Dynamics of a Chromatographic Reactor - American Chemical Society

Ind. Eng. Chem. Res. 1997, 36, 3163-3172

3163

Dynamics of a Chromatographic Reactor: Esterification Catalyzed by Acidic Resins Marco Mazzotti,† Bernardo Neri, Davino Gelosa,‡ and Massimo Morbidelli* Laboratorium fu¨ r Technische Chemie LTC, ETH Zentrum CAB C40, Universita¨ tstrasse 6, CH-8092 Zu¨ rich, Switzerland

Reactive chromatography, i.e., coupling chemical reaction and selective sorption, allows us to drive the chemical reaction beyond equilibrium and to separate its products. Chromatographic reactors exhibit a complex dynamical behavior, whose analysis is the objective of this work. The synthesis of ethyl acetate and water from ethanol and acetic acid on a commercial polystyrene-divinylbenzene acidic resin is considered. The results of experiments run in a laboratory-scale chromatographic reactor are reported. Experimental data are in good agreement with the results obtained using a fully predictive equilibrium dispersive model. This exploits an accurate description of both the multicomponent sorption equilibria on the resin, based on the extended Flory-Huggins model, and the kinetics of the heterogeneously catalyzed chemical reaction. The chromatographic reactor exhibits a rather rich dynamical behavior, which is a consequence of the dual role, as a catalyst and as a selective sorbent, played by the resin. In particular, it is characterized by the development of composition fronts traveling along the fixed bed column at well-defined propagation velocities. By interpreting the obtained results in terms of these classical nonlinear chromatography concepts, a deep insight into the dynamical behavior of the chromatographic reactor can be achieved. These findings can be usefully summarized in a master plot which allows us to identify the different dynamic regimes in the operating parameter space. 1. Introduction Multifunctional reactors, where reaction and separation take place simultaneously in the same vessel, are gaining increasing interest as a feasible and economical solution for complex reactions limited by chemical equilibrium. Among these, chromatographic reactors can be applied to different classes of important reactions, such as esterifications and transesterifications (Sardin and Villermaux, 1979), hydrogenations and dehydrogenations (Ray and Carr, 1995), glucose/fructose enzymatic isomerization (Hashimoto et al., 1983), oxidative coupling of methane (Tonkovich and Carr, 1994), and methanol synthesis (Kruglov, 1994). They can be operated in the batch preparative mode (Sardin and Villermaux, 1979; Sardin et al., 1993) or in the continuous simulated moving bed mode (Bjorklund and Carr, 1995; Kawase et al., 1996; Kruglov et al., 1996; Mazzotti et al., 1996), allowing us to drive the reaction to completion and to recover the products in two distinct outlet streams. In most cases above, the chromatographic reactor is packed with two different solid particles (either mixed or layered), one being the catalyst and the other the adsorbent. Recently, it has been demonstrated that in the case of esterification, a commercial polystyrenedivinylbenzene acidic resin can play the dual role of catalyst and selective sorbent (Kawase et al., 1996; Mazzotti et al., 1996). In particular, the reaction of acetic acid component (1) and ethanol (2), producing water (3) and ethyl acetate (4), has been considered to be a model reaction of this kind. These components * To whom correspondence should be addressed. E-mail: [email protected]. Telephone: +41-1-6323034. Fax: +41-1-6321082. † Present address: Institut fu ¨ r Verfahrenstechnik, ETH Zentrum ML625, Sonnegstrasse 3, CH-8092 Zu¨rich, Switzerland. ‡ Dipartimento di Chimica Fisica Applicata, Politecnico di Milano, Via Mancinelli 7, 20131 Milano, Italy. S0888-5885(96)00634-3 CCC: $14.00

exhibit increasing affinity toward the resin in the following order: ethyl acetate, acetic acid, ethanol, and water (Mazzotti et al., 1996). During the reaction, which takes place in the polymer phase, water is kept by the resin, whereas ethyl acetate is soon desorbed. Thus, the products are separated and the reaction is driven to complete conversion. When a mixture of ethanol and acetic acid is fed to a column initially saturated with ethanol, an ethyl acetate/ethanol stream is first collected at the column outlet until water saturates the resin completely and breaks through together with the steadystate amounts of the other three compounds. From now on, the reactor operates as a heterogeneous catalytic reactor at steady state. In this work, we analyze the dynamic behavior of chromatographic reactors in order to evidence a few peculiarities of these units and to provide a better understanding of their behavior, for which a complete analysis is still lacking. We refer to the ethyl acetate synthesis mentioned above and discuss a number of experimental data and simulation results, obtained using the apparatus and the model described in the next section. An equilibrium dispersive model is used, where axial dispersion and multicomponent sorption equilibria are both accounted for, the latter through the extended Flory-Huggins model. Mass-transfer resistances are neglected, since the characteristic time of transport phenomena, in the conditions considered in this work, is of the order of magnitute of a few minutes, whereas the characteristic times of the reaction and of the process are of the order of magnitude of a few hours (Mazzotti et al., 1997). The model consists of a system of strongly nonlinear parabolic partial differential equations which calls for a numerical solution. In fact, it does not admit any analytical approach, such as the very powerful method of characteristics extensively adopted in the study of chromatographic processes through the socalled equilibrium theory (cf. Helfferich and Klein, 1970; Rhee et al., 1970). © 1997 American Chemical Society

