Reaction Kinetics for Reactive Distillation Using Different Laboratory

Article pubs.acs.org/IECR

Reaction Kinetics for Reactive Distillation Using Different Laboratory Reactors Erik von Harbou,*,† Amir Yazdani,† Markus Schmitt,‡ Christoph Großmann,‡ and Hans Hasse† †

Laboratory of Engineering Thermodynamics, University of Kaiserslautern, Erwin-Schrödinger-Straße 44, 67663 Kaiserslautern, Germany ‡ BASF SE, GCP/TA - L540, 67056 Ludwigshafen, Germany S Supporting Information *

ABSTRACT: The reaction kinetics of the heterogeneously catalyzed esterification of n-hexyl acetate were measured using both a batch reactor and continuous stirred tank reactor (CSTR). The catalyst was Amberlyst CSP2. The results of the batch reactor and CSTR experiments were compared to reaction kinetic measurements carried out in previous work using a plug-flow reactor (PFR). Because the change in the composition of the reaction mixture in the batch reactor is caused not only by reaction but also by component-specific adsorption on the catalyst, the batch reactor is not recommended for reaction kinetic measurements of the present type of chemical system. The results from the CSTR and PFR are in very good agreement with regard to the measured rate of reaction. To address the impact of the conditions present in a heterogeneously catalyzed reactive distillation (HCRD) column on the performance of the catalyst, the influences of boiling and of the reduction of the low-boiling components (here, water) on the rate of reaction were investigated using the CSTR. Neither was found to have a significant impact on the performance of the catalyst. A simple pseudohomogeneous model was fitted to the data of the CSTR experiments using a reparameterized Arrhenius equation to avoid parameter coupling. The model predictions and experimental results are in good agreement.

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INTRODUCTION The potential of heterogeneously catalyzed reactive distillation (HCRD) for improving chemical processes is well-known.1 The kinetics of the occurring chemical reactions plays a major role in the performance of an HCRD process. Therefore, a detailed understanding of the reaction kinetics is necessary for the reliable design, scale-up, and operation of an HCRD apparatus.2 For the esterification of n-hexanol and acetic acid to form nhexyl acetate and water catalyzed by an ion-exchange resin, Schmitt and Hasse3 carried out a detailed investigation of the reaction kinetics in a plug-flow reactor (PFR) involving the development of a model. The same test system was employed for a considerable number of experiments with a laboratoryscale HCRD setup equipped with two different types of catalytic internals.4,5 Surprisingly, predictive simulations of the HCRD experiments using the kinetic model described by Schmitt and Hasse3 did not yield satisfying results, even though the simulations were based on a comprehensive, thoroughly validated database.6 By means of a sensitivity analysis, Schmitt et al.7 demonstrated that the simulation of HCRD experiments is strongly sensitive to the rate of reaction. Obviously, the kinetic model is not able to predict the rate of reactions correctly under the conditions present in an HCRD column. Schmitt6 discusses possible explanations such as experimental errors or differences between the conditions under which the rate of reaction was measured in a laboratory reactor and those present in an HCRD column. Thus, the objective of the present work was to investigate all relevant parameters that are important for the development of a reliable reaction kinetic model that is suitable for the utilization in HCRD process models. © 2012 American Chemical Society

Many measurements of esterification reaction kinetics that are heterogeneously catalyzed by ion-exchange resins have been reported in the literature. Mostly, batch reactor setups were employed for these measurements, for example, in the works of Pöpken et al.,8 Steinigeweg and Gmehling,9 Altıokka and Ç ıtak10 Gangadwala et al.,11 Teo and Saha,12 Calvar et al.,13 Izci and Bodur,14 Patel and Saha,15 and Kolah et al.16 A PFR was employed by both Schmitt and Hasse3 and Lee et al.17 Other groups such as Rehfinger and Hoffmann18 and Pfeuffer et al.19 used continuous stirred-tank reactors (CSTRs) for similar chemical systems also catalyzed by ion-exchange resins. These studies of reaction kinetics have in common that only one type of reactor was used. The present work is dedicated to comparing results from different reactor types, namely, batch reactor, CSTR, and PFR. The PFR results were taken from Schmitt and Hasse.3 The other data were measured in the present work. To enable a direct comparison, the input parameters (e.g., temperature of the reaction mixture, feed composition) for this study were adopted from the base-case experiment carried out by Schmitt and Hasse3 using a PFR. Furthermore, this article addresses the differences between the conditions under which the reaction kinetics are typically studied in a laboratory reactor and those present in an HCRD column. In a laboratory reactor, the liquid, which is in contact with the catalyst, is typically subcooled (not boiling), whereas it is boiling in an HCRD column. As the reaction proceeds, water Received: Revised: Accepted: Published: 624

May 31, 2012 December 5, 2012 December 5, 2012 December 5, 2012 dx.doi.org/10.1021/ie301428w | Ind. Eng. Chem. Res. 2013, 52, 624−637

