Esterification of acrylic acid with methanol by reactive chromatography: Experiments and simulations

Esterification of acrylic acid with methanol by reactive chromatography: Experiments and simulations

Chemical Engineering Science 61 (2006) 5296 – 5306 www.elsevier.com/locate/ces Esterification of acrylic acid with methanol by reactive chromatography...

448KB Sizes 28 Downloads 94 Views

Chemical Engineering Science 61 (2006) 5296 – 5306 www.elsevier.com/locate/ces

Esterification of acrylic acid with methanol by reactive chromatography: Experiments and simulations Guido Ströhlein a , Yolanda Assunção a , Nikhil Dube b , André Bardow c , Marco Mazzotti d , Massimo Morbidelli a,∗ a Department of Chemistry and Applied Biosciences, Institute for Chemical and Bioengineering, ETH Zurich, Hönggerberg, HCI, 8093 Zurich, Switzerland b Indian Institute of Technology Kanpur, Kanpur, India c Institut für Polymere, ETH Zurich, Hönggerberg, HCI, 8093 Zurich, Switzerland d Institute of Process Engineering, ETH Zurich, Sonneggstrasse 3, CH-8092 Zurich, Switzerland

Received 18 November 2005; received in revised form 22 March 2006; accepted 5 April 2006 Available online 21 April 2006

Abstract The esterification of acrylic acid with methanol using Amberlyst 15 as a stationary phase has been investigated using a chromatographic reactor. Several experimental runs at various operating conditions have been conducted on a batch column. A classical reactive chromatography model including lumped kinetics, a linear driving force transport model and a heterogeneous kinetic model for the catalytic reaction has been developed. The additional dispersion of concentration fronts due to density gradient effects has been accounted for in the model. The model parameters have been determined in a fast and reliable way by directly fitting the batch column experiments. In general, a good agreement between experimental and calculated results is obtained. The evaluation of the covariance of the fitted model parameters reveals important insights about the system behavior. Based on the detailed batch column model, a complete model of a simulated-moving-bed reactor has been implemented and its optimal point of operation for the synthesis of methyl acrylate from acrylic acid has been determined. Particularly when considering the low-operating temperature, we can regard this process as a possible competition for current technologies. 䉷 2006 Elsevier Ltd. All rights reserved. Keywords: Adsorption; Chromatography; Dynamic simulation; Parameter identification; Simulated-moving-bed; Catalysis

1. Introduction Acrylic esters are versatile monomers and widely used for the production of coatings, adhesives, textiles and plastics. A conventional acrylic ester production step includes several distillation columns: a column reactor, a water removal column, an azeotropic column and a column to separate the product from the heavy by-products. In addition, an inhibitor has to be used in the whole process to minimize polymerization of acrylic acid and acrylic ester. In order to avoid its local depletion, the inhibitor has to be added in every distillation column. Furthermore, reduced pressures are employed in the distillation columns in order to reduce the boiling temperatures. ∗ Corresponding author. Tel.: +41 1 632 3034; fax: +41 1 632 1082.

E-mail address: [email protected] (M. Morbidelli). 0009-2509/$ - see front matter 䉷 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2006.04.004

Besides polymerization and fouling, one of the major problems of this process is the thermodynamic limitation due to the reaction equilibrium. The temperatures employed for the reaction are about 60–150 ◦ C (c.f. Ullmann’s, 2005; Martan and Nestler, 2004). Although a few publications treat the homogeneously catalyzed esterification of acrylic acid with methanol (Malshe and Chandalia, 1977; Chubarov et al., 1984) much less investigate the reaction with a solid catalyst (Iizuka et al., 1986). Several publications treat the esterification of acrylic acid with alcohols other than methanol, using cation-exchange resins as catalysts (Darge and Thyrion, 1993; Chen et al., 1999; Zaleskova et al., 1983). Due to the drawbacks of the current production process, an increasing interest can be observed to develop alternative production technologies (Collins and Blair, 2005). In particular, the option to employ a heterogeneous catalyst, e.g. a cation-exchange resin, makes the use of integrated