3164 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997

Since, in principle, numerical tools are not best suited to gain a deep insight into the dynamic behavior of the chromatographic reactor, several researchers have tried to simplify either the reacting system or the model in order to recover the possibility of using the equilibrium theory approach. Therefore, on one hand, very simple reactions, namely, A T B isomerizations, have been studied accounting for a finite reaction rate through the method of characteristics (Cho et al., 1982; Loureiro et al., 1993). On the other hand, complex reaction schemes have been analyzed enforcing the assumption of instantaneous attainment of chemical equilibrium (Schweich et al., 1980). Clearly neither approach is feasible in our case, because the reaction is rather slow and involves four species and the description of the phase equilibrium partition requires a complex nonideal thermodynamic model. However, we show that a large amount of information can be extracted from the experimental data and the model results when these are interpreted in terms of classical nonlinear chromatography concepts such as composition fronts and propagation velocities. With this approach, which can be extended to other reacting systems, a master plot has been derived which allows us to readily identify all different types of dynamic behavior in the operating parameter space of the chromatographic reactor. Moreover, this analysis is a valuable help for the design of operating conditions of continuous chromatographic reactors, i.e., simulated moving bed reactors. 2. The Chromatographic Reactor 2.1. Experimental Apparatus. The experiments have been performed in a laboratory-scale chromatographic reactor, constituted of a jacketed column, at atmospheric pressure and a temperature of T ) 60 °C. The fixed bed is packed with about 50 g of resin Amberlyst 15 kindly provided by Rohm & Haas. Its dry properties are average particle diameter d ) 6 × 10-4 m, intraparticle void fraction p ) 0.36, and interparticle void fraction ) 0.42. In the presence of the fluid species, the resin swells, exhibiting a swelling ratio, q, i.e., ratio between swollen and dry volumes of the resin, depending upon the fluid composition and equal to 1.22, 1.30, 1.48, and 1.52 in the case of pure ethyl acetate, acetic acid, ethanol, and water, respectively (Mazzotti et al., 1997). The swelling phenomenon yields changes in the value of the interparticle void fraction, whereas the intraparticle void fraction is assumed to be constant. The length and volume of the fixed bed depend upon the quantity of resin used for the packing and the average swelling ratio of the bed (as a function of the initial and feed compositions). Their average values are l ) 0.38 m and VR ) 130 × 10-6 m3. 2.2. Mathematical Modeling. The behavior of the chromatographic reactor has been described by means of an equilibrium dispersive mathematical model, which implies the assumption of local sorption equilibrium, i.e., negligible mass-transport resistances, on the basis of a characteristic time analysis. Axial dispersion is accounted for as well as changes of the swelling ratio of the resin as a consequence of composition variations. Temperature and fluid flow rate are assumed to be constant and uniform: the former since the heat of reaction is rather small and the column thermostated, the latter for reasons that will be discussed below (cf. eq 9). The reaction rate is finite in the resin, due to its catalytic role, whereas it is negligigble in the fluid phase.

The model equations are constituted by the following system of four second order partial differential equations in the unknown overall concentration of the ith component, cTi ,

( )

∂cTi ∂(ucLi ) ∂cLi ∂ + ) D + µi(1 - *)RP ∂t ∂z ∂z ∂z (i ) 1, N) (1) together with initial and Danckwerts boundary conditions:

cTi (0, z) ) cT0 i (z)

( ) ( )

ucLi (t,0) - D

∂cLi ∂z

∂cLi ∂z

(t,z)0)

(t,z)l)

(i ) 1, N)

) ucFi (t)

)0

(2)

(i ) 1, N)

(3a)

(i ) 1, N)

(3b)

Superscripts P and L indicate the polymer and the liquid phases, respectively, whereas F and 0 refer to the feed and initial states, respectively, l is the bed length, u is the superficial fluid-phase velocity, D is the axial dispersion coefficient, N is the number of components, excluding the polymer, i.e., N ) 4, µi is the stoichimetric coefficient of the ith component, and * ) + (1 - )p is the overall void fraction of the bed. The overall concentration of the ith species is given by the weighted sum of the fluid and polymer concentrations:

cTi ) *cLi + (1 - *)cPi

(4)

Finally, RP is the rate of the chemical reaction given by the following mass action law:

RP ) kcP1 cP2 (1 - Ω)

(5)

In the last equation, k is the Arrhenius-type reaction rate constant, and the term 1 - Ω, where Ω ) N ∏i)1 (aPi )µi/Keq with aPi being the activity of the ith component in the polymer phase and Keq the equilibrium constant, accounts for the presence of chemical equilibrium (Mazzotti et al., 1997). Under the assumption of negligible mass-transport resistances, the model is completed by enforcing multicomponent sorption equilibria, i.e., by equating the liquid- and polymer-phase activities of each component of the fluid mixture:

aPi ) aLi

(i ) 1, N)

(6)

Activities in the liquid phase have been evaluated using the UNIFAC model (Fredenslund et al., 1977) and the behavior of the polymeric phase has been described in the framework of the extended Flory-Huggins model. In particular, the activity aPi of the ith component in the multicomponent polymeric solution is given by N+1

ln aPi ) 1 + ln vPi N+1 j-1

∑ j)1

N+1

mijvPj +

χijvPj ∑ j)1

(

5

mikvPj vPk χkj + ηVi vPp ∑ ∑ 3 j)1 k)1

(1/3)

)

