Continuous Regioselective Enzymatic Esterification in a Simulated

Synchronous and asynchronous SMB processes for gas separation. José P. B. Mota , Isabel A. A. C. Esteves , Mário F. J. Eusébio. AIChE Journal 2007 ...
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Ind. Eng. Chem. Res. 2002, 41, 4722-4732

Continuous Regioselective Enzymatic Esterification in a Simulated Moving Bed Reactor Jonathan P. Meissner and Giorgio Carta* Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904-4741

A simulated moving bed adsorptive reactor (SMBR) has been developed and tested experimentally to conduct a regioselective enzyme-catalyzed diol esterification in a hexane solvent. The reaction is equilibrium limited, and accumulation of water on the biocatalyst causes a reduction in biocatalytic activity. As a result simultaneous removal of water by adsorption on a catalytically inert ion-exchange resin in Na form has been used to improve conversion. A three-zone SMBR system was developed for this purpose integrating reaction, adsorption, and regeneration. The packed beds in the three zones are periodically advanced in a “merry-go-round” fashion to simulate countercurrent flow. The SMBR allows continuous operation while reducing desorbent consumption and improving conversion relative to a conventional fixed-bed reactor. A mathematical model was developed to simulate the SMBR system based on independent analyses of adsorption and reaction phenomena. The model takes into account the interplay of these phenomena and provides a useful tool to understand the effects of process variables and for the selection of optimum operating conditions. Introduction The discovery that certain enzymes, such as lipases, can also function in nearly anhydrous organic solvents1 has greatly expanded the range of substrates usable in biocatalytic reactions, spurring a growing interest in new industrial applications. Much of the industrial interest stems from the chemospecificity, regioselectivity, and stereoselectivity that is often exhibited by these biocatalysts.2-6 Moreover, enzymes are thought to be more environmentally friendly than many conventional catalysts and work at moderate temperatures and pH. Esterifications are among the most industrially interesting reactions in this area.7 However, while, these reactions are of great interest for the synthesis of flavors and fragrances, pharmaceutical intermediates, and specialty chemicals, they are often subject to thermodynamic equilibrium limitations8-10 as well as to loss of catalytic activity when water produced in the reaction accumulates on the biocatalyst.11 Thus, in general, the water produced in these reactions must be controlled in order to attain high conversions and preserve the biocatalyst activity. It has been suggested12,13 that water can be controlled by limiting its thermodynamic activity in the reaction mixture, because that in turn controls the reaction equilibrium and the partitioning of substrates and products between the reaction mixture and the biocatalyst. Several approaches have been proposed to achieve this, including the use of salt hydrates14 pervaporation through water-selective membranes,15,16 free and vacuum evaporation,17 distillation,18 and air sparging.19 Adsorption onto a water-selective medium has also been considered by a number of authors17,20 and is of particular interest because of the ease with which adsorbents can be incorporated into packed bed reactors that are often preferred for enzymatic conversions.21,22 For example, Mensah et al.11,23 and Migliorini et al.24 have * Corresponding author. Telephone: (434) 924 6281. FAX: (434) 982 2658. E-mail: [email protected].

shown that catalytically inert ion-exchange resins are effective for in situ control of water in enzymatic reactions, with the advantage that removal of the adsorbed water can be done with a polar solvent, without having to separate the biocatalyst from the adsorbent. However, to obtain a continuous operation of adsorptive reactor, systems that integrate reaction, separation, and regeneration steps efficiently are desirable. Simulated moving bed reactor (SMBR) systems have been developed for this purpose. SMBR systems simulate a countercurrent flow of the adsorbent/catalyst and the fluid phase through the use of multiple fixed beds advanced in a “merry-go-round” fashion. The technology draws upon the success of simulated moving bed separators that are now used extensively on a large scale25 but incorporates a reactive component. As such, they retain the advantages of true countercurrent reactor systems without the operational complexities of actually moving adsorbent/catalyst particles. A number of laboratory studies of SMBR systems have appeared in the literature in recent years, including reactors for the hydrogenation of mesitylene,26-29 for the oxidative coupling of methane,30-32 and for a number of sulfonic acid resin catalyzed esterifications, transesterifications, and acetylations.33-35 Some experimental applications to enzyme-catalyzed reactions have also been studied such as the enzymatic isomerization of glucose to fructose36 and lipase-catalyzed transesterifications,37 and a number of theoretical studies of adsorptive reactors have been conducted.38-41 However, despite these studies, no industrial scale applications of adsorptive SMBR have been reported. It is hoped that a better understanding of the interplay of adsorptive and reaction phenomena and the exploration of the potential for applications in critical fields such as biocatalysis will allow practical implementation of these reactors. It should be noted that biocatalytic reactions are good candidates because the temperature is low so that adsorption can be effective.