Industrial & Engineering Chemistry Research

Article

is formed. Because water is a low-boiling component in this system, it is mainly present in the vapor phase under distillation conditions. If the evaporation of the water already takes place in the catalyst pores, it might affect the internal mass transfer significantly. A detailed discussion of the effect of gas production in liquid-filled catalyst pores is given, for example, by Datsevich.20 Second, in HCRD columns, the concentrations of the low-boiling components (here, water) are significantly reduced in the liquid phase. As a consequence, the concentration range in a laboratory reactor can differ substantially from that in an HCRD column. This difference in the concentrations of reactants, especially of water, can affect the performance of the catalyst through component-selective swelling of the catalyst and dissociation of the catalytically active sites.21,22 To study these two effects, the CSTR was operated at subcooled and boiling conditions, the latter both with total reflux (reflux mode) and without reflux (flash mode). The experiments at boiling conditions with total reflux can be compared directly to experiments at subcooled conditions (liquid mode) to study the influence of the boiling conditions. The experiments carried out in flash mode, which is under boiling conditions with a complete withdrawal of the aqueous distillate, enable studies in concentration ranges similar to those present in an HCRD column (i.e., low concentrations of water in the liquid phase but with considerable conversion). These results were compared to experiments carried out in liquid mode (i.e., the liquid was subcooled). To arrange the CSTR experiments as effectively as possible, that is, to reduce the experimental effort (e.g., the number of experiments and the consumption of chemicals) and to reduce the impact of experimental errors, a model-based design of experiments was used. The residence time in the CSTR was chosen for each CSTR experiment so that the sensitivity of the output parameters (i.e., the composition of the reaction mixture) to the rate of reaction was maximized. In addition, for the comparison of the CSTR experiments at boiling and subcooled conditions, the sensitivity to the rate of reaction was optimized by suitably choosing the input parameters (e.g., the feed composition and the temperature of the reaction mixture). Using the data from all of the CSTR experiments performed, a global parameter estimation was carried out on the basis of a pseudohomogeneous model. Because the intrinsic mathematical structure of the Arrhenius equation, which describes the temperature dependency of the rate of reaction, introduces a high correlation between the parameters,23,24 the Arrhenius equation was reparameterized as suggested by Buzzi-Ferraris and Manenti.25 The resulting model was validated by the prediction of PFR experiments not included in the parameter estimation. This work contributes to the understanding of the reaction kinetics in HCRD. It serves as a guideline for the development of kinetic models that are necessary for a reliable design, scaleup, and operation of HCRD and other processes in which the heterogeneously catalyzed reactions and evaporation and distillation occur simultaneously.

C6H13−OH + H3C−COOH 1 − hexanol

acetic acid

H+

HooI H3C−COO−C6H13 + H 2O n‐hexyl acetate

water

(I)

The conversion of this reaction is limited by chemical equilibrium. The hexyl acetate system shows strong liquid- and vapor-phase nonidealities.26 Because autocatalysis by acetic acid is very slow,3 the strongly acidic and fully sulfonated ionexchange resin Amberlyst CSP2 (Rohm and Haas) was used as a solid catalyst in the present work. The catalyst has a macrorecticular structure built by a polymer matrix. The macroporous polymer beads consist of microporous microgel particles that are agglomerated together to form clusters. The catalytically active sulfonic acid groups (−SO3H) are bonded to the polymer matrix and located at the surface and within the body of the resin beads.22 A short summary of the most important properties of the catalyst Amberlyst CSP2 is available in the Supporting Information. A systematic investigation of the side products and the reaction network of the hexyl acetate system was carried out by Schmitt and Hasse.3 Dihexyl ether (DHE) and 1-hexene (HEN) were identified as the main side products. In the experiments carried out in the present work, however, no significant formation of side products was observed. For this reason, only the main reaction I is considered here.

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REACTION KINETIC MODEL The reaction kinetics of the synthesis of n-hexyl acetate was studied by Schmitt and Hasse3 using a PFR. They tested both an adsorption-based reaction kinetic model and a pseudohomogeneous model. Despite its simplicity, the pseudohomogeneous model gave better results. For that reason, the pseudohomogeneous model was employed in this work as well. As thermodynamic consistency is important for the implementation of models of reactive distillation,27 the pseudohomogeneous model is formulated on the basis of activities ai ⎛ ⎞ 1 r = k f (T )⎜aHexOHaHAc − aHexAca H 2O⎟ K a (T ) ⎝ ⎠ = k f ( T ) A (T , x )

(1)

In eq 1, kf denotes the rate constant of the forward reaction, which is a function of only the temperature T. A denotes the activity term, which is a function of both the temperature T and the bulk concentrations of the reactants x. The strong nonidealities mentioned above are described by means of activity coefficients γi, calculated with the nonrandom twoliquid (NRTL) model. The NRTL parameters were adopted from Schmitt and Hasse,26 who adjusted them to vapor−liquid equilibrium data. The influence of pressure on the rate of reaction and the chemical equilibrium is negligible because the reaction takes place in the liquid phase only. The temperature dependency of the rate constant kf(T) is modeled with the Arrhenius equation

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CHEMICAL SYSTEM n-Hexyl acetate (HexAc) is a typical representative of fruit esters. It is used as a flavoring agent or in perfumes. n-Hexyl acetate is formed with water as an additional product by the acid-catalyzed esterification of 1-hexanol (HexOH) with acetic acid (HAc)

⎛ EA,f ⎞ k f (T ) = k f0 exp⎜ − ⎟ ⎝ RT ⎠

(2)

where k0f denotes the pre-exponential factor and EA,f is the apparent activation energy. 625

dx.doi.org/10.1021/ie301428w | Ind. Eng. Chem. Res. 2013, 52, 624−637


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concentration of active sites − protons) was determined by titration. Following the titration, the washed catalyst was predried for one day at ambient pressure and 50 °C, and then it was further dried for one day in a vacuum oven at a pressure below 0.1 mbar and a temperature of approximately 80 °C. After this, the mass of the dry catalyst was determined. Batch Reactor Experiments. Apparatus and Procedure. The batch reactor experiments were carried out in a thermostatted glass reactor with a total volume of 240 mL; see Figure 1. The reactor was equipped with a heating jacket

Schmitt and Hasse3 determined the temperature dependency of the chemical equilibrium constant Ka(T) by independent measurements and fitted the integrated form of the van’t Hoff equation to the experimental data

⎛ b⎞ K a(T ) = exp⎜a + ⎟ ⎝ T⎠

(3)

3

Schmitt and Hasse found a dependency of the rate constant on the concentration of the reactants. To improve the accuracy of the model prediction, they described the pre-exponential factor k0f as a simple linear function of the reduced mole fraction of hexanol X*HexOH given by 0 0 * k f0 = k f,a − k f,b XHexOH

* with XHexOH = x HexOH + min(x HexAc , x H 2O)

All parameters determined by Schmitt and Hasse available in the Supporting Information.