7 - vPp (7) 6

Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3165

where vPi is the volume fraction of the ith component in the polymer phase, the polymer is referred to by the P index j ) N + 1 and vPp ) vN+1 , χij represents the binary interaction parameter between components i and j, Vi is the molar volume of the ith component, and mij ) Vi/Vj (note that mip ) 0). The parameter η accounts for the elasticity of the polymeric network, and its definition can be found in Flory (1953). Note that, according to its definition, the swelling ratio, q, equals 1/vPp . It is worth mentioning that the above thermodynamic model accounts implicitly for the interactions between the four chemical species and the different groups of the polymer matrix (i.e., sulfonic groups, hydrocarbon backbone, and aromatic rings) (see Gates (1992)). The local value of * is variable as a function of the swelling ratio according to the following expression:

* ) 1 - q(1 - D) ) 1 - (1 - D)/vPp

(8)

where D is the overall void fraction of the bed packed with the dry resin, i.e., D ) 1 - (W/Fp)/VR, W being the mass of dry resin used, Fp the density of the dry resin, and VR the volume of the reactor. The assumption of constant fluid-phase velocity can be assessed by considering the following equation:

∂u ) (1 - *)RP∆Vr ∂z

(9)

This is obtained by summing eq 1 multiplied by Vi, N N+1 P observing that ∑i)1 cLi Vi ) 1 and ∑i)1 ci Vi ) 1, since the volume additivity law holds true in this case, and using N eq 8. In eq 9, ∆Vr ) ∑i)1 µiVi is the molar volume change of the reaction, which is a rather small value (at T ) 293 K, it is equal to 0.15 mL/mol, i.e., < 1 % of the average molar volume); therefore, we can consider u constant along the bed. It is worth recasting the model equations in dimensionless form by introducing dimensionless time, τ ) tu/ l, and space, x ) z/l, coordinates, by using volume fractions vi ) ciVi instead of mole concentrations, and by defining the following two dimensionless groups:

Da )

l(1 - D)/u V2/k

(10)

d2/D d/u

(11)

Pe )

The Damko¨hler number Da is defined as the residence time divided by the characteristic time of the chemical reaction, which are the numerator and the denominator of eq 10, respectively. The former is defined with respect to the void volume of the dry bed; the latter involves the molar volume of ethanol rather than that of acetic acid, because it has been shown that above a critical ethanol concentration value, the reaction exhibits zeroth and first order with respect to ethanol and acetic acid, respectively (Mazzotti et al., 1996). The Peclet number is the ratio of the characteristic times of axial dispersion and convection on the characteristic length represented by the particle diameter. A heterogeneous liquid system is considered in this work; therefore, the axial dispersion can be calculated with the equation of Chung and Wen (1968):

Pe ) ud/D ) 0.20 + 0.011Re0.48 d

(12)

where Red is the Reynold number referring to the particle diameter. In the conditions of our experiments, the term depending on the Reynolds number is negligible (Red is between 0.5 and 1.5). Therefore, since u is constant, the axial dispersion coefficient can also be assumed to be constant along the column. The following dimensionless model equations are obtained

( )

T ∂vTi ∂vTi 1 d ∂ ∂vi + ) + ∂τ ∂x Pe l ∂x ∂x P P v1 v 2 µimi1Da P (1 - Ω) vp

(i ) 1, N) (13)

together with the corresponding dimensionless form of the initial and boundary conditions:

viT(0, x) ) vT0 i (x) vLi (τ,0) -

( ) ( )

L d ∂vi Pe l ∂x

∂vLi ∂x

(τ,x)0)

(τ,x)0)

)0

(i ) 1, N) ) vFi (τ)

(14)

(i ) 1, N) (15a)

(i ) 1, N)

(15b)

The model equations are solved using the method of lines. Space discretization is performed using finite central differences, except for the entrance and the exit of the reactor where concentration space derivatives are calculated using a forward and a backward first-order discretization, respectively. The discretized equations are integrated in time using a standard routine for stiff ordinary differential equations. 3. Results and Discussion 3.1. Chromatographic Reactor Behavior. The chromatographic reactor can be operated as a batch reaction/separation process, alternating two different stages. These are the reaction stage, where the mixture of the reactants is continuously fed to the fixed bed initially saturated with the solvent, and the following regeneration stage where the same solvent is used to regenerate the stationary phase. In the particular case of the esterification reaction under examination, it is noteworthy that one of the two reactants, in most experiments ethanol, can be used as the solvent. This allows us to directly scale-up this technique to the continuous operation obtained using a simulated moving bed unit (Mazzotti et al., 1996). With reference to the reaction stage, the behavior of the fixed bed chromatographic reactor can be briefly described as follows. A mixture of ethanol and acetic acid is continuously fed to the fixed bed initially saturated with ethanol. As the reactants enter the column, they are sorbed, and under the catalytic effect of the resin, the reaction starts. Water is kept by the resin, whereas ethyl acetate is soon desorbed and carried by the fluid stream along the column. Since one of the products is removed from the reaction locus, esterification proceeds until consumption of the limiting reactant. At each specific location in the bed, this process continues until water saturates the resin; afterwards, the local composition remains constant and equal to the steady-state one. The case where the feed is constituted by an equimolar mixture of the two reactants is illustrated in Figure 1, where the time evolution of the outlet composition is reported (samples


Figure 1. Reaction experiment. Operating conditions: bottomup flow; Q ) 0.73 mL/min; W ) 50 g; initial state, ethanol; acid/ ethanol mole ratio in the feed, 50/50. Experimental data: (b) acetic acid; (×) ethanol; (+) water; (O) ethyl acetate. Model results: (s) acetic acid; (- - -) ethanol; (‚‚‚) water; (- ‚ -) ethyl acetate.