10.1021/ie0202625 CCC: $22.00 © 2002 American Chemical Society Published on Web 08/24/2002

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comprises multiple beds, and the inner arrow shows the direction of bed switching. In practice, of course, this motion is obtained by the periodic switching of valves. The switching time, p, is related to the equivalent solid and liquid velocities in a true countercurrent system by the following equations:

u js )

(1 - )L p

(1a)

L p

(1b)

u j i ) ui Figure 1. Simulated moving bed reactor concept.

The objective of this work is to determine the suitability of an SMBR system for a reversible regioselective enzymatic esterification. The reaction considered is the lipase-catalyzed esterification of propionic acid and 2-ethyl-1,3-hexanediol to form the primary monoester and water according to

The reaction occurs in a nearly anhydrous hexane solvent and is equilibrium limited (K ) 0.6 at 22 °C).24 The biocatalyst is Lipozyme IM (Novo Nordisk Bioindustrials, Inc., Franklinton, NC) and consists of a Mucor miehei lipase immobilized on a macroporous polymeric support. Direct conversions of diols to their monoester are of considerable importance as these products have applications in cosmetics, pharmaceutical intermediates, and surfactants.2 Biocatalytic routes are often desirable for these applications because of regulatory and selectivity considerations. The Lipozyme biocatalyst used in this work is highly selective for the primary monoester and exhibits longterm stability. However, as shown by Migliorini et al.,24 accumulation of water on the biocatalyst reduces its catalytic activity. Thus, adsorption of water onto the biocatalyst must be prevented to maintain the highest reaction rates. Migliorini at al. studied the adsorptionassisted operation of this reaction by incorporating an ion-exchange resin as a water adsorbent together with the biocatalyst in batch and fixed-bed reactors. In situ water removal was shown to provide two distinct advantages: it shifted the thermodynamic equilibrium toward high conversion and it prevented accumulation of water on the biocatalyst, maintaining high activity. Since these advantages are realized only during transient operation of these reactors, the application of an SMBR system integrating reaction, adsorption, and regeneration is developed in this work. SMBR System The SMBR considered in this work is shown schematically in Figure 1. It consists of three separate zones with intermediate feed and product withdrawal points. The acid substrate feed is supplied continuously to zone III, while the diol substrate feed is supplied continuously to zone I. A “raffinate” stream containing the ester product is recovered from zone III, while an “extract” stream containing the water product and excess diol fed to the system is withdrawn from zone I. Each zone

where  is the bed void fraction, L is the bed length, and ui is the fluid-phase velocity. The latter is different in each zone as a result of the addition or withdrawal of streams. The role played by the different zones in the SMBR is as follows. Zone III serves as the reaction/separation zone. In this zone the acid substrate reacts with the diol entering from zone II to form the ester and water. The water produced is adsorbed and is carried upstream by the solid phase with each successive switch. The bulk of the adsorbed water is removed in zone I by the diol substrate, which is fed in amounts in excess of the stoichiometric reaction requirement. The regenerated adsorbent is thus returned to zone III. The excess diol and desorbed water are purged from the system in the extract stream, which is withdrawn between zones I and II. A portion of the diol stream emerging from zone I enters zone II. The function of this zone is to remove water from the diol, preventing a high water concentration from entering the reaction/separation zone (zone III) and preventing the acid and ester produced near the entrance of zone III from being lost in the extract. Figure 1 shows two beds in each zone. While more beds could be added, it has been shown that most of the benefits of the true countercurrent operation can be gained even with only a single bed in each zone. The correct operation of the SMBR requires the selection of fluid velocities in such a way that the adsorbed species (e.g., water) move in the appropriate direction in each zone. Thus, the fluid velocity in the reaction/adsorption zone must be such as to prevent the water produced in the reaction from breaking through in the raffinate. Conversely, the diol feed flow rate must be sufficiently high so that water will be desorbed in zone I and move toward the extract withdrawal point. Finally, the fluid velocity in zone II must be sufficiently low that water is transported by the solid phase toward the extract withdrawal point. Experimental Section Materials and Methods. Lipozyme IM was obtained from Novo Nordisk Bioindustrials, Inc., (Franklinton, NC). The biocatalyst has a particle size of 0.04 ( 0.02 cm and a porosity of 0.53 ( 0.02. The initial water content of the fresh Lipozyme IM used in this work was 2.4 ( 0.4 mmol/g, determined through weight loss on drying in an oven at 120 °C. The adsorbent used in this work is Dowex HCR-W2 in Na+ form (Dow Chemical Company, Midland, MI). This is a sulfonated, gel-type polystyrene-divinylbenzene resin with a nominal degree of cross-linking of 8%. The resin consists of spherical particles 0.04 ( 0.02 cm in size. It was converted to the sodium form with 1 N