(4) 3

are

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EXPERIMENTAL SECTION Chemicals and Analysis. 1-Hexanol (reagent grade) and n-hexyl acetate (FCC grade) were purchased from SigmaAldrich. Acetic acid (technical grade) was provided by BASF. The final purities determined by gas chromatography for 1hexanol, acetic acid, and n-hexyl acetate were 0.994, 0.998, and 0.995 g/g, respectively. Furthermore, water was taken from an ultrapure water system. A Hewlett-Packard HP6890 gas chromatograph equipped with a capillary column (INNOWax, HP 19091N-213, length 30 m, nominal diameter 320 μm, nominal film thickness 0.5 μm), a thermal conductivity detector (200 °C), and a split injector (250 °C, 54.5 kPa excess pressure, split ratio 50:1) was used for the analysis of the liquid samples. The carrier gas was helium. The temperature program was as follows: 60 °C for 1 min, heating to 190 °C at 15 °C/min, 190 °C for 2 min. 1,4Dioxane (Sigma-Aldrich, anhydrous grade, ≥99.8%) was employed as the internal standard. All samples were injected into the gas chromatograph and analyzed three times. If the 95% confidence interval of the results of the three injections was larger than 0.001 g/g (i.e., the standard deviation was high), this anayltical result was rejected, and the analysis was repeated. At regular intervals, the analysis method was checked by using test samples with known compositions covering the entire concentration range. The average absolute error of the test samples for hexanol, hexyl acetate, and acetic acid was approximately 0.002 g/g, and that for water was 0.001 g/g. Hence, the corresponding average relative error was approximately 0.8% for acetic acid and 0.6% for hexyl acetate and hexanol in the concentration range studied in this work. The average relative error for water was approximately 1.0% when the water concentration was higher than 0.03 g/g and up to 8.0% when the concentration was lower than 0.03 g/g. The high quality of the analysis was verified by the 100% test (i.e., summation of the mass fractions of all components, which were independently determined by the internal standard method), whose results varied between 0.99 and 1.01 g/g. At the end of an experimental series, the catalyst was analyzed with regard to its activity and its dry mass. For this purpose, the used catalyst was washed first with methanol to dissolve the hydrophobic organic components adsorbed on the catalyst. Then, it was rinsed well with water until all organic components were washed out. The catalyst activity (i.e., the

Figure 1. Experimental setup of the batch reactor experiments.

connected to a thermostat. The temperature of the reaction mixture was measured by a Pt100 resistance thermometer and recorded during the whole experiment. The reactor was equipped with a polytetrafluoroethylene (PTFE) paddle stirrer. The stirrer drive was connected by magnetic coupling to avoid shaft sealing. To improve mixing, a PTFE baffle was installed. The maximum stirrer speed was approximately 500 rpm. Under these conditions, no grinding of the catalyst particles was observed. To avoid losses of volatile components, the reactor was connected to a condenser that, in turn, was connected to a flushing pipe. The temperature of the cooling water was approximately 10 °C. The reactor pressure was controlled by adjusting the inlet pressure and the flow of nitrogen through the flushing pipe. When a completely dry catalyst is mixed with the reactants, it adsorbs them so rapidly that a great mechanical stress is exerted on the polymer matrix. As a consequence, the catalyst becomes mechanically unstable and is ground to a fine powder by the stirrer. Hence, the catalyst has to be transformed into the swollen form before it can be used in a batch experiment. To establish similar initial conditions, the catalyst was carefully prepared in the following way before each batch experiment: The catalyst was amply washed with water, with hexanol, or with a mixture containing all four components. In the latter case, the composition of that mixture was chosen according to the expected composition at equilibrium of the intended batch reactor experiment. This procedure ensured that the composition of the liquid inside the catalyst was as close as possible to the bulk composition during the experiments. After the washing step, all of the intraparticular liquid was removed from the catalyst by sucking off the liquid. The prepared catalyst was then flushed into the reactor with the desired 626



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of the reactants at chemical equilibrium was predicted reliably. Thus, the equilibrium constant Ka(T) was not included in the parameter estimation carried out in the present work so that the number of parameters was reduced. Overview of the Experiments. To enable a direct comparison between the batch reactor experiments and the PFR experiments, the starting composition (feed A, containing (m) (m) x(m) HexOH = 0.63 g/g, xHAc = 0.15 g/g, xHexAc = 0.22 g/g) and the temperature (120 °C) were kept approximately the same for all experiments and were chosen according to a base-case experiment carried out by Schmitt and Hasse3 using a PFR. The input parameters that were varied and investigated during the batch reactor experiments were the stirrer speed and the mass and pretreatment of the catalyst. In all studies, the mass of catalyst was kept constant at approximately 5 gcat,dry except for the study in which its variation was investigated. Table 1 lists an overview of the experimental studies carried out with the batch reactor. The data from each batch experiment are available in the Supporting Information.

