Analysis of Heterogeneously Catalyzed Ester Hydrolysis Performed in

Apr 14, 2004 - A discontinuously operated chromatographic reactor and a reaction calorimeter were used to study experimentally and theoretically the ...
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Ind. Eng. Chem. Res. 2004, 43, 4691-4702

4691

Analysis of Heterogeneously Catalyzed Ester Hydrolysis Performed in a Chromatographic Reactor and in a Reaction Calorimeter Phong T. Mai,† Tien D. Vu,† Ky X. Mai,‡ and A. Seidel-Morgenstern*,†,§ Institut fu¨ r Verfahrenstechnik, Otto-von-Guericke-Universita¨ t, Universita¨ tsplatz 2, D-39106 Magdeburg, Germany, Faculty of Chemical Engineering, Hanoi University of Technology, 1 Dai Co Viet, Hanoi, Vietnam, and Max-Planck-Institut fu¨ r Dynamik komplexer technischer Systeme, Sandtorstrasse 1, D-39120 Magdeburg, Germany

A discontinuously operated chromatographic reactor and a reaction calorimeter were used to study experimentally and theoretically the heterogeneously catalyzed hydrolysis reactions of four esters (methyl formate, methyl acetate, ethyl formate, and ethyl acetate). Two different batches of an acidic ion-exchange resin were used as catalyst and adsorbent. The relevant distribution equilibria were quantified using pulse chromatographic experiments. The reaction rates were quantified from (a) the shape of the elution profiles and (b) the course of the heat fluxes. To this end, systematic experiments were carried out using fixed beds packed with the catalysts and a reaction calorimeter containing catalyst suspensions. Advantages and disadvantages of these two types of experimental approaches in terms of their potential to extract reliable kinetic parameters were evaluated. A simplified pseudohomogeneous model and the determined parameters were found to be capable of describing the concentration profiles in the chromatographic reactor for all reactions studied under diverse operation conditions. 1. Introduction In the past decade, the concept of multifunctional reactors, in which one or more additional other tasks (in particular, separation processes) are integrated into the reactor, became an important research topic for reaction engineers.1-4 Aside from reactive distillation, reactive extraction, and membrane separation, the coupling of chemical and biochemical reactions with chromatographic separations is attractive for the efficient production of high-purity products. The increasing interest in chromatographic reactors is due, in particular, to the improved availability of tailor-made highly selective adsorbents. Various theoretical and experimental studies of the principle using a single fixed bed have been presented (see, e.g., refs 5-8). In the past few years, the more powerful simulated moving bed concept has received a great deal of interest. This concept is based on applying several fixed beds connected in series and mimicking a countercurrent between the two phases by discretely switching the inlet and outlet positions (see, e.g., refs 9-11). However, to date, no significant industrial breakthrough has been achieved in the promising technology of efficiently combining chemical reactions and in situ separation using chromatographic effects. This appears to be partly due to the fact that too few studies have been performed to quantify thoroughly the underlying processes as a prerequisite to the critical evaluation of the potential of the concept and its successfull application. A typical difficulty encountered in the analysis of chromatographic fixed-bed reactors is the acquisition of * To whom correspondence should be addressed. Address: Otto-von-Guericke-Universita¨t, Universita¨tsplatz 2, D-39106 Magdeburg, Germany. Tel.: +49-391-67-18643. Fax: +49-39167-12028. E-mail: [email protected]. † Otto-von-Guericke-Universita¨t. ‡ Hanoi University of Technology. § Max-Planck-Institut fu¨r Dynamik komplexer technischer Systeme.

reliable data related to the rates of the chemical reactions. Because solids that simultaneously catalyze the reactions and cause separation processes are often involved, it is difficult to decouple and quantify the individual processes. For this reason, complementary experimental investigations using batch reactors are often performed (see, e.g., refs 6 and 12). Unfortunately, the measurement of the relevant concentration time courses is often time-consuming and tedious. An alternative approach to the quantification of reaction rates that is rarely considered in this field is the application of calorimetry.13,14 An accurate measurement of the time dependence of heat effects related to reactions allows one to quantify reaction rates.15 It is the purpose of this work to enlarge the database related to heterogeneously catalyzed reactions performed in a chromatographic reactor. To this end, four different ester hydrolysis reactions were studied experimentally in a single fixed-bed reactor and in addition in a reaction calorimeter. 2. Theory In this work, a fixed bed packed with a solid acting simultaneously as adsorbent and catalyst and a reaction calorimeter containing a suspension of the same solid were used. To describe the development of concentration profiles in the fixed-bed reactor and of heat fluxes due to reaction in the reaction calorimeter, a uniform mathematical model was used as described below. 2.1. Model of the Chromatographic Fixed-Bed Reactor. Standard models of fixed-bed reactors are based on the classical conservation equations.16,17 Because incompressible liquid reactants are considered and relatively small heat effects occur during the coupled reaction and separation processes, only mass balances were considered to describe the fixed bed. The model summarized below is based on further assumptions as follows: (i) No radial concentration and temperature gradients occur in the reactor. (ii) The loading

10.1021/ie0307840 CCC: $27.50 © 2004 American Chemical Society Published on Web 04/14/2004

4692 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004

profiles of the relatively small solid particles can be described using an average value. (iii) Intraparticle transport is quantified using a corresponding linear driving force expression. With these assumptions, the following component mass balance equations can be formulated.