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Ind. Eng. Chem. Res., Vol. 41, No. 19, 2002 Table 1. Experimental Conditions for SMBR Runsa QD QE QA p configuration run (NI - NII - NIII) (cm3/min) (cm3/min) (cm3/min) (min) A B C D E a

1-1-1 1-1-2 1-1-3 1-1-3 2-1-2

0.77 0.77 0.78 0.58 0.40

0.68 0.68 0.69 0.51 0.31

0.11 0.11 0.11 0.11 0.11

180 180 180 240 180

CAF ) 1.0 mol/L, CDF ) 3.0 mol/L, L ) 7.1 cm.

A summary of operating conditions for the different SMBR runs is given in Table 1. In each case, the desorbent fed to zone I was 3 mol/L diol in hexane. A high diol concentration is desirable because it lowers the thermodynamic activity of water that, in turn, is more efficient for desorption. However, since the diol is rather viscous (µ ) 2.8 cp for 3 mol/L diol in hexane at 25 °C), this concentration was used as a compromise. Varied numbers of beds per zone, flow rates, and switch times were used in the different runs. Figure 2. Simulated moving bed reactor apparatus.

Mathematical Model sodium hydroxide, rinsed with deionized distilled water, and dried in an oven at 120 °C. Propionic acid (99% purity), 2-ethyl-1,3-hexanediol (97% purity), and hexane (capillary GC grade) were obtained from Sigma Chemical Co. (St. Louis, MO). The feed solutions were kept nearly anhydrous by storing them under the Dowex adsorbent material. A 80/100 mesh Chromosorb 101 column (Alltech, Deerfield, IL) was used with a Hewlett-Packard model 5890A gas chromatograph (thermal conductivity detection) for analysis. SMBR Apparatus. A schematic of the SMBR apparatus is shown in Figure 2. For simplicity the diagram shows only three beds (one per zone), although the apparatus could accommodate as many as ten beds. Glass chromatographic columns 1.5 cm in diameter (Omnifit, Toms River, NJ) were used, each containing 2 g of Dowex resin and 4 g of the Lipozyme biocatalyst. The two materials were intimately mixed and poured in the columns. The settled bed height was 7.1 ( 0.1 cm. The total void fraction of these columns was estimated to be 0.66, based on b ) 0.4 and the porosity of Lipozyme. Metering pumps with accuracy of (0.01 cm3/min (Eldex A-60-S and Eldex B-100-S, Napa, CA) were used to feed the acid and diol streams dissolved in hexane and withdraw the extract stream. The flow rate of the remaining stream (the raffinate) is determined by a mass balance. The desired stream routing is accomplished using rotary stream selector valves (model C25Z-3180E, Valco Instrument Company, Inc., Houston, TX). Check valves (model CV 3000, Upchurch Scientific, Oak Harbor, WA) are placed between each column to prevent backflow. Connections between the columns and valves were made with 1/16 in. PTFE tubing. Samples were collected from the raffinate and extract streams at predetermined time intervals. To prevent evaporation of these samples, a Gilson model 231 autoinjector was modified to automatically collect the raffinate samples and inject them into septumcapped glass vials. Synchronized switching of the valves was accomplished using electric actuators (model E10, Valco Instrument Company, Inc., Houston, TX) interfaced to a PC-based control system. All experiments were conducted at room temperature 22 ( 2 °C.