G. Ströhlein et al. / Chemical Engineering Science 61 (2006) 5296 – 5306

reactor-separator processes like reactive distillation or reactive chromatography feasible. Since the former process would have similar drawbacks as the conventional one, i.e., fouling and polymerization due to elevated temperatures, the latter one could be a viable option since the separation is accomplished by selective adsorption in the liquid phase. The advantages of reactive chromatography, in particular used in combination with the simulated-moving-bed (SMB) technology (Broughton and Gerhold, 1961), have been shown for a wide variety of heterogeneously catalyzed reactions, e.g. the synthesis of bisphenol-A (Chiang and Fair, 2004), diethylacetal (Silva and Rodrigues, 2005) or vitamin C (Arumugam and Perri, 2003). An overview of the existing literature about simulated-moving-bed reactors (SMBR) can be found elsewhere (Lode et al., 2001; Ströhlein et al., 2004). In order to estimate the performance of a SMBR, i.e., its productivity and solvent requirement as a function of the required purities and yields, short-cut models (Ströhlein et al., 2005) and rigorous simulations (Lode et al., 2001) are generally employed. For both approaches, the model parameters for the reaction and adsorption processes are needed. These can be determined independently from the reactive chromatography experiments, using independent experiments on adsorption equilibrium, reaction kinetics and so on (Lode et al., 2001), or directly from reactive chromatographic column data. The first approach has the limitation that certain information needed for the integrated process cannot be obtained independently, e.g. the information about the competitive adsorption of reacting species. The second approach instead can provide all necessary information and furthermore, it is not as time-consuming as the independent parameter estimation. However, the latter one has to be preferred when validating the model, although it is more time-consuming since it requires extra experimental measurements. Since the model for a reactive chromatographic column is now well established, we proceed in this work with the direct estimation of the model parameters from experimental breakthrough curves. Several reactive chromatographic experiments are performed in a heated batch column and the resulting chromatograms are fitted using a rigorous model. The error between the experimental and the simulated chromatograms is minimized using a genetic algorithm (Deb, 2001). The covariance of the fitted model parameters is estimated and the results are discussed. The obtained model parameters are used in order to predict and optimize the performance of a SMBR for the esterification of acrylic acid with methanol using a detailed SMBR model. 2. Experiments 2.1. Experimental setup The breakthrough and desorption experiments have been performed in a jacketed batch column (Götec Superformance 300-16, Germany) with the dimensions 300 × 16 mm i.d. and the column as well as the column feed were kept at 60 ◦ C using a thermostat (Lauda RE104, Germany). The column was packed with a cation-exchange resin in the hydrogen

5297

form with an average particle diameter of 0.8 mm (Amberlyst 15, Rohm and Haas, USA). The HPLC unit consisted of an online-degasser (GASTORR 104, FLOM, Japan), a quaternary gradient unit (LG-1580-04, JASCO, USA), a doublepiston pump (PU-1580 JASCO, USA), a UV-detector (UV-975 JASCO, USA) and a fraction collector (GILSON FC 203 B). The reactants methanol, acrylic acid (stabilized with hydroquinone monomethyl ether) and methyl acrylate (all purum, > 99% GC; Fluka AG, Buchs, Switzerland) have been used without further purification. Deionized water has been purified with a Simpak2 unit (Millipore, MA, USA) before use. The composition of the liquid sample has been determined with a gas chromatograph (Hewlett Packard 6890) using a thermal conductivity detector with a polyethylene glycol column (HP-FFAP, 30 m × 0.53 mm × 1.0 m).

2.2. Measuring breakthrough and desorption curves As for separative chromatography, also in reactive chromatography an emphasis has to be put on the proper choice of the eluent. The use of an inert solvent as eluent is very often not suitable for reactive chromatography, since it implies that the reactants should have the same adsorptive properties. If they would have different adsorptive properties, a separation of the reactants would occur and the desired reaction could not take place. Instead, it is very common to use one of the reactants as eluent, making it the non-limiting component for the reaction. For the esterification of acrylic acid with methanol, the latter one is chosen due to the easier handling (fewer odors, no risk of polymerization). In order to characterize the batch column properly, the total column porosity, ∗ , has to be determined. Several experiments using a conventional tracer (thiorea) yielded higher porosities than expected, which showed that thiorea might adsorb on the cation-exchange resin. The perturbation method (Seidel-Morgenstern, 2004), i.e., a small pulse injection of pure methanol into a continuous stream of 95/5 vol% methanol–methyl acrylate, was used to cross-check the results and it yielded a total porosity of 0.64, being smaller than the one from the tracer experiments, confirming that thiorea adsorbs on the resin. Together with the particle porosity, P , which is given by the resin manufacturer as 0.32, the bed porosity, b , can be calculated to 0.47. It has to be noted that the value for the bed porosity is relatively high, which is due to fact, that the column was packed by particle sedimentation. Although the dry stationary phase undergoes a strong swelling when immersed into methanol, no significant change of the swelling with changing liquid phase compositions in the range considered in this work was observed. In a preliminary experiment, the breakthrough and desorption outlet methyl acetate concentration profiles for a 80/20 vol% methanol–methyl acrylate mixture have been measured in a bottom up flow configuration and the resulting chromatogram is shown by the asterisks in Fig. 1. The breakthrough occurs at 21.4 min which is the dead time, i.e., the sum of the column and the tubing dead time. The desorption profile shows a long

5298

G. Ströhlein et al. / Chemical Engineering Science 61 (2006) 5296 – 5306 Table 1 Summary of experimental conditions (tInj : feed duration)

Fig. 1. Breakthrough curves for a 80/20 vol% methanol–methyl acrylate mixture, injected for 40 min at 2 ml/min; asterisk: bottom-up flow, downward-triangle: top-down flow.