Liquid phase 

∂ci ∂ci ∂2ci ) -u + Dax 2 + νirhom(cj) + ∂t ∂x ∂x (1 - )βi[qav,i - q/i (cj)]

i ) 1, ..., Nc (1)

In eq 5, Dap stands for an apparent dispersion coefficient describing as a lumped parameter all effects causing band broadening. The equation states that the concentrations of all components in the liquid and solid phases are permanently in equilibrium throughout the entire column. If the corresponding distribution equilibria are linear, the mass balance equation can be furthermore simplified through the introduction of the equilibrium constants Ki (with q/i ) Kici)

[

-u

Solid phase ∂qav,i j av) ) (1 - )νirhet(cj,q (1 - ) ∂t (1 - )βi[qav,i - q/i (cj)]

i ) 1, ..., Nc (2)

In the above equations, ci and qav,i are the liquid-phase concentration and the average loading, respectively, of component i; rhom and rhet are the reaction rates of the homogeneously and heterogeneously catalyzed reactions, respectively;  is the volume fraction of the liquid phase (porosity); βi is the internal mass-transfer coefficient of component i; q/i (cj) is the loading of component i in the solid phase in equilibrium with all liquid-phase concentrations; νi is the stoichiometric coefficient of component i; u is the linear velocity in the column, Dax is an axial dispersion coefficient; and Nc is the number of components involved. To solve this system of mass balance equations, appropriate initial and boundary conditions have to be specified. Assuming that the column is not preloaded, the initial conditions are

ci(x,t)0) ) 0, qav,i(x,t)0) ) 0

i ) 1, ..., Nc

(3)

The standard Danckwerts boundary conditions for a rectangular injection profile are16

{

|

Dax ∂c for 0 e t e tinj u ∂x x)0,t ci(x ) 0,t) ) Dax ∂c for t > tinj u ∂x x)0,t V inj (4a) with tinj ) π u d2  4 cinj i -

|

|

∂c )0 ∂x x)L,t

i ) 1, ..., Nc

(4b)

inj is where cinj i represents the injection concentrations, t the injection time, V inj is the injection volume, L is the reactor length, and d is the reactor diameter. This heterogeneous two-phase model can be transformed into a simpler pseudohomogeneous model if the βi parameters are large. Then, eqs 1 and 2 can be lumped together to give



(

∂ci 1- ) 1+ Ki ∂t 

∂qav,i(cj) ∂ci ∂2ci ∂ci + (1 - ) ) -u + Dap 2 + ∂t ∂t ∂x ∂x νirhom(cj) + (1 - )νirhet(cj)

i ) 1, ..., Nc (5)

)

-1

×

]

∂ci ∂2ci 1 -  het + Dap 2 + νirhom(cj) + ν r (cj) ∂x  i ∂x i ) 1, ..., Nc (6)

2.2. Model of the Reaction Calorimeter. The mass balances for a reaction calorimeter are based on the same differential balances given above for the fixed-bed reactor (eqs 1, 2, 5, and 6). For batch operation, only u is set to 0, and perfect mixing is assumed (i.e., Dax or Dap is large, an assumption that is approximately fulfilled during the experiments described below).

Liquid-phase mass balance 

dci ) νirhom(cj) + (1 - )βi[qav,i - q/i (cj)] dt i ) 1, ..., Nc (7)

Solid-phase mass balance (1 - )

dqav,i(ci) j av) ) (1 - )νirhet(cj,q dt i ) 1, ..., Nc (8) (1 - )βi[qav,i - q/i (cj)]

Initial conditions ci(t)0) ) ci0 and qav,i(t ) 0) ) q/i (ci0)

i ) 1, ..., Nc (9)

Assuming that the internal mass transfer is rapid (large βi values), eqs 7 and 8 can also be lumped together to give the mass balance of the pseudohomogeneous model



dqav,i(cj) dci + (1 - ) ) νirhom(cj) + dt dt i ) 1, ..., Nc (10) (1 - )νirhet(cj)

If, in addition, all of the functions qav,i(cj) are linear, the following simple system of ordinary equations results

dci 1 -  -1 hom 1 -  het ) 1+ Ki νir (cj) + ν r (cj) dt   i i ) 1, ..., Nc (11)

(

) [

]

Obviously, the key to analyzing calorimetric experiments is the energy balance, which contains the rates of heat evolution or consumption due to reaction. Assuming isothermal conditions and neglecting heat effects due to adsorption, stirring, and uncontrolled losses, the measurable time dependence of the heat flux over the calorimeter wall, Q˙ wall, is directly and linearly

Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4693

related to the rates of reactions. Q˙ wall is positive here for endothermal reactions and negative for exothermal reactions. The simplified energy balance of a batch calorimeter operated under isothermal conditions as in this work is hom Q˙ wall ) |Q˙ tot (cj)∆Hhom + chem| ) VRr r

j av(cj)]∆Hhet (12) (1 - )VRrhet[cj,q r where VR is the reactor volume and the ∆Hr represents the enthalpy of a given reaction. 2.3. Numerical Solution. To solve the balance equations of the chromatographic reactor and the reaction calorimeter, the software Presto18 was employed. This software provides efficient ODE and PDE solvers in combination with robust tools for parameter estimation. It further allows for the flexible incorporation of different kinetic models and the convenient input and analysis of various types of primary experimental data. 2.4. Simplified Kinetics of Reversible Hydrolysis Reactions. Reversible hydrolysis reactions can generally be described by eq 13, in which A stands for the esters, B for water (W), C for the acids, and D for the alcohols