Figure 2. Regeneration experiment. Operating conditions: topdown flow; Q ) 0.97 mL/min; W ) 50 g; initial state, steady-state achieved during the reaction experiment of Figure 1; acid/ethanol mole ratio in the feed, 0/100. Symbols as in Figure 1.

of the outlet stream have been periodically collected and analyzed). First, the weakly sorbed product, i.e., ethyl acetate, breaks through together with ethanol. After water saturates the whole bed of resin, water and acetic acid break through together and the steady-state equilibrium composition is attained. At this time, the reactor has achieved steady-state conditions; in terms of space concentration profiles along the column, these correspond to the monotonically increasing and decreasing concentration profiles of products and reactants, respectively, asymptotically approaching the equilibrium composition, which are typical of tubular reactors. Before starting a new reaction, the resin must be regenerated by removing all the sorbed species. This can be accomplished using ethanol itself as the desorbent as illustrated in Figure 2. The weakly sorbed components, i.e., ethyl acetate and acetic acid, are soon desorbed through a rather sharp transition. On the contrary, eluting water requires much more time, as expected, based on classical chromatographic theory since water is more strongly retained by the resin than ethanol. Two other reaction experiments are illustrated in Figures 3 and 4, corresponding to a 30/70 and 70/30 acetic acid/ethanol mole ratio in the feed mixture, respectively.

Figure 3. Reaction experiment. Operating conditions: bottomup flow; Q ) 1.07 mL/min; W ) 50 g; initial state, ethanol; acid/ ethanol mole ratio in the feed, 30/70. Symbols as in Figure 1.

Figure 4. Reaction experiment. Operating conditions: bottomup flow; Q ) 1.11 mL/min; W ) 48 g; initial state, ethanol; acid/ ethanol mole ratio in the feed, 70/30. Symbols as in Figure 1.

In all of the above mentioned figures, not only the experimental data but also the results obtained using the model presented in the previous section are reported. It can be observed that the agreement between experiment and theory is satisfactory, in particular if one takes into account that the model is fully predictive. Even though some discrepancies in the breakthrough times and in the peak shapes can be found, the overall picture of the profiles and the values of the concentration corresponding to the composition plateaus are well predicted. Special attention should be paid to the fact that the model correctly predicts the breakthrough profiles in Figure 4, exhibiting three composition fronts instead of only two as in Figures 1 and 3. This issue will be deepened in section 3.4. 3.2. Hydrodynamic Regime. The chemical species involved in the reaction under examination exhibit rather large differences in their density values. In particular, at 20 °C, the densities are 1.05, 0.79, 1.00, and 0.90 g/mL for acetic acid, ethanol, water, and ethyl acetate, respectively. These differences have important consequences on the hydrodynamic regime of the chromatographic reactor, as it is illustrated in Figures 5 and 6. Here two different experiments performed in the fixed bed column in the absence of reaction are illustrated; in both cases, bottom-up flow is adopted. In Figure 5, water displaces ethanol, which initially saturates the column. The model prediction is in very good


Figure 5. Breakthrough experiment: water displacing ethanol. Operating conditions: bottom-up flow; Q ) 4.63 mL/min; W ) 47 g. (*) Experimental data. (s) Model results.

Figure 6. Breakthrough experiment: ethanol displacing water. Operating conditions: bottom-up flow; Q ) 1.10 mL/min; W ) 50 g. (*) Experimental data. (s) Model results. PeL ) Pe(l/d) ) 125 (real experimental conditions): (- - -) PeL ) 12.5; (- ‚ -) PeL ) 5.8.

agreement with the experimental data. Since water is more favorably sorbed than ethanol, the breakthrough front is self-sharpening. However, it is worth noting that the upper part of the front is more rounded than its lower part; this is in very good agreement with the thermodynamic behavior of the water-ethanol binary system whose selectivity decreases to 1 when the ethanol concentration becomes very small (Mazzotti et al., 1996). In Figure 6, ethanol displaces water, but in this case, the experimental breakthrough front of ethanol is rather unusual and differs drastically from the model prediction. These two quite different results can be explained by considering the density differences. Since ethanol has a lower density than water, when the ethanol layer is below the water layer, as in the case of the second experiment, the front between the two layers is unstable. On the contrary, the front is stable when water is below ethanol, as in the first experiment. These conclusions are confirmed by a third experiment, which is illustrated in Figure 7. This again refers to ethanol displacing water, but in this case, the flow is top-down, thus keeping the lighter ethanol layer above the heavier water layer. Theory and experiment are again in good agreement. The concentration front has a dispersive character, as expected, since a weaker component, i.e., ethanol, displaces a stronger one, i.e., water. However, also in this case, the selectivity

Figure 7. Breakthrough experiment: ethanol displacing water. Operating conditions: top-down flow; Q ) 2.60 mL/min; W ) 43 g. (*) Experimental data. (s) Model results.