tail, indicating a strong non-linear behavior although it was expected from the physico-chemical properties of the system that methyl acrylate should adsorb only slightly. Due to the different densities of methanol and methyl acrlyate, i.e., 755 and 909 g/l (at 60 ◦ C), respectively, and the similar viscosities, i.e., 0.36 and 0.31 cP (at 60 ◦ C), respectively, it was suspected that the shape of the ad- and desorption profile could be influenced by the density gradient in the column and the flow direction. This hypothesis was verified by carrying out a top-down flow experiment, keeping all other conditions constant and the resulting chromatogram is shown in Fig. 1 by downward-triangles. The top-down flow experiment shows a fronting breakthrough curve and a sharp desorption profile, i.e., the opposite behavior as for the bottom-up flow. This behavior can be explained by an instable interface between the liquid being initially in the column and the one replacing it. In general, this instability can occur due to density or viscosity gradients. In this case, the viscosity effects are negligible and the instable interface occurs if a heavier liquid is replaced with a lighter liquid in bottom-up flow and vice versa for top-down flow. This effect is called ‘fingering’, hinting at the experimentally observed shapes of the instabilities (Kretz et al., 2003) one can regard as an additional axial dispersion. Accordingly, for the experiments shown in Fig. 1, we expect an unaffected breakthrough profile in the bottom-up flow, while for the desorption profile, the heavier methanol–methyl acrylate mixture is replaced with the lighter, pure methanol, thus leading to an instable interface, an additional axial dispersion and eventually the tailing desorption profile. For the top-down flow, an instable interface occurs for the adsorption profile, since the replaced liquid, i.e., pure methanol, is lighter than the replacing fluid, i.e., the methanol–methyl acrylate mixture. This is in accordance with the top-down flow chromatogram in Fig. 1, which shows a very broad breakthrough profile and a sharp, unaffected desorption profile. Since the ‘fingering’ effect could not be circumvented by experimental means, it had to be taken into account in the modeling of the column behavior.

Run

tInj (min)

Flow rate (ml/min)

Flow direction

Feed composition: MeOH, AcAc, MeAc, H2 O (vol%)

#1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20

30.1 30.1 30.1 30.1 30.1 30.1 40.1 40.1 40.1 40.1 40.1 40.1 40.1 30.1 30.1 40.1 40.1 30.1 30.1 40.1

4 4 4 6 2 6 2 4 3 4 4 4 2 6 4 2 3 6 4 4

Bottom-up Bottom-up Bottom-up Bottom-up Bottom-up Bottom-up Bottom-up Bottom-up Bottom-up Bottom-up Top-down Top-down Top-down Top-down Top-down Top-down Top-down Top-down Top-down Top-down

70, 30, 0, 0 30, 70, 0, 0 50, 50, 0, 0 70, 30, 0, 0 50, 50, 0, 0 50, 50, 0, 0 80, 0, 20, 0 80, 0, 20, 0 90, 0, 0, 10 80, 0, 0, 20 80, 0, 0, 20 80, 0, 20, 0 80, 0, 20, 0 90, 0, 0, 10 70, 30, 0, 0 90, 0, 0, 10 70, 0, 30, 0 70, 30, 0, 0 75, 0, 20, 5 65, 25, 0, 10 Re-equilibration: 75, 0, 25, 0

In order to measure the breakthrough and desorption behavior of different mixtures, the column is first equilibrated with methanol, then a mixture of methanol–acrylic acid, methanol–methyl acrylate, methanol–water or methanol–methyl acrylate–water is injected for a time sufficiently to reach steady-state and finally the column is re-equilibrated with pure methanol. In order to increase the consistency and to decrease the covariance of the fitted parameters, several experiments at different feed compositions and flow rates have been performed. The ranges of the concentrations of acrylic acid, methyl acrylate and water have been chosen according to the expected operating conditions in a SMBR, e.g. no pure acrylic acid, methyl acrylate or water will ever occur in the unit. The experimental conditions are summarized in Table 1 and the components involved in the reaction, that is methanol, acrylic acid, methyl acrylate and water, are abbreviated as MeOH, AcAc, MeAc, H2 O, respectively. It has to be noted, that in experiment #20, the re-equilibration of the column was done with a mixture of methanol and methyl acrylate instead of pure methanol. The resulting chromatograms are indicated by symbols in Fig. 2 . From the experiments with non-reacting pairs, i.e., methanol–methyl acrylate and methanol–water, it can be seen that only water shows significant adsorption on the stationary phase while methyl acrylate is always eluted at the dead time of the unit. When comparing experiments #7, #8, #10 to #13, #12, #11, the influence of the flow direction on the shape of the breakthrough and desorption curve is clearly visible, i.e., a more dispersed breakthrough and a sharp desorption profile for the top-down flow and vice versa for the bottom-up flow. From experiments where a feed mixture of the reactants has

G. Ströhlein et al. / Chemical Engineering Science 61 (2006) 5296 – 5306

5299

Fig. 2. Experimental and simulated chromatograms for esterification of acrylic acid with methanol, experiments #1–#20; symbols: experimental data (upward-triangle: MeOH, asterisk: AcAc, downward-triangle: MeAc, dot: H2 O), lines: simulations (dotted line: MeOH, dashed line: AcAc, dash-dotted line: MeAc, solid line: H2 O).