amounts of hexanol and hexyl acetate (a nonreactive mixture). Both the virgin and used catalysts were prepared in this way for each batch experiment. Typically, the catalyst was reused in several experiments. The maximum reduction of the catalyst activity (loss of active sites) of the used catalyst compared to the virgin catalyst was below 5% . Having flushed the system several times with nitrogen, the reactor was pressurized up to 3 bar to avoid boiling during the experiment. After that, the reactor was heated. Once the desired temperature had been reached, acetic acid and water were added to the reactor according to the desired overall starting composition. The total mass of reactants filled into the reactor was approximately 100 g. After a few minutes, when the temperature of the reaction mixture had returned to the desired level, the first liquid sample was taken, defining the zero time (t = 0) of the measurement. Until equilibrium was reached, about 10 liquid samples of approximately 0.8 mL each were taken using a syringe, and the time and mass of the samples were recorded. During the measurements, the temperature was typically maintained within ±1 K. Determination of the Rate Constant. The rate constant was determined for each batch reactor experiment independently by solving the model equations of the batch reactor and applying a parameter estimation procedure. As the objective function of that minimization problem, we employed the sum of the squares of the errors, SSE, given by Mobs Ncomp

SSE(θ ) =

∑∑

[xi(m) ,obs(t j)

−

2 ! xi(m) ,model(t j)] =

j=1 i=1

Table 1. Overview of the Experimental Studies with the Batch Reactor study

min

50−450

4.8−5.3

pretreatment

EQa, HexOH, H2O EQa

250

5.0−5.3

250

5.3, 8.3

exp B1, B4− B7 B3, B4, B8 B2, B4

Mixture at chemical equilibrium.

CSTR Experiments. Apparatus and Procedure. The CSTR experiments were carried out in the same glass reactor as was also used for the batch experiments (see preceding section). The experimental setup, however, was changed to enable continuous operation. The setup is depicted in Figure 2. To prevent autocatalytic reaction of the feed, the reactants (i.e., acetic acid and hexanol) were stored in two different feed tanks. The reactants were fed into the reactor by two highperformance liquid chromatography (HPLC) piston pumps (HPD Pump Multitherm 200, Bischoff Analysetechnik and -geräte GmbH, Leonberg, Germany) that could each supply a maximum feed rate of 20 mL/min. Before the feed entered the reactor, it was preheated by electrical heating. The volume of the reaction mixture in the reactor was kept constant with the help of the product overflow. To avoid loss of catalyst particles, a sieve (mesh opening 0.5 mm) is installed outside the overflow. The overflow is connected to a membrane pump (Ritmo R05, Fink Chem + Tec, Bad Dürrheim, Germany) with which the product can be discharged even when the reactor is operated below atmospheric pressure. Generally, the reactor can be operated in three different modes: subcooled liquid (liquid mode), boiling with total reflux (reflux mode), and boiling without reflux (flash mode). In liquid mode, no vapor is produced in the reactor, and the entire liquid phase leaves the reactor over the product overflow. When the reactor is operated in reflux mode, the reaction mixture is partially evaporated, and the vapor leaving the reactor is condensed and fed back completely into the reactor (total reflux). In flash mode, the reaction mixture is partially evaporated and condensed as well, but the distillate is completely withdrawn by a membrane pump (Ritmo R05, Fink Chem + Tec, Bad Dürrheim, Germany). The

+

H Miccat,dry mcat,dry νi dxi(m) r(k f , x(m), T ) = dt mreact (t )

mass of catalyst (gcat,dry)

EQa

a

In eq 5, Mobs denotes the number of observations, that is, the number of samples taken during the batch experiment, and Ncomp denotes the number of components. x(m) i,obs(tj) is the mass fraction of the sample taken at the point in time tj, and x(m) i,model(tj) is the mass fraction described by the model equation. Assuming that the reactor is well-mixed, the model equations of the batch reactorthe component balanceare given by

stirrer speed (min−1)

mass transfer

mass of catalyst

(5)

pretreatment of catalyst

(6)

The rate of reaction r in eq 6 is described with the pseudohomogeneous model given in eq 1. Mi is the molar mass, and νi is the stoichiometric coefficient of component i. + mcat,dry denotes the mass of the dried catalyst, and cHcat,dry is the concentration of active sites (catalyst activity) as determined for each charge of catalyst after the end of an experimental series (for details, see above). mreact(t) is the actual mass of the reaction mixture. Because of the sampling, it is a decreasing step function. The overall decrease was approximately 10% from the start to the end of a batch experiment. By numerical integration of the model equations (see eq 6), the concentrations x(m) i,model(tj) are obtained. Because the model equation of the batch reactor (cf. eq 6) is a set of ordinary differential equations (ODEs), an initial condition, namely, the starting composition, has to be given to obtain the concentration profile as a function of time. Because the starting composition was measured in the same way as all other compositions in the batch experiments, it was influenced by the same measurement error. For that reason, the starting composition was included in the estimated parameters. Because of the high quality of the chemical equilibrium model determined by Schmitt and Hasse3 (cf. eq 3), the composition 627



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Figure 2. Experimental setup of the CSTR experiments.