As discussed above, the correct operation of an SMBR system requires the selection of appropriate fluid-phase velocities in the different zones. For certain idealized conditions (e.g., linear isotherms or Langmuir isotherms) and in the absence of mass transfer and kinetic effects, these operating conditions can be selected on the basis of explicit expressions (see Lode et al.).41 In our case, however, reaction kinetic effects and mass transfer resistances are substantial. Moreover, the adsorption equilibria are dependent on the thermodynamic activity coefficients, which, in turn, vary dramatically as a function the composition of the reactions mixture and, thus, with conversion. A detailed mathematical model was thus developed based on independently determined rate expressions. The equations used to simulate the SMBR system are summarized in Table 2 and are based on the fixed-bed model developed by Migliorini et al.24 Each bed is assumed to be uniformly packed with a homogeneous mixture of the biocatalyst (bed density Fc ) 0.32 g/cm3) and the adsorbent (bed density Fa ) 0.16 g/cm3). The model comprises (a) the conservation equations (eq 2.1) for each fixed bed assuming axially dispersed plug flow; (b) boundary conditions and mass balances to describe the addition and removal of the fluid streams (eqs 2.2af); (c) rate equations based on the LDF approximation (eqs 2.3a-b) to describe the rates of mass transfer between the fluid phase and the biocatalyst and between the fluid phase and the adsorbent; (d) the rate equation for the reaction (eqs 2.4a-b); and (d) adsorption isotherms describing the equilibrium distribution of substrates and products between the fluid phase and the adsorbent and between the fluid phase and the biocatalyst (eqs 2.5a-c). The effects of intercolumn dead volumes were found to be negligible in our experimental system. Thus, this volume was neglected in the mass balances and boundary conditions connecting adjacent columns. The reaction kinetics is described by the reversible Ping Pong Bi-Bi rate expression including substrate inhibition (eq 2.4a) according to the results of Migliorini et al.24 Since the amount of adsorbed water on Lipozyme IM has a strong effect on the biocatalyst activity but no effect on the substrate concentration dependence of the rate,11 the maximum rate parameter rm in the rate

Ind. Eng. Chem. Res., Vol. 41, No. 19, 2002 4725 Table 2. SMBR Model Equationsa Bed conservation equations

∂qi,jc ∂qi,ja ∂ci,j ∂2ci,j ∂ci,j + Fc + Fa + uj ) bDL 2 + Fcvir(c,qw,ic) ∂t ∂t ∂t ∂z ∂z

(2.1)



Boundary conditions and mass balances

∂ci,j z ) 0: ujci,j0 ) ujci,j - bDL ∂z z ) L:

(2.2a)

∂ci,j )0 ∂z

(2.2b)

j ) 1:

cA,j0 ) cE,j0 ) cW,j0 ) 0, cD,j0 ) cDF

(2.2c)

j ) 2,NI + NII:

ci,j0 ) ci,j-1(L) for i ) A,D,E,W

(2.2d)

j ) NI + NII + 1:

cA,j0 )

QD - QE QA QD - QE c (L) + c F, c 0 ) c (L) for i ) D,E,W QD - QE + QA A,j-1 QD - QE + QA A i,j QD - QE + QA i,j-1

j ) NI + NII + 2,N: ci,j0 ) ci,j-1(L) for i ) A,D,E,W

(2.2e) (2.2f)

Adsorption rate equations

∂qi,jc ) kic(qi,jc* - qi,jc) ∂t

(2.3a)

∂qi,ja ) kia(qi,ja* - qi,ja) ∂t

(2.3b)

Reaction kinetic model

r)

rm(cA,jcD,j - cE,jcW,j/K) cA,jcD,j + KDmcA,j(1 + cA,j/KAi) + KAmcD,j(1 + cD,j/KDi)

rm ) rm° [0.63 - 0.35 tanh (0.66qW,jc - 3.3)]

(2.4a) (2.4b)

Adsorption equilibria

qW,jc* ) 13.6aW,j - 19.7aW,j2 + 22.2aW,j3

(2.5a)

qW,ja* ) 56.4aW,j - 106aW,j2 + 105aW,j3

(2.5b)

qA,jc* ) 57.2aA,j/(1 + 19.7aA,j)

(2.5c)

a Subscripts: A ) acid, D ) diol, E ) ester, W ) water, j ) 1,2,.....N with N ) N + N + N . Superscripts: c ) catalyst, a ) adsorbent, I II III F ) feed value, 0 ) bed inlet, L ) end of bed, * ) equilibrium value.