been used, e.g. #3, one can clearly see the effect of selective adsorption. For example, the ‘overshoot’ of the methyl acrylate concentration profile in the time interval 10–20 min occurs due to the displacement of adsorbed methyl acrylate by water since the latter adsorbs more strongly than the former. Furthermore, from the desorption profiles in #3, it is obvious that water adsorbs more strongly since it is the last component leaving the column. 3. Modeling and simulation As mentioned earlier, the simulation models of reactive chromatographic columns are well established. In this work the

isothermal, lumped kinetic rate model with a linear driving force has been used leading to the following set of equations: ∗

jci j2 ci jci eq + (1 − ∗ )km (qi − qi ) + u = b Deff 2 jt jz jz

jqi eq = km (qi − qi ) + i r jt

(1) (2)

where (1) and (2) are derived from the mass balance in the liquid and solid phase, respectively. The concentrations of component i in the liquid and solid phase are denoted ci and qi , respectively, t is time and z the space coordinate, ∗ and b denote the total and bed porosity, respectively, u the superficial flow velocity, km the solid–liquid mass transfer coefficient,

5300

G. Ströhlein et al. / Chemical Engineering Science 61 (2006) 5296 – 5306

Fig. 2. (continued).

G. Ströhlein et al. / Chemical Engineering Science 61 (2006) 5296 – 5306

5301

Fig. 2. (continued).

Deff the effective axial dispersion coefficient, i the stoichiometric reaction coefficient and r the reaction rate. The solid phase concentration being in equilibrium with ci is called eq qi and is given by the adsorption isotherm, which in this case is the stoichiometric Langmuir isotherm: N i Ki c i eq , qi =  j K j cj

(3)

where Ni and Ki denote the saturation capacity and the adsorption constant of component i, respectively. The reaction rate r is given by the second order model as   qMeAc qH2 O (4) r = kR qMeOH qAcAc − Keq

with Keq and kR being the reaction equilibrium and the reaction rate constant, respectively. It has to be noted that these equations represent a truly heterogeneously catalyzed reaction, i.e., first both reactants adsorb and then partially react to the products, which are subsequently desorbed into the bulk stream. Since the temperature effects of the reaction are negligible in the present case and since the column was thermostated, isothermal operation has been assumed. As discussed in detail earlier in the experimental section, it has been observed that there is a strong influence of the flow direction on the elution profiles due to density gradients in the column. The effect of viscosity and/or density gradients in a flow through a porous medium has been described analytically by Welty and Gelhar (1991) who proposed an exponential relationship between the density gradient and the additional axial

5302

G. Ströhlein et al. / Chemical Engineering Science 61 (2006) 5296 – 5306

dispersion. Their results have been further simplified by Kretz et al. (2003), who also verified the validity of this approach experimentally. Based on these findings, the effective axial dispersion Deff , modified by the presence of the density gradient is obtained as the product of the usual (i.e., no density gradient) axial dispersion coefficient and a factor containing the exponential of the density gradient, as follows: Deff = dax ueg(a/u)(j/jz) ,

Table 2 Fixed model parameters

∗ (dimensionless) b (dimensionless) KH2 O (l/mol) # of discretization elements MeOH , AcAc , MeAc , H2 O (dimensionless) Extra-column dead volume (ml)

0.64 0.47 1 50 −1, −1, 1, 1 4.6

(5)

where dax u denotes the usual axial dispersion coefficient due to flow inhomogeneties, j/jz the local density gradient, a is an empirical constant and g takes the value of 1 if the direction of the gravitational force is in opposite direction to the flow direction, i.e., bottom-up flow, and −1 in the opposite case. The local density gradient can be obtained from the local concentration gradient and the molar mass of component i, Mi , as follows: jci j  Mi = . jz jz

(6)

i

It can be seen, that (5) reduces to the simple linear relationship Deff = dax u if the density gradient is zero. For a positive density gradient in bottom-up flow, i.e., a higher density fluid is replaced with a lower density fluid, the exponent is positive and Deff > dax u. If the density gradient is negative, then Deff < dax u, i.e., a self-sharpening of the front occurs. The analogous argumentation applies for the case of top-down flow. The partial differential equations (1) and (2) have been discretized in space and the space derivatives of the concentrations variables are approximated by finite differences. The obtained system of ordinary differential equations is solved with the DIVPAG routine of the IMSL library (Visual Numerics, San Ramon, USA) using Gear’s BDF method, a banded Jacobian matrix and a solver tolerance of 10−6 . Numerical tests showed that the solutions converged for 50 discretization elements. The extra-column dead volume of 4.6 ml is taken into account as an ideal plug-flow pipe, which leads simply to a time shift of the chromatogram. 4. Results 4.1. Parameter fitting After the experiments have been carried out and the simulation model has been set up, the determination of the model parameters describing the esterification of acrylic acid with methanol can be performed. Inspecting (1)–(5), it can be seen that 12 model parameters need to be determined: 7 for the adsorption isotherm (8 parameters Ni and Ki appear in (3), but only 7 are linearly independent, hence KH2 O is fixed to 1), 2 parameters describing the reaction equilibrium and kinetics (kR and Keq ), and 3 parameters for the mass transfer kinetics and the flow dispersion (km , dax , a). The porosities ∗ and b had been determined in preliminary experiments as described in the previous section. A summary of the model parameters values determined a priori is reported in Table 2.