product stream, which is directly related to the product composition, was measured online. The mass flows of the feed, the liquid product, and the withdrawn distillate were measured indirectly by differential weighing and were constantly recorded. Product, feed, and (if applicable) distillate samples were taken when the conductivity and temperature of the reaction mixture were constant. To confirm that the reactor behaved as an ideal CSTR, mixing and residence time distribution measurements were carried out. Through the addition of a small amount of concentrated hydrochloric acid to a sodium hydroxide solution stirred in the reactor and colored by the indicator phenolphthalein, the dependency of the mixing time on the stirrer speed was evaluated. Furthermore, by measuring the conductivity (SevenEasy, Mettler Toledo, Greifensee, Switzerland) in the liquid product stream, the response to a tracer impulse of a sodium chloride solution injected in the feed stream was determined, and the residence time distribution of the reactor setup was calculated. The mixing time was found to be at least an order of magnitude shorter than the hydrodynamic residence time τ in the reactor when the stirrer speed was higher than 100 rpm. For these stirrer speeds, the residence time distribution indicated ideal flow behavior of the CSTR. The stirrer speeds used in the reaction kinetic experiments were not below 250 rpm. Determination of the Rate of Reaction. In contrast to the batch reactor experiments, the rate of reaction can be determined directly from the CSTR experiments by applying the model equation of the CSTR, derived from the mass balance, expressed as

condenser is connected to the pressure control unit. The reactor can be operated in a pressure range from 0.3 to 3.0 bar, using either a vacuum pump or pressurized nitrogen. The vacuum pump was connected to a cooling trap to avoid losses of volatile components. Before the start of an experiment, the catalyst was filled into the reactor, and the reactor was sealed. In all studies, the mass of catalyst was kept between approximately 3 and 5 gcat,dry. Typically, the catalyst was reused in several experiments. After approximately 20 h in operation, however, the catalyst was replaced. By comparison of the catalyst activity of the reused catalyst and the virgin catalyst, it was shown that the reduction of the catalyst activity (loss of active sites) was below 5%, which is in the same range as observed during the HCRD experiments (cf. von Harbou et al.5). Once the system had been flushed several times with nitrogen, the experiments were started by pressurizing the reactor to 3 bar and heating it to the desired temperature. When the temperature was reached, the pumps were started: the feed pumps; the product pump; and in reflux and flash modes, the distillate pump. By adjusting the temperature of the feed preheater and the oil thermostat, the temperature of the reaction mixture was controlled. For all experiments that were carried out in liquid mode, the reactor pressure was kept at the maximum operating pressure of 3 bar to avoid partial evaporation. To operate the reactor in reflux or flush mode, the reactor pressure was reduced until boiling started. The amount of vapor leaving the reactor was adjusted by the temperature of the heating jacket. Because temperatures higher than 130 °C cause desulfonation that leads to a release of sulfonic acid and therefore to a reduction of the catalytic activity,22 all experiments were carried out below 125 °C. In reflux and flash modes, the temperature and pressure cannot be chosen independently because of the boiling conditions in the reactor. The lower limit of the reactor pressure was determined by the performance of the product membrane pump used to discharge the products and was approximately 0.3 bar. The resulting lowest temperature of the reaction mixture in reflux and flash modes was approximately 100 °C. To ensure that the reactor had reached steady state, the conductivity of the

∑

0=

ṁ iin −

all inputs

robs =

∑

̇ ṁ iout + Miνξ i

all outputs

ξ̇ H+ ccat,dry mcat,dry

(7)

= f (T , x out) (8)

In eq 7, ṁ i denotes the mass flow of the component i, which is calculated from the total mass flow and the mass fraction. ξ̇ is 628



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Therefore, it is important to carry out the experiments as effectively as possible to reduce the experimental effort, specifically, the number of experiments and the consumption of chemicals. From eqs 7 and 8 together with the pseudohomogeneous model given in eq 1, it follows that the composition of the liquid product x(m),out is a function of the kinetic parameters, namely, the rate constant kf, the equilibrium constant Ka, the feed composition x(m),in, and the pseudoresidence time τPS. The pseudoresidence time τPS was introduced in the present work as the ratio of the mass of the catalyst mcat,dry to the mass flow of the feed ṁ in. Considering a CSTR experiment with a given feed composition and temperature, the pseudoresidence time τPS can be chosen independently by changing the mass flow of the feed, for example. This leaves the question: Which pseudoresidence time is the best choice for experiments? The aim of these studies was to investigate the rate of reaction r and thereby to determine the rate constant of the forward reaction kf. A very short pseudoresidence time results in a low conversion, that is, the liquid product composition is almost the same as the feed composition. In this case, only small errors in the measurement of the composition lead to large errors in the observed rate of reaction. If a very long pseudoresidence time is chosen, the liquid product is in equilibrium, which means that the rate of reaction is zero. Obviously, the optimal pseudoresidence time is between these two cases. Mathematically, this can be expressed by the sensitivity s of the observable parameter, the liquid product composition, with respect to the parameter of interest, the rate constant28, as given in the equation

the extent of the reaction per unit of time for the esterification (see reaction I). Because of measurement errors, typically, the total mass balance is not satisfied, and the evaluations of the mass balance of the four individual components in this chemical system do not result in the same extent of reaction. To obtain a consistent data set of the redundant measurements, data reconciliation was carried out. Mathematically, data reconciliation is a constrained optimization problem. In this work, the measured component mass flows were reconciled using the four component mass balances (cf. eq 7) as constraints. From the reconciled component mass flows, the reconciled total mass flows ṁ and the reconciled mass fractions x(m) were calculated i directly so that the overall mass balance and the summation condition of the mass fractions were inherently satisfied as well. In addition, the unknown extent of reaction ξ̇ was determined by the data reconciliation procedure so that the stoichiometry of reaction I was satisfied. Only minor adjustments of the measured values were necessary to satisfy the physical constraints. The maximum difference between the reconciled and measured mass fractions of the reaction mixture was less than 0.004 g/g. The maximum difference between the measured and reconciled rate of reaction was less than 2 × 10−3 mol·molH+−1·s−1 for water and 5 × 10−4 mol·molH+−1·s−1 for the remaining three components (hexanol, acetic acid, and hexyl acetate), which correspond to a maximum relative difference of 10% for water and 3% for the remaining three components. Hence, the difference between the measured and reconciled rates of reaction was larger for water than for the remaining three components. The measured rate of reaction for water was subjected to higher experimental errors because of propagation of errors from analysis. As an example, Table 2

si(x(m),in , T , τPS , k f ) =

Table 2. Comparison of the Measured and Reconciled Mass Fractions of the Reaction Mixture and Extent of Reaction for CSTR Experiment CL22 measured