A+B/C+D

(13)

In this work, conventional laws for reversible reactions were used to describe the rates. Concentrations or loadings were applied to formulate the driving forces for the rates of the homogeneously and heterogeneously catalyzed reactions. For the homogeneous hydrolysis reactions, the following expression was assumed

(

rhom(cj) ) khom cAcB -

cCcD Khom eq

)

(14)

Because water was always in excess in the experiments performed and its concentration did not change significantly, the following rate equation was used to describe the heterogeneously catalyzed reaction

(

j av) ) khet qav,AcB rhet(cj,q

qav,Cqav,D Khet eq

)

(15)

Obviously, these rate laws simplify the complex situations significantly. A more detailed description would require the consideration of activities and the explicit incorporation of the actual surface concentrations of water. 2.5. Distribution Equilibria. In agreement with previous results12 and for the sake of simplicity, the equilibrium functions used in this work were assumed to be decoupled and linear, i.e.

q/i ) Kici

i ) 1, ..., Nc

(16)

Using this assumption for eq 15, the following expression should hold under equilibrium conditions

rhet eq

(

het

)0)k

KAcAcB -

)

KCcCKDcD Khet eq

(17)

Thus, to ensure that the reactions are simultaneously in equilibrium in both phases, the following two relationships must hold

Khom eq )

cCcD cAcB

hom Khet eq ) Keq

(18)

K CK D KA

(19)

3. Experimental Section 3.1. Model Reactions. The heterogeneously catalyzed reversible hydrolysis reactions of four carboxylic esters, namely, methyl formate (MF), methyl acetate (MA), ethyl formate (EF), and ethyl acetate (EA), producing methanol (M), ethanol (E), formic acid (FA), and acetic acid (AA), respectively, were studied. The stoichiometric equations of the hydrolysis reactions are in the form of eq 13. 3.2. Catalyst. Two batches of the strongly acidic cation-exchange resin Dowex 50W-X8 (Dow Chemical Company) were used. This resin is based on a microporous styrene-divinylbenzene copolymer. It acts as both adsorbent and catalyst. The difference between the two batches was essentially the range of particle sizes. The catalyst with the smaller particle size (Cat1) has already been used extensively in other investigations.7,12 The second (Cat2) was purchased prior to the study discussed here. Several physical and chemical properties of the catalysts are listed in Table 1. 3.3. Equipment. 3.3.1. Fixed-Bed Reactors. Two empty standard HPLC columns (both d ) 0.8 cm, L ) 25 cm) were packed with the two catalysts (column 1 with Cat1, column 2 with Cat2) by an HPLC supplier (VDS Optilab, Berlin) using a slurry technique. The columns were placed into a double-jacketed glass tube allowing for control of the temperature. Conventional HPLC equipment (Knauer, Berlin) was used to carry out experiments for different conditions. Temperature, flow rate, feed concentration, and injection volume were varied. Water was continuously pumped into the columns and thus acted, in addition to being a reactant, as the mobile phase for elution. A degasser (Jour X-Act) was placed before the columns to remove air/oxygen from the mobile phase. Elution profiles were recorded with a refractive index detector (RI, Knauer K-2300) and a UV-vis detector (Hitachi L-7420). In preliminary experiments, it was determined that these detectors behave linearly in the concentration range covered, and calibration factors for all components were determined. 3.3.2. Reaction Calorimeter. To quantify heat effects related to the course of the reactions, a commercially available reaction calorimeter was used (RC1, Mettler-Toledo). The double-jacketed reactor (AP01) allowed for the analysis of volumes between 0.5 and 2 L. The stirrer speed could be varied between 30 and 850 rpm. Both the jacket temperature, Tj, and the temperature of the reactor contents, Tr, could be measured precisely. This allowed for the calculation of the heat flux through the reactor wall. In this study, the isotherTable 1. Physical and Chemical Properties of the Two Catalysts catalyst characteristic

Cat1

particle size, µm type active group matrix ionic form density, kg/m3 feature

32-45

Cat2

38-75 Dowex 50W-X8 sulfonic acid styrene-divinylbenzene H+ 800 old (5 years in use) new (2003)