approaching 1 at large water concentration makes the corresponding lower part of the front rather sharp. The phenomenon described above has a negative effect on the separation efficiency and must be avoided. It has already been observed in other applications, for example, in the chromatographic treatment of sugar solutions, where it is kept under control by properly choosing the column configuration and the flow rates (Hongisto, 1977). In our case, it is rather evident that the reaction experiments (cf. Figures 1, 3, and 4) should be run with a bottom-up flow, because the feed mixture constituted of ethanol and acetic acid is heavier than ethanol alone. On the contrary, the regeneration experiment illustrated in Figure 2 has been performed adopting a top-down flow, since the regenerating agent, i.e., ethanol, is the lightest species and the steady-state composition profile within the column at the end of the reaction experiment has certainly a larger density. If the same regeneration experiment is run with a bottomup flow, then very disperse concentration profiles occur at the column outlet, which hinder the efficiency of both the regeneration step and the overall process. The front instability observed during the experiment illustrated in Figure 6 yields axial mixing on a larger scale than the solid particle diameter, which is considered to be the characteristic length when estimating the Peclet number according to eq 12. Enhanced axial mixing due to density gradients has been observed and measured in extraction columns of different kinds (Baird et al., 1992; Aravamudan and Baird, 1996), and a relationship has been developed which accounts for up to 10-20-fold increase of the axial dispersion coefficient in the presence of density gradients (Holmes et al., 1991). This approach is not feasible in our case since, under these conditions, the porous nature of the fixed bed produces wall effects and channeling which cannot be described by simply using a modified Peclet number. This is confirmed in Figure 6, where the calculated results obtained using Peclet number values 10 and 20 times smaller than those in the absence of channeling are shown. In neither case do the model results get close to the experimental data, thus indicating that the observed phenomenon cannot be accounted for by assuming homogeneous flow conditions on a cross section of the fixed bed. 3.3. Composition Fronts. To the aim of achieving a deeper understanding of the behavior of the chromatographic reactor, it is rather useful to analyze the


Figure 8. Volume fractions of the various components in the fluid phase along the column, at different times, during the reaction experiment of Figure 1.

experimental and model results in terms of composition fronts and propagation velocities. These are classical concepts in nonlinear chromatography, which we are going to use also in the case of reactive chromatography. The aim of this and the next section is to clarify the analogies between these two situations and to underline how appropriate and enlightening this approach can be. The outcome of the reaction experiment illustrated in Figure 1 indicates the existence of two concentration fronts propagating along the reactor. The faster front is the breakthrough front of ethyl acetate, or the elution front of ethanol, which comes out between dimensionless times 0.5 and 0.8. This is a separative front, since no reaction takes place in the presence of only ethanol and ethyl acetate. The slower front is the breakthrough front of water and acetic acid or, in other words, that of the steady-state equilibrium composition corresponding to the selected acetic acid-to-ethanol mole ratio in the feed stream. This comes out at about τ ) 1.3 and is a reactive front where esterification and separation of products take place. Between the two fronts, an ethyl acetate rich composition plateau is observed, due to the occurrence of the following events: ethyl acetate is produced at the reaction front; then, it is soon desorbed by the resin; finally, it is pushed ahead of the reactive

front by water, which is progressively saturating the stationary phase along the column. The analysis of the above composition fronts can be better done by considering their propagation along the column. This is not possible experimentally, but it is very simple using the model. Therefore, let us consider the fluid concentration profiles along the column calculated using the same operating conditions of Figure 1. For each chemical species, four concentration profiles are drawn in Figure 8, each corresponding to a different time between τ ) 0.3 and τ ) 0.9, so that the dimensionless time interval between two successive profiles is ∆τ ) 0.3. First let us consider Figure 8a concerning acetic acid. The envelope of all the concentration profiles is the steady-state concentration profile of acetic acid, which indicates that this is consumed in the first portion of the reactor, until it reaches and maintains its equilibrium concentration level; i.e., vL1 ) 0.175. With reference to the transient concentration profiles, say, for example, the ninth profile given by the solid line dropping to zero close to x ) 0.8 and corresponding to τ ) 0.9, two sharp concentration transitions can be observed: the first one occurs at the entrance of the reactor and corresponds to the consumption of acetic


acid due to the reaction taking place in a zone of the reactor where steady-state conditions have already been achieved. This first transition does not propagate along the column; hence, it is not a traveling front, as those observed in nonlinear chromatography. After the reaction has reached the equilibrium conversion (at about x ) 0.4), the acetic acid concentration does not change any more until the second transition occurs (at about x ) 0.8). This last transition corresponds to the reaction front breaking through at about τ ) 1.2 in Figure 1. This is indeed a self-sharpening traveling front since it can be readily seen that it exhibits constant pattern behavior; i.e., it propagates along the column at constant velocity without changing its shape (cf. Rhee and Amundson, 1974; Mazzotti et al., 1994). Thanks to the selective role of the resin, the reaction is driven to completion, and therefore, on the right-hand side of the reaction front, the acetic acid concentration vanishes. By inspection of the reaction rate profiles along the reactor (not reported here), it is verified that the esterification reaction proceeds only in the first part of the reactor and across the reaction front, i.e., when the acetic acid concentration varies. These observations indicate that the fluid mixture starts reacting again when it takes over the reaction front, even though its composition has already reached chemical equilibrium condition. This happens because the fluid mixture gets in contact with the stationary phase on the right-hand side of the reaction front, having a different composition with respect to the equilibrium one corresponding to the fluid mixture itself. As a consequence, mass-transport processes between the two phases are activated; these drive the two phases away from chemical equilibrium, thus starting the chemical reaction again. It is remarkable that the second transition in Figure 8a, i.e., the reaction front, exhibits a constant pattern behavior, which is typical of self-sharpening fronts in nonreactive nonlinear chromatography, even though a chemical reaction occcurs. The space concentration profiles of water drawn in Figure 8c are very similar. The only differences are the following ones: firstly, water concentration increases at the entrance of the reactor because water is a product of the reaction; secondly, it decreases through the reaction front because water is sorbed by the resin while it is produced; finally, though a reactant, water cannot run over the reaction front, as ethyl acetate does, because the whole amount of water produced there is kept by the resin. Now let us consider Figure 8d dealing with ethyl acetate. With particular reference to the profile at τ ) 0.9, three concentration changes are observed: the first one corresponds to the steady-state reaction zone at the entrance of the reactor where ethyl acetate is produced. The second one involves again an increase of ethyl acetate concentration through the reaction front and is due to production and immediate desorption. It is worth noting the buildup of a large amount of ethyl acetate on the right-hand side of this last front. The third transition, which marks a fall of concentration from almost 0.9 to 0, corresponds to the breakthrough front of ethyl acetate, through which ethanol is eluted as illustrated in Figure 8b. This is a purely separative front, since no reaction takes place, and as expected, due to the stronger affinity of ethanol with respect to ethyl acetate, it has a dispersive character. In fact, it can be readily observed that the slope of the transition decreases while it travels along the column. Moreover, its propagation velocity is larger than that of the