∂xi(m),out ∂k f

(9)

Figure 3 shows as an example the sensitivity of the liquid product concentration of hexyl acetate as a function of the

Δrel (%)

reconciled −1

Mass Fraction in the Reaction Mixture (g·g ) 0.490 0.492 0.072 0.072 0.412 0.413 0.022 0.022 0.996 1.000 Extent of Reaction (1 × 10−5 mol·s−1) HexOH 9.92 9.87 HAc 9.89 9.87 HexAc 9.96 9.87 H2O 9.75 9.87

HexOH HAc HexAc H2O sum

0.4 0.4 0.3 1.0

0.4 0.2 0.9 1.3

Figure 3. Sensitivity of the liquid product concentration of hexyl acetate as a function of the pseudoresidence time for a CSTR experiment in liquid mode with an equimolar feed and a temperature of 120 °C.

shows a comparison between the measured and reconciled composition of the reaction mixture and rate of reaction for a CSTR experiment in liquid mode. The minor adjustments of the measured data necessary to fulfill the physical constraints illustrate the quality of the primary experimental data. In the following discussion, the observed values for variables such as the rate of reaction and the mass fraction of the reaction mixture correspond to the reconciled values only and not to the primary experimental data. The data reconciliation procedure is described in detail in the Appendix. Model-Based Design of Experiments. The disadvantage of a CSTR is that, within one experimental run, only one set of observable values, namely, the rate of reaction, the composition, and the temperature of the reaction mixture, are obtained.

pseudoresidence time τPS for an experiment with given feed composition and temperature. The optimal choice of the pseudoresidence time τopt PS is determined by the maximum of the sensitivity sHexAc. Note that the location of the maximum of the sensitivity si of the other three components (hexanol, acetic acid, and water) is the same. Only the absolute value is different, with the value of hexyl acetate being highest. This approach, however, can be applied only if reasonable estimates for the rate constant kf and the chemical equilibrium constant Ka of the reaction are known beforehand, which is often not the case. In this work, however, the kinetic parameters given by 629



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Schmitt and Hasse3 were available and were used for the design of experiments. Before each CSTR experiment, the optimal pseudoresidence time was determined as just described according to the set points of the temperature, feed composition, and operation mode. To investigate the rate of reaction at different compositions of the reaction mixture, the pseudoresidence time was varied in the range of the expected maximum of the sensitivity while the other input parameters were kept constant. The employed pseudoresidence times for the CSTR experiments were between 16 and 136 s·g−1·gcat,dry. As mentioned already, the sensitivity as defined in eq 9 is also a function of the temperature and feed composition. Thus, the sensitivity can be globally maximized with respect to the pseudoresidence time and these two additional input parameters. This optimization shows that the sensitivity is highest if the temperature is chosen as high as possible and if an equimolar feed of hexanol and acetic acid is employed. Overview of the Experiments. First, to compare the rates of reaction measured in this work with the rates of reaction measured by Schmitt and Hasse3 using a PFR, a temperature study in liquid mode was carried out at the same temperatures (80, 100, and 120 °C) and feed composition (feed A, (m) (m) containing x(m) HexOH = 0.63 g/g, xHAc = 0.15 g/g, and xHexAc = 3 0.22 g/g) as used by Schmitt and Hasse. The next study investigated the influence of boiling. Three experiments were carried out in liquid mode (i.e., the liquid was subcooled), and three experiments were carried out under boiling conditions in reflux mode. In this mode, the liquid is evaporated, condensed, and completely refluxed into the reactor. Hence, no low-boiling components are withdrawn, and the composition of the reaction mixture is not shifted. Furthermore, the same three values of the pseudoresidence time were chosen (20.7, 23.9, and 30.2 s·g−1·gcat,dry) in both operation modes, so that a direct comparison of the experiments in the two different modes would be possible. These values of the pseudoresidence time are in the range of high sensitivity to the rate constant (cf. Figure 3). The temperature (approximately 120 °C) and the feed composition (m) (feed B, containing x(m) HexOH = 0.63 g/g, xHAc = 0.37 g/g) were the same in this study. Only the pressure was changed to induce boiling. The high temperature and the equimolar feed composition of hexanol and acetic acid was chosen so that the experiments were carried out under conditions with the highest expected sensitivity with regard to the rate constant. The third study addressed the influence of the low-boiling components (mainly water) on the reaction kinetics. For that reason, experiments were carried out in flash mode, that is, under boiling conditions with complete withdrawal of the aqueous distillate. These results were compared to experiments carried out in liquid mode (i.e., the liquid was subcooled). In this study, the feed composition and the temperature of the reaction mixture were varied. First, an equimolar feed (m) composition (feed B, containing x(m) HexOH = 0.63 g/g, xHAc = 0.37 g/g) and the highest possible temperature of the reaction mixture (approximately 125 °C) were used to achieve a high sensitivity with regard to the rate constant. Second, the feed (m) compositions (feed A, containing x(m) HexOH = 0.63 g/g, xHAc = (m) (m) 0.15 g/g, and xHexAc = 0.22 g/g, and feed C, containing xHexOH = (m) 0.74 g/g, x(m) HAc = 0.24 g/g, xHexAc = 0.22 g/g) and the temperatures of the reaction mixture (115−125 °C) were chosen so that the compositions of the reaction mixture were as close as possible to the compositions and temperatures