Fig. 3. Convergence of the objective function in the fitting algorithm.

The determination of the remaining 12 parameters mentioned above is accomplished by least-squares fitting, i.e., the parameter values are changed by an optimization algorithm so that the overall error between the experimental and the simulated chromatograms is minimized. The overall absolute error is calculated as the sum of the squared differences between simulated and experimental concentrations for each component at each experimental point for all 20 experiments. As optimization algorithm, the non-sorted genetic algorithm (NSGA) has been used which has proven to be very robust even for highly non-linear problems in chromatography (Zhang et al., 2003). Convergence of the algorithm is obtained after 60 generations with a population size of 100 and the required CPU time (Intel Pentium 4, 3.2 GHz) is about 13 h, yielding an average simulation time of 0.4 s per chromatogram. The development of the overall absolute square errors as a function of the number of simulations is shown in Fig. 3. The obtained parameter values are summarized in the first column of Table 3. In order to check the reliability of the developed model it is convenient to compare the estimated values of the model parameters with corresponding values that can be obtained from independent sources, at least for those cases where this is possible. The Henry coefficient of water, HH2 O , with methanol as eluent can be easily calculated from (3) and is given by Pure ) where cPure indicates the HH2 O =NH2 O KH2 O /(KMeOH cMeOH MeOH concentration of pure methanol, i.e., 23.5 mol/l. Using the parameters from the first column in Table 3, HH2 O = 3.67 is obtained, which is in the same range as the value of HH2 O = 2.78,

G. Ströhlein et al. / Chemical Engineering Science 61 (2006) 5296 – 5306 Table 3 Values of fitted model parameters and their estimated absolute and relative standard deviation

NMeOH (mol/l) NAcAc (mol/l) NMeAc (mol/l) NH2 O (mol/l) KMeOH (l/mol) KAcAc (l/mol) KMeAc (l/mol) kR (l/mol/min) km (1/min) Keq (dimensionless) dax (cm) a (l cm2 /g/ min)

Fitted value

Absolute standard deviation

Relative standard deviation (%)

5.14 4.50 10.20 13.74 0.16 0.032 0.012 69.58 3.41 2.27 1.45 0.58

± 0.09 ± 0.37 ± 3.13 ± 0.15 ± 0.004 ± 0.002 ± 0.0035 ± 69.58 ± 0.16 ± 0.13 ± 0.0208 ± 0.008

± 1.78 ± 8.15 ± 30.65 ± 1.05 ± 2.38 ± 7.03 ± 30.08 ± 100.00 ± 4.70 ± 5.77 ± 1.44 ± 1.42

estimated by Yu et al. (2004) for the water–methanol adsorption on Amberlyst 15 for the esterification of acetic acid with methanol at 50 ◦ C. It has to be noted that their value actually underestimates the breakthrough time of water (c.f. Fig. 2(c) in Yu et al. (2004)) and hence a larger Henry should be expected, thus diminishing the difference to the value in Table 3. The Henry coefficients for acrylic acid and methyl acrylate, i.e., HAcAc = 0.04 and HMeAc = 0.03, indicate that the adsorption of these two components with methanol as eluent is very low. The reaction equilibrium constant, Keq = 2.27, which is based on the solid phase concentrations (c.f. (4)), cannot be compared to the one obtained by Malshe and Chandalia (1977) for the homogeneously catalyzed system, since the presence of an adsorbent fundamentally changes the system properties. The lumped mass transfer coefficient, km = 3.41 (1/min), has been cross-checked by lumping the film and pore mass transfer resistances as summarized elsewhere (Miyabe and Guiochon, 2000). The external film mass transfer coefficient is estimated via a Sherwood correlation (Wilson and Geankoplis, 1966), the intraparticle diffusion from the effective pore diffusivity (Chang and Wilke, 1955; Galinada et al., 2005) assuming a tortuosity of 4 (Perry and Green, 1997) and the solid diffusion is considered to be negligible. This yields a value of km = 3.0 (1/min), which is virtually independent of the flow rate since the pore diffusion predominates the mass transfer process. A comparison of the experimental chromatograms with the simulated ones is shown in Fig. 2. It can be seen that in average, the simulations and the experiments agree well, although the extent of the agreement seems to be dependent on the operating conditions, e.g the reactive experiments with the highest flow rate, i.e., 6 ml/min, show very low deviations to the simulation as can be seen in experiments #4, #6 and #14. Instead, the reactive experiment involving the lowest flow rate of 2 ml/min, i.e., #5, seem to be more difficult to model. This might be due to diffusive phenomena, which have a more pronounced effect for lower residence times and which cannot be described with the linear driving force model as introduced in Chapter 3. The effect of additional axial dispersion due to the density gradient