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mal mode was applied to perform experiments, i.e., Tr was kept constant. 3.4. Procedures. 3.4.1. Characterization of the Catalysts. In addition to the experiments performed in the chromatographic fixed-bed reactor and in the reaction calorimeter, selected preliminary experiments were performed to characterize the swelling behavior and acidity of the catalysts. The dry resins swell when they come into contact with liquids until an equilibrium is reached.19 The swelling ratio, i.e., the volume ratio of the swollen resin at 0 equilibrium (Veq Re) to the dry resin (VRe), depends on the nature of the liquid. In this work, the swelling ratios of the resins were estimated at 25 °C for all single components (MF, AF, MA, EA, W, FA, AA, M, and E). To this end, the resin was kept in contact with each of the liquid components until no further volume change could be detected. This was usually achieved after only a few minutes. Nevertheless, the final volume of the swollen resin was measured the next day after the resin had been separated from the liquid phase by centrifugation. To compare the acidities of Cat1 and Cat2, the amounts of sulfonic acid groups per unit mass of the resins were quantified by titrating approximately 0.15 g of each of the catalysts with sodium hydroxide solution (0.1 N). 3.4.2. Estimation of Reaction Equilibrium Constants in the Batch Reactor. The estimation of reaction equilibrium constants was based on performing batch experiments in the reaction calorimeter. The compositions of the reaction mixtures at equilibrium were determined using a GC system equipped with a polyethylenglycol capillary column (25.0 m × 320 µm × 0.25 µm) and a thermal conductivity detector. Helium was used as the carrier gas. The reaction equilibrium constants of the homogeneous reaction, Khom eq , were calculated from eq 18. The equilibrium constants of the heterogeneous reaction, Khet eq , were derived later from and the constants Ki describing the distribution Khom eq equilibria (section 4.3) using eq 19. 3.4.3. Chromatographic Experiments in the Fixed Beds. To apply eq 6 in the analysis of elution profiles, several free parameters need to be determined. Total Porosity (E). The total porosities of the two columns were estimated from the retention times of the nonretained component Dextran Blue at 25 °C, to, the corresponding volumetric flow rates, V˙ , and the volume of the column, Vcol, according to

 ) V˙ to/Vcol

(20)

Equilibrium Constants (Ki). To determine the equilibrium constants, Ki, pulse experiments were carried out in an excess of water at 25 and 30 °C. These constants can be calculated using the following equation

Ki )

( )( ) tRi  -1 1 -  to

(21)

To determine whether the isotherms are linear, i.e., whether the retention times, tRi, are independent of concentration, the amounts injected were varied. For the reactive esters, the flow rate was also varied to change the conversion and, thereby, to distinguish correctly between the ester peaks and the products peaks.

Table 2. Overview of All Chromatographic Experiments Performeda run

reactant

temperature (°C)

flow rate (mL/min)

1A 1B 2 3A 3B

MF, EF MA, EA MF, MA, EF, EA MF, EF MA, EA

25 25 25/35/45/55 55 55

0.3, 0.5, 1.0, 1.5, 4 0.1, 0.3, 0.5, 1.0, 1.5, 4 0.75 0.5, 1.0, 1.5, 2 0.1, 0.3, 0.5, 1.5

a

Always for both columns.

Dispersion Coefficient (Dap). The apparent dispersion coefficient (Dap, eq 5) can be estimated from the number of theoretical plates in the columns, N; the linear velocity, u; and the length of the fixed bed, L16

Dap )

uL 2N

(22)

For symmetrical (Gaussian) peaks, N can be calculated from the retention times, tR, and the peak width at halfheight, w0.5, using20

N ≈ 5.54(tR/w0.5)2

(23)

Elution Experiments. In this work, the feed concentrations of the four esters were varied between 0.1 and 0.5 mol/L. The injection volumes were typically 100 µL. In each experiment, the flow rate and the temperature were kept constant. Systematic experiments were conducted over a broad range of operating conditions as summarized in Table 2. 3.4.4. Calorimetric Experiments Using Catalyst Suspensions. Preliminary Experiments. In preliminary experiments, a semibatch mode was applied to estimate the extent of heat effects due to the mixing of water and esters in distinction from the heat effects caused by the chemical reactions. To this end, water and the catalyst were initially charged into the reactor at ambient conditions, and a temperature ramp was then applied to set the desired initial temperature. Approximately 15 min later, a certain amount of ester was added to the reactor using a dosing pump at a constant flow rate for about 4 min. A constant stirring rate of 200 rpm was employed throughout these experiments. Systematic Measurements. When a reactant is dosed in the semibatch mode, a heat flux due to mixing and reaction is induced. Splitting this overall flux into its individual contributions is complicated. Thus, in the main part of this study, batch reactions were considered to analyze the effect of the reaction separately. For these reactions, an initial sample was taken approximately 5 min after the ester dosing was finished (long enough to ensure that mixing was complete) and analyzed off-line. This time was used as the starting time of a batch run. A second sample was taken when the reaction was completely finished, i.e., when the heat flux was zero. The samples were analyzed by GC (see section 3.4.2). In this way, batch hydrolysis reactions were conducted in the calorimeter at various temperatures and feed concentrations using suspensions of both catalysts. 4. Results and Discussion 4.1. Catalyst Characterization. The swelling ratios obtained for all single components are listed in Table 3. From these data, it can be concluded that water has a higher affinity toward the resin than the other

Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4695 Table 3. Swelling Ratios of the Resins in Different Reactants swelling ratioa