reaction front. As a consequence, the high-concentration peak of ethyl acetate gets larger and larger along the reactor. The ethanol concentration profiles in Figure 8b deserve a final comment. They exhibit a rather evident peak just on the left-hand side of the reaction front, which, in this particular case, corresponds to a rather small change of the ethanol concentration. Nevertheless, this peak is indeed a realistic feature of the process since it can be observed also in the experimental and calculated breakthrough curves in Figure 1 (cf. also Figure 5 of the paper by Mazzotti et al. (1996), referring to a similar reaction experiment, where the mole fraction representation emphasizes this concentration peak in the experimental profile). It is remarkable that in the case of ethanol, this part of its concentration profile as a whole, i.e., the peak and the immediately following decreasing front, behaves as a constant pattern. This is a behavior that cannot exist in nonreactive chromatography and can be explained by considering that two counteracting phenomena occur when the equilibrium composition on the left-hand side of the reaction front takes over the ethyl acetate rich state on the right-hand side of it. At that time, as already discussed above, an ethanol-rich polymer phase, with neither water nor acetic acid, comes into contact with a fluid phase at chemical equilibrium. The tendency toward the attainment of physical equilibrium promotes the sorption of water and some acetic acid and the desorption of ethanol and even more ethyl acetate. This is the first phenomenon which would increase the fluid phase ethanol concentration if it occurred alone. On the other hand, these transport processes between the fluid and the polymer phase move the system away from chemical equilibrium. Thus, esterification proceeds, and ethanol is consumed; this is the second phenomenon yielding a decrease of ethanol concentration. The combination of the two is responsible for the peculiar observed shape of the ethanol concentration profile. Thus summarizing, the analysis of the concentration spatial patterns has proved that several concepts of nonlinear chromatography can be applied also to the case of reactive chromatography, even though the system under examination is not only reactive but also characterized by complex multicomponent sorption equilibria. We believe that these findings can be exploited, in particular, for scale-up purposes. In fact, based on well-established theories, concepts such as composition fronts and propagation velocities can be easily scaled up in classical chromatography. The results presented above indicate that the same may be done also in the case of reactive chromatography. 3.4. Dynamic Behavior. In the frame of equilibrium theory, the solution of a displacement or elution problem in dimensionless coordinates depends only on the initial and feed compositions (Helfferich and Klein, 1970; Rhee et al., 1970). Knowing the solution, information about the composition of the concentration plateaus and the speed of propagation of the transitions separating them can be easily derived and applied to whatever column size or feed flow rate. As we have seen, also the breakthrough profiles observed in a chromatographic reactor can be interpreted in terms of composition fronts. Therefore, also in this case, it is interesting to analyze the effect of changing feed composition on its dynamic behavior. This effect is indeed important, as it can be readily noted by considering again Figures 1, 3 and 4, dealing


with feed mixtures with acetic acid-to-ethanol mole ratios of 50/50, 30/70, and 70/30, respectively. The first two figures illustrate a similar dynamic behavior from the qualitative point of view, being characterized by two composition fronts breaking through at similar dimensionless times. However, due to the different feed composition, from the quantitative point of view differences are observed in the concentration profiles in Figures 1 and 3, in particular in the ethyl acetate rich concentration plateau and the steady-state equilibrium compositions. On the contrary, the overall picture is not only quantitatively different but also qualitatively different in the case illustrated in Figure 4. Here three composition fronts occur; the first one is the well-known nonreactive dispersive front corresponding to the breakthrough of ethyl acetate and the elution of ethanol. The third front is the main reactive front through which the final steady-state equilibrium plateau breaks through. The second front separates an ethyl acetate rich state, which consists of the ethyl acetate peak at about τ ) 0.8, and a composition plateau where not only large concentrations of ethyl acetate and acetic acid but also very small amounts of water and ethanol are present (notice that this is indeed the case, even though the concentration profiles of water and ethanol in Figure 4 are very close to the horizontal axis in the elution time period corresponding to this plateau). It can be shown that this composition plateau is at chemical equilibrium and that the second front is reactive and self-sharpening. The existence of a new front and a new intermediate state with respect to the case illustrated in Figure 1 is due to the presence of an acetic acid excess in the feed. In fact, acetic acid is not completely consumed through the main reactive front (the third one in Figure 4). Thus, beyond this reactive front, i.e., on its left-hand side in Figure 4, the produced ethyl acetate and the unreacted acetic acid are certainly present, thus forming a well-defined acetic acid rich composition plateau. The mixture constituting this plateau is separated while traveling along the column and the weakly sorbed ethyl acetate travels faster than the mixture itself. Therefore, an ethyl acetate rich state is formed, which desorbs ethanol through a dispersive nonreactive front (the first one in Figure 4) exactly in the same manner as in the cases illustrated in Figures 1 and 3. When the acetic acid rich mixture takes over the ethyl acetate rich state, acetic acid reacts with ethanol until complete consumption, because the produced water is immediately separated by ethyl acetate due to its preferential sorption. This composition transition constitutes the second front, which is indeed reactive. Behind this front, i.e., on its right-hand side in Figure 4, the produced and sorbed water is present together with ethyl acetate and acetic acid, as explained above; therefore, also a small amount of ethanol must be present as well, in accordance to the rules of chemical equilibrium. The correctness of this interpretation is assessed by considering experiments where the column is initially saturated with acetic acid. In this case, a similar dynamic behavior is observed; when the amount in the feed of the species initially present in the column, i.e., acetic acid in this case, is equal or larger than the stoichiometric one, then only two fronts are present. On the contrary, when acetic acid is the limiting reactant, then three fronts are present, the second one being necessary to complete the reaction of ethanol, i.e., the excess reactant. The latter behavior is illustrated in