expression is a strong function of the water content of the biocatalyst, qWc. This relationship is expressed by an empirical function (eq 2.4.b). Accordingly, the reaction rate is maximum when qWcf0, it remains nearly constant up to qWc∼3 mmol/g, and then decreases rapidly over the range of qWc ) 3.5 to 6.5 mmol/g to a lower limit where the rate is only 30% of the initial value.24 As a result, it is desirable to keep the adsorbed water concentration on the biocatalyst at or below 3 mmol/g. This water content will be referred to as the “deactivation limit”. Adsorption equilibrium isotherms are used to describe the partitioning of solutes for both the biocatalyst and the adsorbent resin. As shown by Migliorini et al.,24 only two of the components are significantly adsorbed: propionic acid, which is adsorbed on the biocatalyst only, and water, which is adsorbed on both the biocatalyst and the adsorbent resin. In both cases, the adsorption isotherms are expressed as empirical functions of the thermodynamic activity in the reaction mixture, which were calculated using the UNIFAC model42 with the parameter set of Hansen et al.43 Inclusion of activity coefficients is necessary in this system because of the

highly nonideal nature of the reaction mixture. The latter causes the thermodynamic activity and, hence, the adsorption isotherm, to vary dramatically as a function of conversion. As shown by Migliorini et al.,24 the water adsorption isotherms are S-shaped (type V) when plotted as a function of aW. For low aW values, water adsorption on the resin is about four times greater than on the biocatalyst. Adsorption of propionic acid on the biocatalyst follows a favorable type I isotherm, but the maximum amount adsorbed is low for our experimental conditions. All of the model parameters, with the exception of the axial dispersion coefficient, were determined by Migliorini et al.24 and are summarized in Table 3. The activity of the biocatalyst sample used in this work was lower than that used by Migliorini et al.;24 however, the concentration dependence and the effect of adsorbed water were the same. As a result, the only variation is the value of the rate coefficient r0m. The axial dispersion coefficient, DL, was determined as follows. First, breakthrough experiments using noctane as a nonadsorbed tracer in hexane were per-

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Table 3. Model Parametersa parameter 0

rm KDm KAm KDi KAi K kWc kAc kWa

value

units

1.0 6.5 × 10-5 3.0 × 10-2 5.0 1.1 × 10-4 0.6 7.9 3.0 1.3

mmol/(h g) mol/L mol/L mol/L mol/L h-1 h-1 h-1

Figure 3. Experimental and predicted diol profiles. Experimental conditions: 3.0 mol/L diol, diol loading step u ) 0.13 cm/min, hexane rinse step u ) 0.15 cm/min, L ) 7.1 cm. Lines show model predictions with different values of Pe ) udp/bDL.

formed.23 A Peclet number Pe ) udp/bDL ) 0.3 was found, in good agreement with the Peclet number predicted by the correlation of Chung and Wen.44 Tracer experiments were then done using 3 mol/L diol in hexane. These experimental results are shown in Figure 3 along with model calculations. Although the diol is not adsorbed, the results of positive and negative concentration steps are quite different. In both cases, the stoichiometric centers of the curves occur at V/Vc ∼ 0.66, which coincides with the total void fraction of the column. However, while the positive concentration step yields a sharp curve, the negative concentration step yields a strongly tailing curve. This difference is attributable to viscous fingering. This is likely to occur when the more viscous diol solution (µ ) 2.8 cp) is displaced by the less viscous hexane solvent (µ ) 0.33 cp). In this case, the less viscous displacing fluid forms “fingers” that extend into the more viscous fluid at the rear boundary between the two fluids. These fingers become increasingly pronounced as the displacing fluid moves through the column, resulting in a long elution tail. Conversely, viscous fingering is not expected to affect the response to the positive concentration step because, in this case, the viscosity difference actually stabilizes the front. As seen in Figure 3, while Pe ) 0.3 provides a good prediction of the response to the positive concentration step, a much lower Pe value is needed to fit the response to the negative concentration step. It should be noted that in describing the SMBR system, axial dispersion and viscous fingering affect different components to a different extent. They have the greatest effect on the nonadsorbed species (the diol and the ester), while they are expected to have almost no effect on the adsorbed

Figure 4. Experimental and predicted profiles for run A (1-1-1 configuration): (a) raffinate; (b) extract. Conditions are given in Table 1.