measured in HCRD experiments by Harbou et al. 5 Furthermore, the concentration of water in the reaction mixture was diminished in all experiments of this study to values below 0.008 g/g and 0.05 mol/mol, which corresponds to the concentration range of water measured in the reactive zone of an HCRD column.5 The concentration of water in the reaction mixture was adjusted in each experiment by varying the mass flow of the distillate. Under boiling conditions, the mass flow of the distillate is directly controlled by the heat flow (i.e., the temperature of the oil in the heating jacket). An overview of the CSTR studies is provided in Table 3. The data from each CSTR experiment are available in the Supporting Information. Table 3. Overview of the Experimental Studies with the CSTR study

temperature (°C)

feed compositiona

operation mode

temperature

80−125

feed A

liquid

influence of boiling influence of water

120

feed B

115−125

feeds A−C

liquid, reflux liquid, flash

exp CL1−CL13, CL19, CL20, CL22 CL14−CL16, CR1−CR3 CL17, CL18, CL21, CF1− CF11

a (m) (m) Feed A: x(m) HexOH = 0.63 g/g, xHAc = 0.15 g/g, xHexAc = 0.22 g/g. Feed B: (m) = 0.63 g/g, x = 0.37 g/g (equimolar). Feed C: x(m) x(m) HexOH HAc HexOH = 0.74 (m) (m) g/g, xHAc = 0.24 g/g, xHexAc = 0.02 g/g.

Quality of the Experiments. Typically, the reactor reached steady state after 1 h of operation. The 95% confidence interval of the temperature measurement for all experiments was below 0.1 K. The 95% confidence intervals of the observed mass flows of the feed and liquid product were approximately 0.02 and 0.05 g/min of the distillate, respectively. The data from an experimental run were rejected if the global test applied in the course of data reconciliation indicated a gross error. Typically, a gross error was detected if the error of the mass balance (related to the mass flow of the feed) or the coefficient of variation of the observed individual molar conversion (extent of reaction) of the four components (cf. eq 7) was greater than 2%. The quality of the measurements was tested on a regular basis by reproduction runs. The differences between the rate of reaction measured in the base case and measured in the reproduction experiments were typically below 2%.

■

RESULTS AND DISCUSSION Batch Reactor Experiments. General Results. A typical concentration profile measured in the batch reactor experiments is presented in Figure 4. The concentration of water first rose, as expected for the esterification (see reaction I), before it decreased slightly again even though the concentrations of all other components increased or decreased according to the chemical reaction. Table 4 reports the individual molar conversions of each component at the end of two batch reactor experiments. The three components hexanol, acetic acid, and hexyl acetate had almost the same molar conversion, whereas the molar conversion of water was significantly lower. Obviously, water was removed from the bulk after it was formed by the reaction. As a loss into the vapor phase can be excluded, water must have been adsorbed by the catalyst. As mentioned previously, the catalyst has a very strong affinity to 630



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however, was not within the scope of this work, as specific adsorption does not play an important role in steady-state operation of an HCRD column. Influence of the Mass Transfer Resistance. To investigate the influence of external mass transfer effects on the observed rate of reaction, the stirrer speed was varied over a large range. The results are presented in Figure 5. It is clear from Figure 5

Figure 4. Composition of the reaction mixture as a function of time for batch reactor experiment B5 (pretreatment of the catalyst, equilibrium mixture; stirrer speed, 100 min−1; mass of catalyst, 5.3 gcat,dry). Symbols: Measured mole fractions of hexanol (○), acetic acid (□), hexyl acetate (▽), and water (Δ). Lines: Model predictions.

Table 4. Comparison of the Measured Molar Conversion of the Reactants at the End of Two Batch Experiments Using Two Different Amounts of Catalyst molar conversion (mol) exp

mcat,dry (g)

HexAc

HexOH

HAc

W

B2 B7

8.3 5.3

0.069 0.138

0.065 0.128

0.059 0.125

0.006 0.042

Figure 5. Rate constant as a function of stirrer speed for the batch reactor experiments (pretreatment of the catalyst, equilibrium mixture; mass of catalyst, 4.8−5.3 gcat,dry).

that the external mass transfer resistance was negligible above 200 rpm. Hence, all other batch reactor experiments and all experiments with the CSTR were performed at stirrer speeds of at least 250 rpm. The influence of the internal mass transfer is controversially discussed in literature. For similar reaction systems that were also heterogeneously catalyzed by acid ionexchange resins, most authors, such as Gimenez et al.,30 Gonzalez and Fair,31 Mazzotti et al.,29 and Pfeuffer et al.,19 have found that the influence of the internal mass transfer resistance can be neglected. Pöpken et al.,8 however, observed an increase in the rate of reaction when the catalyst was subjected to grinding or abrasion for particle diameters below 65 μm. This result indicates the existence of mass transfer resistance in the large catalyst particles. Because the aim of this work was to develop a kinetic model for use in models of HCRD, where almost monodisperse catalyst particles are immobilized within the column and are not subjected to grinding or abrasion, we carried out no further studies into this subject. Influence of the Pretreatment of the Catalyst. Table 5 lists the results of three batch reactor experiments carried out with approximately the same mass of dry catalyst (5.0−5.3 gcat,dry) but different pretreatments of the catalyst. The comparison of the rate constants in Table 5 reveals that the pretreatment had a significant influence on the observed rate of reaction. When the catalyst pores were filled with water at the beginning of a batch

