technology for the Ramo´n y Cajal grant. Special thanks to Felicı´simo Go´mez for collaboration in pervaporation experiments. List of Symbols A ) membrane area (m2) A1 ) parameter in eq 14 (kg m-2 h-1) A2 ) parameter in eq 15 A3 ) parameter in eq 16 A4 ) parameter in eq 17

a ) acetic acid i ) permeating component w ) water Superscripts f ) feed solution m ) membrane phase p ) permeate

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Received for review July 22, 2004 Revised manuscript received November 5, 2004 Accepted November 22, 2004 IE0493560