components (water and propionic acid), for which mass transfer resistances are dominant. Moreover, the effects of viscous fingering are expected to be different in the different zones of the SMBR system. Thus, to simplify the analysis, a single Pe value was used in the model simulations, chosen to provide the best fit of the SMBR data. A value of Pe ) 0.06 was optimal and is intermediate between the two Pe values obtained in the diol tracer experiments. This value of Pe was used in all the simulations. More rigorous models incorporating an explicit description of viscous fingering could be developed.45 However, it will be shown that the approximate modeling approach used in this work produces results in reasonable agreement with the experimental data without occurring in the detailed description of the fluid mechanics of viscous fingering which, as a minimum, would require a two-dimensional transient model. Results and Discussion Experimental results for SMBR run A are shown in Figure 4. The top figure shows the raffinate concentrations while the bottom figure shows those for the extract stream. This run corresponds to a 1-1-1 SMBR configuration with one bed in zone I, one bed in zone II, and one bed in zone III. Starting with initially clean beds, the concentrations build up in the system gradually during the first few cycles. As a result of the periodic switching of beds, a periodic steady-state is reached by

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Figure 5. Experimental and predicted raffinate profiles for period 5, run A. Experimental conditions as in Figure 4.

Figure 7. Experimental and predicted profiles for run B (1-1-2 configuration): (a) raffinate; (b) extract. Conditions are given in Table 1.

Figure 6. Predicted adsorbed water profiles as a function of reactor length: (a) zone I; (b) zone III. Experimental conditions of Figure 4. Profiles are shown at the end of the period.

the fourth cycle. At this point the effluent concentrations become periodic functions of time with a period equal to the bed switching time. A better understanding of the interplay of the zones and of the periodic steadystate profiles can be obtained by plotting the raffinate concentrations as a function of the number of column volumes in zone III, V/Vc, rather than time. The results for the fifth period are shown in Figure 5 on an enlarged scale. At the start of the period, the bed that was just moved to zone III is filled with the 3 mol/L diol feed solution. Thus, initially, a high concentration of diol is

seen in the raffinate. This diol is then rapidly displaced as this bed fills with the zone III feed. As this occurs the concentration of the ester formed in the reaction begins to rise. As shown by Migliorini et al.,24 the acid in zone III forms a reactive front whose speed depends on both the reaction rate and its adsorption isotherm. Downstream of this front no reaction takes place because the acid is absent. Thus, initially, only a portion of the reactor zone is active. As seen in Figure 5, the maximum ester concentration is attained approximately when the acid breaks through. When this occurs, acid and diol are simultaneously present throughout the length of the reactor zone and the maximum rate of ester production is obtained. It can be seen that the water concentration is kept very low in the raffinate. When the water begins to break through, the ester concentration begins to decline, indicating that equilibrium limitations have reduced the reaction rate. The extract profiles in Figure 4b demonstrate the regeneration of the adsorbent in zone I. During the first few cycles the beds contained little water so that the water concentration in the extract is low. By the third cycle, water produced by the reaction in zone III begins to appear in the extract, building up until the periodic steady state is reached. Predicted effluent concentration profiles are shown in Figures 4 and 5. In general there is a good agreement between the model predictions and the experimental data for both the extract and raffinate. In fact, the agreement is quite impressive when one considers that

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Figure 8. Experimental and predicted profiles for run C (1-1-3 configuration): (a) raffinate; (b) extract. Conditions are given in Table 1.

Figure 9. Predicted adsorbed water profiles as a function of reactor length; (a) zone I; (b) zone III. Experimental conditions of Figure 8. Profiles are shown at the end of the period.

the thermodynamic activity coefficient of water varies over 2 orders of magnitude in the reactor zone for these experimental conditions. The initial acid breakthrough is not as well predicted. Most likely this is due to slight inaccuracies in the description of the highly favorable acid adsorption isotherm24 and by the fact that the LDF approximation is used to describe the rate of adsorption. The corresponding predicted axial profiles of adsorbed water on the biocatalyst and the adsorbent in zones I and III are shown in Figure 6 at the end of the period in the periodic steady state. The profiles in zone I show that both the Dowex resin and Lipozyme are sufficiently regenerated. The biocatalyst leaving zone I is in the fully active state (adsorbed water less than 3 mmol/g). Similarly, there is a very low concentration of water adsorbed on Lipozyme in zone III as most of the water formed in the reaction is adsorbed on the Dowex resin. Since the biocatalyst remains below 3 mmol/g of adsorbed water, full activity is maintained throughout the period. For these conditions, the conversion attained is limited by the rate of reaction and the reaction equilibrium, since the simultaneous removal of water keeps the biocatalyst away from the deactivation limit. The effect of adding a second bed to the reaction/ adsorption zone (run B) is shown in Figure 7. The flow rates in this 1-1-2 SMBR configuration are the same as in run A. Thus the residence time in zone III is doubled. The extract and raffinate concentration profiles are qualitatively similar to the previous run. However,