5303

in the column is accurately taken into account by the model as can be seen for example in experiments #7 and #13, which were done under the same operating conditions, except for the flow direction which was bottom-up for the former and topdown for the latter. Emphasis should be placed here on the adsorption front in experiment #7, which is relatively sharp and the plateau concentration is reached after about 5 min, where instead in experiment #13, the first occurrence of methyl acrylate in the column effluent is detected about 10 min earlier than in the previous experiment and it takes about 30 min to reach the plateau concentration. The model is able to describe this strongly different behavior only through the modification of the axial dispersion term introduced in (5). The largest deviation between simulation and experiment occurs in experiment #20, where the production of methyl acetate in the breakthrough profile is underestimated. This indicates that in the presence of high concentrations of water and acrylic acid, the reaction kinetic model introduced in (4) may not be accurate. However, it has to be noted that, inside the SMBR these conditions are not encountered, i.e., high water concentration cannot be present simultaneously with high acrylic acid concentration. 4.2. Determination of parameter covariance Further insights into the reliability and precision of the veloped fitting procedure can be obtained by computing covariance matrix of the system parameters following the proach taken by Bard (1974). The covariance matrix V least-squares is approximated by  n  −1  jf (, i )   jf (, i ) T , V = 2exp j j

dethe apfor

(7)

i=1

where  is the parameter vector containing the variables of Table 3, n is the number of experiments, i a vector containing the operating conditions of experiment i, e.g. flow rate and feed concentration as in Table 1, 2exp is the variance of the experimental values and f represents the function computing the chromatogram for given  and i , i.e., a vector containing the weight fractions of all components in the chromatogram. The derivative df/d is the sensitivity of the simulated chromatogram with respect to the system parameters and it has been approximated in the following by a finite difference method using central differences. The standard variation of the experimental values,exp , per se is well below 0.3 wt%, but in order to take the model inaccuracies also into account, this has been computed as the standard deviation of the errors between the experiments and the simulations, which yields 1.9 wt% (c.f. Bard, 1974). The standard deviations of the system parameters can be obtained from the square root of the elements in the diagonal of V and the corresponding values are summarized in the second and third columns of Table 3. It is seen that, while the majority of the parameters can be estimated with a very high accuracy, three exceptions appear: the saturation capacity and adsorption constant of methyl acrylate and the reaction rate constant. The first two exhibit a high standard deviation because the isotherm is nearly linear for the

5304

G. Ströhlein et al. / Chemical Engineering Science 61 (2006) 5296 – 5306

methyl acrylate concentrations considered in this work, hence it is very difficult to determine the saturation capacity and the adsorption constant individually, while only their product, being proportional to the Henry coefficient, can be determined accurately. A further insight is given here by the correlation matrix R with Rij =V,ij (V,iiV,jj )−1/2 (c.f. Bard, 1974), which yields a correlation coefficient of −0.98 between the estimate of the saturation capacity and the adsorption constant of methyl acrylate, i.e., the two values are highly negatively correlated, indicating that they cannot be determined separately. From the third column of Table 3, it can be seen that also the reaction rate constant cannot be determined accurately from the experiments performed, due to the fact that in the experimental runs considered the rate determining step is the mass transport and not the chemical reaction. Hence the reaction rate constant has practically no influence on the quality of the fitting, as long as it is above a certain limit below which the chemical reaction would become the rate determining step. It has to be noted that it is still necessary for the fitting procedure to keep the three parameters discussed above as free variables, since it is not known a priori how the isotherm will look like and how the characteristic times of reaction and mass transfer relate to each other. The correlation matrix obtained from (7) shows, that all other system parameters are virtually independent of each other, indicating that the information content of the experiments is sufficient to reliably determine their values.

Table 4 Optimal operating conditions of a SMBR for methyl acrylate synthesis at 98% conversion m1 (dimensionless) 3.01 m2 (dimensionless) 0.25 m3 (dimensionless) 0.82 −0.14 m4 (dimensionless) t ∗ (min) 15.38 Molar ratio of methanol to acrylic 0.40 acid in the feed (dimensionless)

Table 5 Optimal performance parameters for a SMBR operating at 98% conversion Solvent requirement (mol MeOH/mol MeAc) Average raffinate composition (wt% MeOH, AcAc, MeAc, H2 O) Average extract composition (wt% MeOH, AcAc, MeAc, H2 O)

11.8 31.5, 1.0, 67.5, 0.04 94.6, 0.06, 0.1, 5.2

4.3. Optimization of the simulated-moving-bed reactor The model parameters obtained from the batch experiments can now be used in order to estimate the performance of a SMBReactor for the synthesis of methyl acrylate from methanol and acrylic acid. Having a validated rigorous model for the batch column, little work is needed in order to build the model for an SMBR (Lode et al., 2001), which consists only of connected batch columns with additional in- and outlet flows and a port switching algorithm. Using the same model parameters as above, i.e., for the operation at 60 ◦ C (Tables 2 and 3), the DIVPAG solver of the IMSL library as described in Chapter 3 and a SQP-based optimization algorithm (FMINCON, MATLAB optimization toolbox, MathWorks, USA), the minimal solvent requirement of the SMBR, i.e., the amount of methanol required per amount of methyl acrylate obtained in the raffinate, can be determined (c.f. Ströhlein et al., 2004). The constraint to the optimization has been set so that the conversion of acrylic acid in the SMBR should be 98%. It has to be noted that the inner column diameter was set to 2.54 cm and the distribution of the columns in the four unit sections was chosen to be 3-2-3-2 (Lode et al., 2001). The influence of the additional axial dispersion due to the density gradient has been neglected since it is assumed that the flow directions in the columns of the SMBR are tailored so as not to affect the breakthrough and desorption fronts, e.g. a top-down and a bottom-up flow are chosen for the columns in Sections 1 and 4, respectively. The optimization variables are the flow rate ratios for each section, m1 − m4

Fig. 4. Optimized internal concentration profiles in a SMBR for 98% conversion at the beginning of a switch at cyclic steady-state; dotted line: methanol, dashed line: acrylic acid, dash-dotted line: methyl acrylate, solid line: water.