Figure 9. Reaction experiment. Operating conditions: top-down flow; Q ) 1.16 mL/min; W ) 48 g; initial state: acetic acid; acid/ ethanol mole ratio in the feed: 30/70. Symbols as in Figure 1.

Figure 10. Effect of feed composition on the dynamic behavior of the chromatographic reactor initially saturated with ethanol. Regions corresponding to different composition states appearing at the outlet of the reactor at different dimensionless times. (s) Reactive self-sharpening fronts; (- - -) edges of nonreactive dispersive fronts. Composition states: E, pure ethanol; L, ethyl acetate breakthrough/ethanol elution front; H, ethyl acetate rich plateau; Q1, acetic acid rich equilibrium state; Q2, steady-state equilibrium composition.

Figure 9. It is worth noting that in this case, a topdown flow has been adopted, since the feed mixture containing ethanol has a smaller density than pure acetic acid. Nevertheless, the last reactive front is rather disperse due to unfavorable density gradients which occur between the upper steady-state equilibrium layer (F ≈ 0.86 g/mL) and the lower ethanol-rich layer (F ≈ 0.85 g/mL). The overall picture of the effect of feed composition on the dynamic behavior of the chromatographic reactor initially saturated with ethanol is provided by Figure 10. This is a master plot which reports the breakthrough times of the different composition fronts as a function of the feed composition, expressed in terms of ethanol mole fraction. Thanks to the use of the dimensionless time coordinate, this diagram is independent of column size and flow rate provided that the residence time, i.e., the Damko¨hler number, is large enough to guarantee an efficient separation. In particular, solid


lines represent reactive self-sharpening shocks, whereas broken lines represent the edges of the nonreactive dispersive transition through which ethyl acetate breaks through; the region corresponding to this transition is labeled with the symbol L. Below this region, i.e., for shorter elution times, the pure ethanol initial state E is observed. Above the L region, there are three more regions. For large elution times, the chromatographic reactor achieves the steady-state equilibrium composition. The corresponding region is labeled Q2 and is constituted by points sharing the property of representing equilibrium steady states. Along vertical lines, the states have the same composition, whereas different vertical lines correspond to different equilibrium compositions: examples of these are the steady-state equilibrium compositions observed in Figures 1, 3 and 4 obtained for different feed mixtures. The second region constituted by points representing chemical equilibria is labeled Q1; this is observed only when the acetic acid concentration in the feed is above the stoichiometric value and represents the intermediate equilibrium state where mainly acetic acid and ethyl acetate are present (also in this case, vertical segments in this region correspond to the same composition, whereas along horizontal lines different compositions are found). Finally, region H consists of points corresponding to the ethyl acetate rich intermediate plateau (also in this case, the region is characterized by a qualitative feature rather than by a specific fluid composition). This is the most interesting region from an applicative point of view since here ethyl acetate is present at large concentrations in the absence of water and can be rather easily recovered. However, the time interval corresponding to the occurrence of this plateau at the outlet of the reactor is very short when the ethanol mole fraction in the feed is smaller than 0.5, i.e., when the state Q1 is present. This implies that operating with an excess of ethanol in the feed is recommended whenever the recovery of pure ethyl acetate is the main objective of the process; this excess should not be too large, to avoid an unacceptable dilution of ethyl acetate in the recovered stream. Thus summarizing, for a given feed composition, the master plot in Figure 10 allows us to derive the dynamic behavior of the chromatographic reactor in terms of composition of the outlet stream. This may be done by following the vertical straight line corresponding to the given ethanol mole fraction in the feed from the horizontal axis, i.e., from the beginning of the reaction, until the achievement of the final steady-state equilibrium. This master plot, which provides a synthetic representation of the different operative regimes of the chromatographic reactor, can be very useful in applications, since it allows us to identify the best operating conditions for a desired process performance. Nomenclature a ) activity c ) molar concentration d ) particle diameter D ) axial dispersion coefficient Da ) Damko¨hler number defined by eq 10 k ) kinetic constant Keq ) equilibrium constant l ) reactor length mij ) ratio of molar volumes, mij ) Vi/Vj N ) number of liquid components, N ) 4

Pe ) Peclet number defined by eq 11 PeL ) Peclet number referring to the bed length, PeL ) Pe(l/ d) q ) swelling ratio Q ) fluid flow rate RP ) reaction rate t ) time T ) temperature u ) superficial fluid-phase velocity v ) volume fraction V ) molar volume of the ith specie ∆Vr ) molar volume change of reaction VR ) reactor volume x ) dimensionless axial coordinate, x ) z/l W ) mass of dry resin z ) axial coordinate Greek Letters ) interparticle porosity p ) intraparticle porosity * ) overall void fraction of the bed, * ) + (1 - )p D ) overall void fraction of the bed packed with the dry resin η ) elasticity parameter µ ) stoichiometric coefficient F ) density τ ) dimesionless time, τ ) tl/u χ ) Flory-Huggins binary interaction parameter N (aPi )µi/Keq Ω ) chemical equilibrium parameter, Ω ) ∏i)1 Subscripts and Superscripts 1 ) acetic acid 2 ) ethanol 3 ) water 4 ) ethyl acetate F ) feed L ) liquid phase p ) resin P ) polymer phase T ) overall quantity 0 ) initial quantitySection 5 Bibliography