in this case a nearly complete conversion of the acid substrate occurs, and a much higher conversion of the diol leads to a higher purity ester product. Correspondingly, a higher concentration of water is seen in the extract (Figure 7b). Figure 8 shows the effect of adding a third bed to the reaction/adsorption zone. For simplicity, only the final five cycles are shown (from 12 to 27 h). For this 1-1-3 SMBR configuration (run C), the diol substrate concentration approaches small values in the raffinate stream toward the end of the period, resulting in an even higher ester purity. The corresponding predicted axial adsorbed water profiles in zone III are shown in Figure 9. It can be seen that although most of the water produced is adsorbed on the Dowex resin, the adsorbed water concentration on the biocatalyst has risen slightly above the 3 mmol/g deactivation limit in the first 40% of the first bed. This suggests that the switch time is near the maximum because any increase, corresponding to a decrease of the equivalent adsorbent velocity (see eq 1a), would cause further accumulation of water and a reduction in the catalytic activity. The effect of increasing the switch time to 240 min for the 1-1-3 configuration is shown in Figure 10. The acid feed rate is the same as run C. However, the diol feed rate and the extract flow rates are lower. Conversion of the acid is, however, now far from being complete, and a significant acid concentration breaks through. The adsorbed water profiles are shown in

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Figure 10. Experimental and predicted profiles for run D (1-1-3 configuration): (a) raffinate; (b) extract. Conditions are given in Table 1.

Figure 11. In this case, the adsorbed water concentration has risen above the deactivation limit over the entire length of the first bed as well a portion of the second bed. The lower reaction rates caused by the accumulation of water, in turn, resulted in a lower conversion of the acid substrate. Since the diol feed rate was reduced for this run, a higher concentration of water is seen in the extract (Figure 10b). Finally, the effect of adding an additional bed to the regeneration zone, zone I, is shown in Figure 12 (run E). The addition of another bed to the desorption section is expected to increase the desorption efficiency, allowing the diol feed flow rate to be lowered while maintaining a similar amount of regeneration. In this run, the diol feed flow rate was reduced from 0.77 to 0.40 cm3/ min while keeping the switching time equal to 180 min and the acid feed flow rate equal to 0.11 cm3/min. The experimental and predicted raffinate profiles are quite similar to those obtained in the 1-1-2 configuration (see Figure 7). The extract water concentration profiles are quite different, however, as in this case a much smaller amount of diol feed is used as a desorbent. Because essentially the same amount of water is produced and recovered in the extract as in run C, the efficiency of using the desorbent has been increased substantially by the countercurrent operation with two beds in series in zone I. The axial profiles of adsorbed water corresponding to this run are shown in Figure 13 at the end of the period in the periodic steady state.

Figure 11. Predicted adsorbed water profiles as a function of reactor length: (a) zone I; (b) zone III. Experimental conditions of Figure 10. Table 4. Performance Parameters % acid conversion

% ester purity in raffinate

run

exp.

model

exp.

model

A B C D E

79 92 93 80 88

85 93 96 87 90

25 35 43 44 37

31 40 47 56 40

a

From ref 24.

As seen from these profiles, at the end of the period the first bed in zone I is regenerated sufficiently so that the water adsorbed on the biocatalyst is below the deactivation limit while more than half of the water adsorbed on the Dowex resin has been removed. Process Performance Parameters. In general, the optimization of the SMBR is dependent on the definition of an economic objective function. However, for simplicity, only the acid conversion and the ester purity in the raffinate stream were used in this work to compare different experimental conditions. A summary of the experimental and predicted values for these two quantities is given in Table 4 for periodic steady state conditions. The acid conversion is based on the periodaverage concentration in the raffinate, while the ester purity is calculated from the average raffinate concentrations excluding the bed void volume. These quantities can be compared directly with the corresponding equilibrium values for a nonseparating plug flow reactor,

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Figure 12. Experimental and predicted profiles for run E (2-1-2 configuration): (a) raffinate; (b) extract. Conditions are given in Table 1.