a

component

Cat1

Cat2

W E M FA AA MA EA MF EF

3.08 2.56 2.42 2.22 1.78 1.79 1.78 1.49 1.37

2.89 2.38 2.27 2.06 1.79 1.67 1.67 1.42 1.38

0 Swelling ratio ) Veq Re/VRe.

Table 4. Reaction Equilibrium Constants at 25 °C (Eq 18) reactant

Khom eq

MF EF MA EA

0.22 0.38 0.14 0.33

components. This is due to the strong polarity inside the resin created by the sulfonic acid groups, which attract water most strongly, followed by the alcohols, acids, and esters. It can be also seen from the data that the swelling ratios of the two catalysts are similar. Cat1 seems to swell slightly more than Cat2. The corresponding sulfonic acid group concentrations of Cat1 and Cat2 were found by titration to be 3.9 × 10-3 and 4.8 × 10-3 equiv/g. It should be also noted that the swelling rates of the resins were found to be rather high. It took only seconds to minutes for the resins to reach their equilibrium volumes. 4.2. Reaction Equilibrium Constants. In the experiments, it was found that equilibrium was reached overnight for all cases studied. The reaction equilibrium constants determined at 25 °C from the final compositions of the batch runs using eq 18 are reported in Table 4. Obviously, the formation of methyl acetate is least favorable, and the formation of ethyl formate is most favorable. 4.3. Fixed-Bed Reactor. Porosities. The total porosities of the columns depend on particle size of the catalyst and the packing pressure. According to the results of the swelling experiments, they should also depend on the composition of the liquid phase. Because water is present in all experiments in excess,  was determined only for the column equilibrated with pure water. The corresponding porosities of column 1 filled with Cat1 and column 2 filled with Cat2 were estimated using eq 20 to be  ) 0.240 and  ) 0.328, respectively. Distribution Equilibria. In Figure 1 are shown the elution profiles for various injection concentrations of FA, AA, M, and E with Cat1. For each component, rather symmetrical peaks were observed at the same specific retention times. This indicates that the linear equilibrium model (eq 16) is adequate. Because of the occurrence of the hydrolysis reactions, it was found to be difficult to get a single peak for the esters (especially for MF). For this reason, the pure esters had to be injected into the columns with an appropriate injection volume at a sufficiently high flow rate so that a significant amount was not converted. Table 5 summarizes the determined equilibrium constants for Cat1 and Cat2 calculated using eq 21. The elution order of the components in water is FA, AA, M, E, MF, EF, MA, and EA. Most of the equilibrium constant values (except

Figure 1. Elution profiles for various injection concentrations (0.1-0.5 mol/L) of FA (solid), AA (dashed), M (dotted), and E (dashed-dotted) (Cat1, flow rate ) 0.75 mL/min, injection volume ) 100 µL, temperature ) 25 °C).

Figure 2. Influence of the flow rate on the number of theoretical plates N of column 1 filled with Cat1 (0) and column 2 filled with Cat2 (4) (injection volume ) 100 µL of formic acid, concentration ) 0.5 mol/L, temperature ) 25 °C). Table 5. Distribution Equilibrium Constants Ki at 25 °C component

Cat1

Cat2

FA AA M E MF EF MA EA

0.432 (0.476)12 0.520 0.628 (0.693)12 0.736 0.850 (0.913)12 0.995 1.085 1.327

0.380 0.476 (0.462)a 0.673 (0.663)a 0.781 ∼0.65b 0.819 1.009 (0.910)a 1.219

a At 30 °C. b Uncertain value due to difficulties in identifying the corresponding peak.

those of the alcohols) are slightly smaller for Cat2 than for Cat1 (Table 5). Because of differences in the surface characteristics between the two catalyst batches, there are differences in the elution orders and in the individual equilibrium constants. For the alcohols, acids, and esters, the elution orders correspond to the order of molecular weights. In a previous study performed with the same batch of Cat1 some years ago,12 a smaller column (d ) 0.46 cm, L ) 25 cm,  ) 0.313) was used to determine constants describing the distribution equilibria for MF, FA, and M. The obtained values were found to be slightly larger and are also included in Table 5 for comparison. Plate Numbers. The number of theoretical plates (N) and the corresponding apparent dispersion coefficient (Dap) mainly depend on the flow rate. In the investigated

4696 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004

Figure 3. Comparison of hydrolysis reactions using Cat1 (solid) and Cat2 (dashed): (a) MF, (b) EF, (c) MA, and (d) EA (flow rate ) 0.3 mL/min, injection volume ) 100 µL, concentration ) 0.5 mol/L, temperature ) 25 °C).

Figure 4. Influence of the flow rate (0.3-1.5 mL/min) on the hydrolysis reactions of (a) MF, (b) EF, (c) MA, and (d) EA (Cat1, injection volume ) 100 µL, concentration ) 0.5 mol/L, temperature ) 25 °C).

range of flow rates (from 0.5 to 4.0 mL/min), N was estimated essentially from the variances of FA pulse

responses recorded at 25 °C. Figure 2 shows that N decreases with increasing flow rate. Because of the

Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4697

Figure 5. Influence of the temperature on the hydrolysis reactions of (a) MF, (b) EF, (c) MA, and (d) EA at temperatures 25 °C (s), 35 °C (4), 45 °C (- - -), and 55 °C (0) (Cat1, flow rate ) 0.75 mL/min, injection volume ) 100 µL, concentration ) 0.5 mol/L).