(c.f. Ströhlein et al., 2005; Mazzotti et al., 1997), the switching time and the molar ratio between methanol and acrylic acid in the feed. The optimal values of the operation variables and the resulting performance parameters are reported in Tables 4 and 5, respectively, and the corresponding internal concentration profiles in the SMBR at the beginning of a switch at cyclic steady-state are shown in Fig. 4. It can be seen that water is adsorbed heavily on the resin and a lot of methanol has to be used in order to regenerate the resin in Section 1. Therefore, water is obtained only highly diluted in the outlet stream, i.e., the average water concentration in the extract is about 2.3 mol/l, i.e., 5.2 wt%. Furthermore, it should be emphasized that the molar ratio of methanol to acrylic acid in the feed is not equal to the stoichiometric ratio of the reactants, i.e., 1, neither equal to 0, i.e., pure acrylic acid feed, but takes some value in between. This intermediate value can be

G. Ströhlein et al. / Chemical Engineering Science 61 (2006) 5296 – 5306

explained by the two underlying, competing effects: on the one hand, the performance of the SMBR, i.e., the productivity and the solvent requirement, generally improves with the feed concentration of acrylic acid (as in the case of a purely separative SMB), but on the other hand, an increasing acrylic acid feed concentration leads to a local depletion of methanol in Section 3 of the SMBR, i.e., methanol becomes the limiting reactant and the SMBR is less efficient. 5. Conclusions A detailed, lumped kinetics, linear driving force model taking into account the additional axial dispersion due to density gradients has been shown to accurately describe the dynamic behavior of a batch chromatographic column for the esterification of acrylic acid with methanol on Amberlyst 15. The necessary model parameters for reaction and adsorption have been obtained by minimizing the error between the experimental and the simulated chromatograms, using a genetic algorithm for the optimization. The analysis of the covariance of the fitted model parameters reveals that the reaction rate constant in the solid phase cannot be determined from the experiments since the mass transfer is the rate determining step while all other model parameters show a fairly low standard deviation. The only other exceptions are the saturation capacity and the adsorption constant for acrylic acid which appear to be highly correlated, due to the fact that at the investigated operating conditions, acrylic acid follows a linear adsorption isotherm. The presented approach to simultaneously determine the model parameters from a series of dynamic batch column experiments is applicable in general to all chromatographic reactors, shortening the development time significantly. A complete model of a simulated-moving-bed reactor (SMBR) has been implemented and its optimal point of operation was determined, yielding that about 12 mol of methanol per mol of methyl acrylate are needed in order to obtain 98% conversion of acrylic acid and complete separation of the reaction products at a relatively low operating temperature of 60 ◦ C. This indicates that the SMBR might be a viable option to overcome the drawbacks of the conventional production processes. Notation a ci Deff g Hi km kR Keq Ki Mi Ni

empirical constant (5), l cm2 /g/ min liquid phase concentration of component i, mol/l effective axial dispersion coefficient, cm2 / min empirical constant indicating flow direction (5), dimensionless Henry constant, dimensionless mass transfer constant, 1/min reaction rate constant, l/mol/min reaction equilibrium constant, dimensionless isotherm adsorption constant, l/mol molar mass of component i, g/mol saturation capacity of component i, mol/l

qi eq qi r R t u V z

5305

solid phase concentration of component i, mol/l solid phase equilibrium concentration of component i, mol/l reaction rate, mol/l/min correlation matrix time coordinate, min superficial liquid velocity, cm/min covariance matrix, dimensionless space coordinate, cm

Greek letters i b P ∗  i 2exp j/jz

vector containing operating conditions of experiment i column bed porosity, dimensionless particle porosity, dimensionless total column porosity, dimensionless parameter vector containing variables of Table 3 stoichiometric coefficient of component i, dimensionless variance of the experimental values, dimensionless local density gradient, g/l/cm