Figure 13. Predicted adsorbed water profiles as a function of reactor length: (a) zone I; (b) zone III. Experimental conditions of Figure 12.

which are calculated from the following relationships:

conversion during the transient operation of fixed-bed reactors.24 While these adsorptive reactors offered these advantages over conventional reactors, their operation was necessarily discontinuous. A continuous SMBR system, integrating reaction, adsorption of water, and regeneration, has been shown to be effective for this reaction. The process operates in a nearly continuous manner while overcoming equilibrium limitations and preventing deactivation of the biocatalyst by adsorbed water. The SMBR system offered two additional advantages: reduced desorbent consumption due to maximizing the driving force for desorption through countercurrent operation, and internal recycle through zone II of a portion of the diol used as the regenerant. A mathematical model, based on independently determined descriptions of adsorption and reaction phenomena, was developed to predict the behavior of the SMBR system. In all cases, model predictions were in good agreement with the experimental results obtained in our laboratory scale system. Ester concentration profiles were predicted well, whereas the diol concentration profiles were predicted less accurately because of strong tailing behavior of this species. These predictions are impressive when one considers that they are dependent on the simultaneous description of a number of independent effects, including the calculation of activity coefficients that vary as much as 2 orders of magnitude over the conditions studied. The level of model accuracy attained was useful as a means of directing the experimental investigation and elucidating the performancegoverning parameters. The model provides a useful tool

K)

(x*)2 (1 - x*)(cFD/cFA - x*)

ester purity )

x* 1 + cFD/cFA

where x* is the equilibrium conversion of the acid. For feed concentrations of the acid and diol substrates of 1 and 3 mol/L, we obtain x* ) 67% and an ester purity of 17%. As seen in Table 4, the SMBR runs achieved both acid conversion and ester purity much higher than the corresponding equilibrium values. Increasing the number of beds in zone III from one to three (runs A-C) increases the acid conversion and the ester purity because of the longer residence time. Increasing the switching time from 180 to 240 min (runs C and D) increases the average ester purity in the raffinate because the diol concentration is reduced to a low value. Finally, including an additional bed in zone I (run E) yields a performance similar to that of run B, but with greatly reduced diol consumption. Conclusions In this study, an enzymatic esterification has been coupled with the adsorption of water. Previously, this coupling has been shown to enhance the rate and ultimate conversion in batch reactors as well as the

Ind. Eng. Chem. Res., Vol. 41, No. 19, 2002 4731

to investigate the effects of process variables and ultimately a powerful tool for process optimization. Notation ai ) thermodynamic activity of species i ci,j ) concentration of species i in column j, mol/L dp ) particle diameter, cm DL ) axial dispersion coefficient, cm2/h K ) reaction equilibrium constant kia ) LDF adsorption rate constant for species i on the adsorbent, 1/h kic ) LDF adsorption rate constant for species i on the catalyst, 1/h Kii ) substrate inhibition constant in kinetic model, mol/L Kim ) Michealis-Menten constant in kinetic model, mol/L L ) bed length, cm Nj ) number of beds in zone j p ) switching time, h Pe ) Peclet number ( ) udp/bDL) Qj ) fluid flow rate in zone j for j ) I, II, or III or fluid flow rate of acid feed, diol feed, and extract for j ) A, D, and E, respectively, cm3/min qi,ja ) adsorbed concentration of species i in adsorbent particles, mmol/g qi,jc ) adsorbed concentration of species i in the catalyst, mmol/g r ) reaction rate, mmol/g rm ) reaction rate coefficient in kinetic model, mmol/(g h) t ) time, h u ) fluid velocity, cm/h uj ) fluid velocity in column j, cm/h u j i ) true countercurrent equivalent fluid velocity in column i of a SMBR, cm/h u j s ) true countercurrent equivalent solid velocity in column i of a SMBR, cm/h V ) effluent volume, cm3 Vc ) column volume, cm3 x* ) equilibrium conversion of limiting reactant z ) axial coordinate measured from entrance to zone, cm Greek Symbols  ) total void fraction b ) bed extraparticle void fraction p ) particle porosity νi ) stoichiometric coefficient of species i Fa ) mass of adsorbent per unit column volume, g/cm3 Fc ) mass of catalyst per unit column volume, g/cm3

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Received for review April 5, 2002 Revised manuscript received July 17, 2002 Accepted July 24, 2002 IE0202625