smaller particle size, the number of theoretical plates in column 1 is much higher than that in column 2 at the same flow rate. Elution Profiles for the Chromatographic Reactor. In Figure 3a-d are shown typical elution profiles for columns 1 and 2 at 25 °C and a flow rate of 0.3 mL/ min. In all cases, the same amount of ester was injected. Although the corresponding shapes of the elution profiles are similar for the two columns, because of its larger plate numbers, column 1 gives sharper peaks than column 2. In agreement with the determined equilibrium constants, there is a difference between the retention times of the same component eluting from column 1 and from column 2 (e.g., Figure 3a). Because both reactant peaks disappeared for MF and EF (Figure 3a and b, respectively), it can be concluded that the corresponding hydrolysis reactions are faster than the hydrolysis reactions of MA and EA, where reactant peaks are still visible (Figure 3c and 3d, respectively). The conversions of the esters depend strongly on the contact times. The influence of the flow rate on the course of the hydrolysis reactions is illustrated in Figure 4. Again, the absence of MF and EF in the chromatograms shown in Figure 4a and b indicates that these esters are converted almost completely throughout the range of flow rates studied (0.3-1.5 mL/min), whereas MA and EA still elute from the column even at the lowest flow rate. This figure also indicates that the resolution is significantly improved when the flow rate is decreased (exploiting larger N). Very complex elution profiles are shown in Figure 4c and 4d (particularly for the lower flow rates). The shapes of these profiles are discussed later in this paper using the model developed. To estimate the influence of temperature, additional experiments were performed. For comparison, the mea-

sured elution profiles are presented in two ways. Elution profiles of the same component at different temperatures are shown in Figure 5. Elution profiles of different components at the same temperature are shown in Figure 6. Although the influence of temperature on column efficiency (N) was not studied quantitatively, an effect can clearly be observed by comparing chromatograms a and b in Figure 5. The peak widths are reduced considerably as the temperature is increased. This means that the number of theoretical plates is augmented and the resolution is improved. Apparently and in contrast, there is no severe effect of temperature on retention time in the range studied. In Figure 6b-d, the peaks of FA produced by the hydrolysis of MF and EF at 35, 45, and 55 °C, respectively, have the same retention time and area, whereas differences can be seen in Figure 6a (25 °C). This means that the conversions of MF and EF at 25 °C were different and not complete. In Figure 6d, the reactants MA and EA still exist and elute from the column. This indicates again that the hydrolysis reactions of MA and EA are the slowest among the four reactions studied. Simulation of Elution Profiles and Estimation of Reaction Rate Constants. To determine the reaction rate constants, khet, an attempt was made to match simulated and measured elution profiles. The simulations of detector signals were based on the concentration profiles of the components calculated by eq 6 and the calibration factors. Because of the dense packing of the columns, it was assumed in the optimization study that the homogeneous reaction does not play an important role in the chromatographic reactor, so this reaction was neglected. The input parameters of the model were the porosity, the equilibrium constants, the linear velocity, and the corresponding plate number. Thus, only the rate

4698 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004

Figure 6. Comparison of elution profiles for the hydrolysis reactions of MF (0), EF (- - -), MA (4), and EA (s) at the temperatures (a) 25, (b) 35, (c) 45, and (d) 55 °C (Cat1, flow rate ) 0.75 mL/min, injection volume ) 100 µL, concentration ) 0.5 mol/L). Table 6. Reaction Rate Constants at 25 °C 103 khet [L/(mol min)] reactant

Cat1

Cat2

MF EF MA EA

14.0 7.26 0.38 0.36

21.4 13.6 0.76 0.65

constant of the specific heterogeneously catalyzed reaction, khet, was a free parameter. The optimizer based on standard stochastic algorithms provided by Presto18 was used to estimate this parameter. The reaction rate constants obtained from the elution profiles for the four cases measured at 25 °C and a flow rate of 0.75 mL/min are given for both catalysts in Table 6. It was checked that these values also describe elution profiles at other flow rates after specification of the corresponding N value. The obtained values of khet indicate that the reactivities of the esters decrease in the order MF, EF, MA, EA and the hydrolyses of all of the esters are faster using Cat2 than using Cat1. This is in agreement with the different amounts of sulfonic acid groups on the two catalysts. An example of simulating the hydrolysis of MF in column 2 with the obtained khet MF value is given in Figure 7a. The results shown are for simulations performed for three different flow rates. In addition, the simulations were also performed with another value of khet MF estimated from an experiment performed in the reaction calorimeter. Similar agreement between simulations and experiments was found also for other reactions and conditions. To further test the model, the obtained value of khet MA ) 0.38 × 10-3 L/(mol min) (Table 6) was used to simulate the more complex elution profile for the hydrolysis of

MA mentioned above (flow rate ) 0.3 mL/min, T ) 25 °C, column 1, Figure 4c). Figure 7b shows the corresponding simulation results for the individual components in addition to the measured total profile. Because the profiles of AA and M overlap and do not have a Gaussian shape, a complex overall elution profile results. The good agreement between the measured and simulated detector signals confirms that the applied assumptions and model are relatively reliable. 4.4. Reaction Calorimetry. Measured Heat Fluxes. Figure 8 shows a typical heat flux measured during the methyl formate hydrolysis in semibatch mode. The complex part in the first few minutes of the profile is due to the joint effects of mixing and initial reaction. It can be seen that the contribution of the mixing effect is significant and complicated. After about 10 min, the heat flux is caused exclusively by chemical reaction. All subsequent experiments were analyzed only as batch runs after an initial sample had been taken. Batch hydrolysis reactions of the four esters were conducted systematically at various feed concentrations and temperatures with Cat1 and Cat2. From the experimental results, a severe limitation of the applicability of the available reaction calorimeter was found. For the slower hydrolysis reactions of ethyl formate and ethyl acetate, the reaction calorimeter could not precisely detect the behavior of the heat flux. This is due to several joint effects: relatively low reaction enthalpies, low reaction rates, and limited sensitivity of the reaction calorimeter. However, the difference in reaction kinetics between hydrolysis reactions of methyl formate and methyl acetate could be detected properly, as shown in Figure 9a. It is apparent that these hydrolysis reactions are endothermal. It is further

Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4699

Figure 7. (a) Comparison of response detector signals for MF: -3 L/(mol min) (0) measured, simulated using (s) khet MF ) 14.0 × 10 determined from the shape of the elution profiles and (- - -) khet MF ) 10.6 × 10-3 L/(mol min) determined from the course of heat fluxes (Table 7) [Cat1; flow rate ) 0.5 (N ) 435), 0.75 (N ) 355, used to fit the rate constant), and 1.0 mL/min (N ) 330); injection volume ) 100 µL; concentration ) 0.5 mol/L; temperature ) 25 °C). (b) Comparison of response detector signals for MA: (0) measured, -3 L/(mol min) (Cat1, (s) sum simulated using khet MA ) 0.38 × 10 flow rate ) 0.3 mL/min, N ) 990, injection volume ) 100 µL, concentration ) 0.5 mol/L, temperature ) 25 °C; compare Figure 4c).

Figure 9. Measured heat fluxes of ester hydrolysis reactions: (a) MF (solid) and MA (dashed), Cat2, T ) 25 °C; (b) MF, Cat1, T ) 25 °C, c0MF ) 1.42 mol/L (solid) and c0MF ) 2.66 mol/L (dashed); (c) MA, Cat2, T ) 25 °C (solid) and T ) 30 °C (dashed).

Figure 8. Heat flux for the hydrolysis of MF performed in semibatch mode (Cat1, T ) 25 °C).

evident that the heat consumed by methyl formate hydrolysis is significantly higher than that consumed by the hydrolysis of MA for the same feed concentration, temperature, and catalyst. Figure 9b shows the heat fluxes for the hydrolysis of MF at 25 °C with Cat1 and different feed concentrations.

It is obvious that the higher the initial ester concentration, the higher the heat consumed by the reaction. The hydrolysis of MA was studied with Cat2. Figure 9c compares the heat fluxes obtained at 25 and 30 °C. From this figure, the typical effect of temperature on the reaction kinetics can be clearly observed. However, as can also be seen, there is considerable noise in the measurements, indicating that the sensitivity limit of the calorimeter is reached. Simulation of Heat Fluxes and Estimation of Reaction Rate Constants. Reaction rate constants of the two hydrolysis reactions studied in the calorimeter were quantified by applying the heterogeneous model (eqs 7 and 8) and the pseudohomogeneous model (eq 11)

4700 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004

Figure 10. Comparisons of the simulated (lines) and measured (symbols) heat fluxes. (a) MF, T ) 25 °C, c0MF ) 2.0 mol/L, Cat1: (solid) eqs 7 and 8, β ) 0.01 min-1, khet ) 10.5 × 10-3, khom ) 4.68 × 10-3 L/(mol min); (dashed) eq 11, khet ) 10.6 × 10-3, khom ) 4.82 × 10-3 L/(mol min). (b) MA, T ) 25 °C, Cat2, khet ) 0.69 × 10-3, khom ) 0.11 × 10-3 L/(mol min), eq 11. (c) MA, T ) 30 °C, Cat2, khet ) 1.34 × 10-3, khom ) 0.24 × 10-3 L/(mol min), eq 11. (d) MF, T ) 25 °C, c0MF ) 1.42 mol/L, Cat1: (solid) khet ) 12.0 × 10-3 and khom ) 5.13 × 10-3 L/(mol min) (determined from the course of the heat fluxes, eq 11); (dotted) khet ) 12.0 × 10-3 and khom ) 0; (dashed) khet ) 14.0 × 10-3 L/(mol min) and khom ) 0 (determined from the shape of the elution profiles). Table 7. Selected Results for the Hydrolysis Reactions of Methyl Formate and Methyl Acetate Conducted in the Reaction Calorimeter Methyl Formate Hydrolysis with Cat1 run

T (°C)

c0MF (mol/L)

c0W (mol/L)

ceq MF (mol/L)

ceq W (mol/L)

ceq M,FA (mol/L)

VR (L)



Iwalla (J)

∆Hrb (J/mol)

103 khet [L/(mol min)]

103 khom [L/(mol min)]

1 2 3

25 25 25

1.42 2.00 2.66

49.77 47.08 44.86

0.24 0.46 0.75

48.59 45.54 42.95

1.59 2.02 2.55

1.11 1.17 1.22

0.96 0.96 0.96

3970 5750 7080

3030 3190 3040

12.0 (14.0)c 10.6 10.5

5.13 4.82 4.55

run

T (°C)

c0MA

(mol/L)

c0W

(mol/L)

ceq MA

(mol/L)

ceq W (mol/L)

eq cM,AA (mol/L)

VR (L)



Iwalla (J)

∆Hrb (J/mol)

103 khet [L/(mol min)]

103 khom [L/(mol min)]

4 5

25 30

2.83 2.82

43.82 43.83

0.73 0.73

41.72 41.74

2.10 2.09

1.20 1.01

0.92 0.91

8300 6870

3290 3250

0.69 (0.76)c 1.34

0.11 0.24

Methyl Acetate Hydrolysis with Cat2

a

0 eq Iwall ) ∫Q˙ wall(t) dt. b ∆Hr ) Iwall/(cester - cester )VR. c Quantified from elution profiles, Table 6.

in combination with the energy balance (eq 12). In addition to the experimentally measured heat fluxes, Q˙ wall, the input parameters of the models were the and Khet reaction equilibrium constants (Khom eq eq ), the distribution equilibrium constants (Ki), the initial liquidphase composition, the reaction enthalpies (here, and ∆Hhet were taken identically from the ∆Hhom r r integrals of the heat fluxes given in Table 7), and the porosity  (which was between 0.91 and 0.96 in the calorimeter). The parameters to be determined were the rate constants khom and khet and, in the case of the heterogeneous model, the internal mass-transfer coefficients βi. Again, the optimizer provided by Presto was used to estimate these parameters.