Subscripts AcAc H2 O MeAc MeOH

acrylic acid water methyl acrylate methanol

Acknowledgments The financial support of DSM Nutritional Products, Basel, Switzerland, is gratefully acknowledged. Y. A. is very grateful to the “Eidgenössische Stipendienkommission für ausländische Studierende”, which made her contribution to this work possible. A. B. gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft. References Arumugam, B.K., Perri, S.T., 2003. WO 03 068 764. Bard, Y., 1974. Nonlinear Parameter Estimation. Academic Press, New York. Broughton, D.B., Gerhold, C.G., 1961. U.S. Patent 2 985 589. Chang, P., Wilke, C.R., 1955. Some measurements of diffusion in liquids. Journal of Physical Chemistry 59, 592–596. Chen, X., Xu, Z., Okuhara, T., 1999. Liquid phase esterification of acrylic acid with 1-butanol catalyzed by solid acid catalysts. Applied Catalysis A-General 180, 261–269. Chiang, C.-C., Fair, L.D., 2004. U.S. Patent 2 004 019 241. Chubarov, G.A., Danov, S.M., Logutov, V.I., Obmelyukhina, T.N., 1984. Esterification of acrylic acid with methanol. Journal of Applied Chemistry of the USSR 57, 192–193. Collins, N.A., Blair, L.W., 2005. (Meth)Acrylates by reactive chromatography. 18th International Symposium on Preparative/Process Chromatography, Ion Exchange, Adsorption/Desorption Processes & Related Separation Techniques, 8–12 May 2005, Philadelphia, PA, USA. Darge, O., Thyrion, F.C., 1993. Kinetics of the liquid-phase esterification of acrylic-acid with butanol catalyzed by cation-exchange resin. Journal of Chemical Technology and Biotechnology 58, 351–355.

5306

G. Ströhlein et al. / Chemical Engineering Science 61 (2006) 5296 – 5306

Deb, K., 2001. Multi-Objective Optimization using Evolutionary Algorithms. Wiley, Chichester, UK. Galinada, W.A., Kaczmarski, K., Guiochon, G., 2005. Influence of microwave irradiation on the mass-transfer kinetics of propylbenzene in reversed-phase liquid chromatography. Industrial & Engineering Chemistry Research 44, 8368–8376. Iizuka, T., Fujie, S., Ushikubo, T., Chen, Z.H., Tanabe, K., 1986. Esterification of acrylic-acid with methanol over niobic acid catalyst. Applied Catalysis 28, 1–5. Kretz, V., Berest, P., Hulin, J.P., Salin, D., 2003. An experimental study of the effects of density and viscosity contrasts on macrodispersion in porous media. Water Resources Research 39, 1032. Lode, F., Houmard, M., Migliorini, C., Mazzotti, M., Morbidelli, M., 2001. Continuous reactive chromatography. Chemical Engineering Science 56, 269–291. Malshe, V.C., Chandalia, S.B., 1977. Kinetics of liquid-phase esterification of acrylic-acid with methanol and ethanol. Chemical Engineering Science 32, 1530–1531. Martan, H., Nestler, G., 2004. U.S. Patent 2 004 236 143. Mazzotti, M., Storti, G., Morbidelli, M., 1997. Optimal operation of simulated moving bed units for nonlinear chromatographic separations. Journal of Chromatography 769, 3–24. Miyabe, K., Guiochon, G., 2000. Kinetic study of the mass transfer of bovine serum albumin in anion-exchange chromatography. Journal of Chromatography A 866, 147–171. Perry, R.H., Green, D.W., 1997. Perry’s Chemical Engineer’s Handbook. seventh ed. McGraw-Hill, New York. Seidel-Morgenstern, A., 2004. Experimental determination of single solute and competitive adsorption isotherms. Journal of Chromatography A 1037, 255–272.

Silva, V.M.T.M., Rodrigues, A.E., 2005. Novel process for diethylacetal synthesis. A.I.Ch.E. Journal 51, 2752–2768. Ströhlein, G., Lode, F., Mazzotti, M., Morbidelli, M., 2004. Design of stationary phase properties for optimal performance of reactive simulated-moving-bed chromatography. Chemical Engineering Science 59, 4951–4956. Ströhlein, G., Mazzotti, M., Morbidelli, M., 2005. Optimal operation of simulated-moving-bed reactors for nonlinear adsorption isotherms and equilibrium reactions. Chemical Engineering Science 60, 1525–1533. Ullmann’s Encyclopedia of Industrial Chemistry, seventh ed. Wiley-VCH Verlag, Weinheim, 2005. Welty, C., Gelhar, L.W., 1991. Stochastic analysis of the effects of fluid density and viscosity variability on macrodispersion in heterogeneous porous-media. Water Resources Research 27, 2061–2075. Wilson, E.J., Geankoplis, C.J., 1966. Liquid mass transfer at very low Reynolds numbers in packed beds. Industrial & Engineering Chemistry Fundamentals 5, 9. Yu, W.F., Hidajat, K., Ray, A.K., 2004. Determination of adsorption and kinetic parameters for methyl acetate esterification and hydrolysis reaction catalyzed by Amberlyst 15. Applied Catalysis A-General 260, 191–205. Zaleskova, N.I., Fomin, V.A., Selyakova, V.A., Zavadovskaya, A.S., 1983. Catalytic activity of sulfonated cation-exchange resins in the esterification of acrylic-acid with normal-butanol. Journal of Applied Chemistry of the USSR 56, 1792–1794. Zhang, Z., Mazzotti, M., Morbidelli, M., 2003. Multiobjective optimization of simulated moving bed and varicol processes using a genetic algorithm. Journal of Chromatography A 989, 95–108.