Literature Cited Aravamudan, K.; Baird, M. H. I. Effect of unstable density gradients on back-mixing in a reciprocating plate column. AIChE J. 1996, 42, 2128. Baird, M. H. I.; Aravamudan, K.; Rama Rao, N. V.; Chadam, J.; Peirce, A. P. Unsteady axial mixing by natural convection in a vertical column. AIChE J. 1992, 38, 1825. Bjorklund, M. B.; Carr, R. W. The simulated countercurrent moving bed chromatographic reactor: a catalytic and separative reactor. Catal. Today 1995, 25, 159. Cho, B. K.; Aris, R.; Carr, R. W. The mathematical theory of a counter-current catalytic reactor. Proc. R. Soc. London. 1982, A383, 419. Chung, S. F.; Wen, C. Y. Longitudinal dispersion of liquid flowing through fixed and fluidized beds. AIChE J. 1968, 14, 857. Flory, P. J. Principles of Polymer Chemistry; Cornell University: London, 1953. Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier: Amsterdam, 1977. Gates, B. C. Catalytic Chemistry; Wiley: New York, 1992. Hashimoto, K.; Adachi, S.; Noujima, H.; Udea, Y. A New Process combining adsorption and enzyme reaction for producing higher fructose syrup. Biotechnol. Bioeng. 1983, 25, 2371. Helfferich, F. G.; Klein, G. Multicomponent chromatography: theory of interference; Marcel Dekker: New York, 1970. Holmes, T. L.; Karr, A. E.; Baird, M. H. I. Effect of unfavorable continuous phase density gradient on axial mixing. AIChE J. 1991, 37, 360. Hongisto, H. J. Chromatographic separation of sugar solutions. Int. Sugar J. 1977, 79, 100.

3172 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 Kawase, M.; Suzuki, T. B.; Inoue, K.; Yoshimoto, K.; Hashimoto, K. Increased esterification conversion by application of the simulated moving-bed reactor. Chem. Eng. Sci. 1996, 51, 2971. Kruglov, A. V. Methanol synthesis in a simulated countercurrent moving-bed adsorptive catalytic reactor. Chem. Eng. Sci. 1994, 49, 4699. Kruglov, A. V.; Bjorklund, M. B.; Carr, R. W. Optimization of the simulated countercurrent moving-bed chromatographic reactor for the oxidative coupling of methane. Chem. Eng. Sci. 1996, 51, 2945. Loureiro, J. M.; Soares, R. C.; Rodrigues, A. E. Dynamics of Adsorptive Reactors. In Preparative and Production Scale Chromatography; Chromatographic Science Series; Ganetsos, G. Barker, P. E., Eds.; Marcel Dekker: New York, 1993; Vol. 61, pp 741-767. Mazzotti, M.; Storti, G.; Morbidelli, M. Shock layer analysis in multicomponent chromatography and countercurrent adsorption. Chem. Eng. Sci. 1994, 49, 1337. Mazzotti, M.; Kruglov, A.; Neri, B.; Gelosa, D.; Morbidelli, M. A continuos chromatographic reactor: SMBR. Chem. Eng. Sci. 1996, 51, 1827. Mazzotti, M.; Neri, B.; Gelosa, D.; Kruglov, A.; Morbidelli, M. Kinetics of the liquid-phase esterification catalysed by acidic resin. Ind. Eng. Chem. Res. 1997, 36, 3. Ray, A.; Carr, R. W. Experimental study of a laboratory-scale simulated countercurrent moving bed chromatographic reactor. Chem. Eng. Sci. 1995, 50, 2195. Rhee, H.-K.; Amundson, N. Shock layer in two solute chromatography: effect of axial dispersion and mass transfer. Chem. Eng. Sci. 1974, 29, 2049.

Rhee, H.-K.; Aris, R.; Amundson, N. On the theory of multicomponent chromatography. Phil. Trans. R. Soc. London 1970, A267, 419. Sardin, M.; Villermaux, J. Este´rification catalyseé par une re´sine ećhangeuse de cation dans un reácteur chromatographique. Nouv. J. Chim. 1979, 3, 255. Sardin, M.; Schweich, D.; Villermaux, J. Preparative fixed-bed chromatographic reactor. In Preparative and Production Scale Chromatography; Chromatographic Science Series; Ganetsos, G., Barker, P. E., Eds.; Marcel Dekker: New York, 1993; Vol. 61, pp 477-521. Schweich, D.; Villermaux, J.; Sardin, M. An introduction to the nonlinear theory of adsorptive reactors. AIChE. J. 1980, 26, 477. Tonkovich, A. L.; Carr, R. W. A simulated countercurrent movingbed chromatographic reactor for the oxidative coupling of methane: experimental results. Chem. Eng. Sci. 1994, 49, 4647.

Received for review October 9, 1996 Revised manuscript received March 20, 1997 Accepted March 20, 1997X IE9606348

X Abstract published in Advance ACS Abstracts, June 15, 1997.

Dynamics of a Chromatographic Reactor - American Chemical Society

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