In the heterogeneous model, the mass-transfer coefficicients βi were assumed to be equal for all components. For the runs performed, a value of β ) 0.01 min-1 was estimated to be most probable. For values of β g 0.25 min-1, no effect of the mass-transfer resistance remained, and the results were identical to those obtained using the pseudohomogeneous model for the same rate constants. Figure 10a shows the comparison of simulated heat fluxes using the two models. It is obvious that the influence of β is only very small. Consequently, as in the analysis of the fixed-bed reactor experiments, in further calculations, only the pseudohomogeneous model (β ) ∞) was applied to quantify the reaction rate constants.

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An overview of the obtained reaction enthalpies and reaction rate constants is given in Table 7. Figure 10b and 10c shows comparisons of the measured and the simulated heat fluxes for hydrolysis of MA at (a) 25 and (b) 30 °C with Cat2. It can be seen that the simulation is in slightly better agreement with the measured heat fluxes for the reaction at 30 °C (Figure 10c) than 25 °C (Figure 10b). Figure 10d shows a comparison of the measured and simulated heat fluxes for the hydrolysis of MF at 25 °C with Cat1 performed in the calorimeter. In addition, a simulation of this run was also performed with the khet MF value determined from the analysis of the chromatograms measured in the fixed-bed reactor. From this figure and the results in Table 7, it can be observed that the rate constants quantified from both the chromatograms and the heat fluxes are in relatively good agreement. This was also demonstrated already earlier in Figure 7a. Because of the higher liquid-phase fraction, the contribution of the homogeneous reaction is more significant in the calorimetric reactor than in the well-packed fixed-bed reactor with the smaller porosity . This is also visible in Figure 10d, where the contribution of homogeneous reaction is eliminated in one of the curves by setting khom ) 0. 5. Conclusions This work enlarges the database regarding heterogeneously catalyzed hydrolysis reactions of esters. These reactions were studied in a chromatographic reactor and in a reaction calorimeter. The hydrolysis reactions of four esters (methyl formate, methyl acetate, ethyl formate, and ethyl acetate) were chosen as model systems. Simplified mathematical models describing the essential features of both reactors were applied. Distribution equilibria were quantified by analyzing retention times in fixed beds of acidic ion-exchange resins. Reaction rate constants were quantified from elution profiles and heat fluxes. The influence of temperature, feed composition, and flow rate of the mobile phase (for the chromatographic reactor) on the reactor performances was also studied. Regarding the quantification of reaction rate constants, this work demonstrated that heat flux signals measured with reaction calorimeters can provide a rapid method for determining rate constants of simple reactions, provided that the sensitivity of the device is sufficient. The results obtained further reveal interesting tendencies concerning the changes of reaction rate constants and reaction and distribution equilibrium constants relevant for the four hydrolysis reactions studied. The presented data could prove useful in the design of more complex multicolumn systems. Acknowledgment The financial support provided by the state of SaxonyAnhalt (Germany), the Vietnamese government, Schering AG (Berlin), and Fonds der Chemischen Industrie is gratefully acknowledged. Notation c ) liquid-phase concentration (mol/L) d ) fixed-bed diameter (cm) Dax ) axial dispersion coefficient (cm2/min) Dap ) apparent dispersion coefficient ∆H ) reaction enthalpy (J/mol) k ) reaction rate constant [L/(mol min)]

Keq ) reaction equilibrium constant K ) constant describing the distribution equilibrium L ) fixed-bed length (cm) N ) number of theoretical plates Nc ) number of components qav ) average loading (mol/L) q* ) equilibrium loading (mol/L) Q˙ wall ) heat flux over the calorimeter wall (J/s) tot ) overall heat flux due to reaction (J/s) Q˙ chem r ) reaction rate [mol/(L min)] t ) time coordinate (min) T ) temperature (°C) tR ) retention time (min) u ) linear velocity (cm/min) V˙ ) volumetric flow rate (mL/min) 3 Veq Re ) volume of resin at equilibrium (cm ) V0Re ) volume of dry resin (cm3) Vcol ) column volume (Vcol ) π/4d2L) (cm3) VR ) reactor volume (L) VRe ) volume of resin (cm3) x ) axial coordinate (cm) Greek Letters β ) internal mass-transfer coefficient (min-1)  ) porosity or liquid-phase fraction ν ) stoichiometric coefficient Superscripts and Subscripts ap ) apparent av ) average ax ) axial c ) component cal ) calibration Cat ) catalyst col ) column eq or * ) equilibrium het ) heterogeneous hom ) homogeneous i ) ith component inj ) injection tot ) total 0 ) initial

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Received for review October 2, 2003 Revised manuscript received February 2, 2004 Accepted February 3, 2004 IE0307840