water because of the small size of the molecule and its strong hydrogen bonds compared to the other components.3 According to the values of the specific adsorption given in the Supporting Information, the masses of catalyst used in the two experiments listed in Table 4 could adsorb approximately 0.5 and 0.3 mol of pure water, which is more than the amount of water formed by the reaction (approximately 0.07 and 0.12 mol, respectively). Furthermore, the differences between the molar conversions of the three components hexanol, hexyl acetate, and acetic acid always showed the same trend, with the molar conversion of hexyl acetate being highest followed by the molar conversions of hexanol and acetic acid. This is in line with the order of the specific adsorption data given in the Supporting Information. Obviously, the specific adsorption has an impact on the measured conversions and concentration profiles. By a parameter estimation procedure (cf. eq 5), the rate constant kf as defined in eq 1 was fitted to the measured concentration profiles of each batch reactor experiment. Because the concentration profile of water was severely distorted, the concentration of water was excluded from the calculation of the sum of squared errors (cf. eq 5). The results of the parameter estimation for a typical batch reactor experiment are presented in Figure 4. The measured mole fractions are in good agreement with the predictions of the pseudohomogeneous model at the beginning of the measurements. However, as the reaction proceeded into chemical equilibrium, large deviations between the measured mole fractions and the model predictions occurred. Because the pseudohomogeneous model does not account for the catalyst phase and component-specific adsorption, the measured starting composition of the bulk does not proceed to the chemical equilibrium composition as predicted by the model. Only if the selective adsorption on the resin were properly taken into account would it be possible to predict the effect of the amount of resin on shifting the equilibrium conversion in batch reactor experiments.29 The investigation of this effect,

Table 5. Influence of the Mass and of the Pretreatment of the Catalyst on the Rate Constant for Batch Reactor Experiments exp

mcat,dry (g)

pretreatmenta

B3 B4 B8 B2

5.3 5.3 5.0 8.3

H2O EQ HexOH EQ

kf (mol·molH+−1·s−1) 0.102 0.135 0.168 0.155

± ± ± ±

0.006 0.013 0.019 0.025

a

Pretreatment of the catalyst with water (H2O), with a mixture at chemical equilibrium (EQ), and with hexanol (HexOH). 631



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reactor experiment, the rate of reaction was reduced. In this case, either the rate of reaction was impeded by mass transfer inside the pores, or the active sites were shielded by the water molecules. In contrast, when the catalyst pores were filled with hexanol at the beginning of a batch reactor experiment, the rate of reaction increased. Because of the absence of water and the high concentration of hexanol in the catalyst pores, the active sites were not shielded by water molecules, and the reaction proceeded more rapidly. Influence of the Mass of Catalyst. Because the pseudohomogeneous kinetic model as defined in eq 1 is independent of the mass of catalyst, the fitted rate constant should remain constant when the mass of catalyst is increased and all other input parameters are kept constant. Table 5, however, shows that the observed rate of reaction was higher when 8.3 gcat,dry of catalyst was employed for the batch reactor experiment instead of 5.3 gcat,dry. Obviously, the rate constant depends on the mass of catalyst, indicating that the pseudohomogeneous model as defined in eq 1 cannot describe the concentration profiles observed in the batch reactor experiments correctly. The reason for this behavior is the superposition of the reaction and specific adsorption of the reactants on the catalyst in the batch reactor experiments. CSTR Experiments. Influence of Boiling. In this study, the influence of boiling on the rate of reaction was investigated. First, an experimental series was carried out in liquid mode (CL14−CL16), followed by an experimental series in reflux mode (i.e., under boiling conditions) (CR1−CR3) using the same experimental parameters (temperature, feed composition, and pseudoresidence time) (cf. Table 3). The results of this study are presented in Figure 6. Obviously, boiling had no

Figure 7. Rate of reaction as a function of the activity term A for CSTR experiments at 121 ± 1 °C. Symbols: Flash mode experiments with concentrations of water below 0.050 mol/mol (■), liquid mode experiments with concentrations of water greater than 0.05 mol/mol (Δ). Line: Linear fit r = kfA.

concentrations of water, as well as in flash mode (CF1, CF2, CF5, CF7), which corresponds to low concentrations of water. All of the rates of reaction, including those measured at low concentrations of water, were found to be scattered around the line r = kfA (cf. Figure 7) defined by the pseudohomogeneous model. No dependency of the rate of reaction or the rate constant on the concentration of water was observed. Obviously, the performance of the catalyst was not affected at low concentrations of water. Results of a Global Fit. The results presented in the two previous sections indicate that neither boiling nor the concentration of water influence the performance of the catalyst or the rate of reaction. Thus, these two factors can be excluded as reasons for the deficiencies of the kinetic model of Schmitt and Hasse3 in predicting the rates of reaction of the present HCRD process. This leaves the question of whether the model of Schmitt and Hasse3 (see eqs 2 and 4) is able to predict the rate of reaction and rate constants determined in the CSTR experiments of the present work. Figure 8 presents a

Figure 6. Observed rate of reaction as a function of the pseudoresidence time of CSTR experiments carried out with feed B (equimolar composition) at 120 °C in liquid mode (no boiling, *) and in reflux mode (boiling conditions, ▽). Figure 8. Parity plot of the observed rate of reaction and of the rate of reaction given by the model of Schmitt and Hasse.3 Symbols: Flash mode experiments with concentrations of water below 0.050 mol/mol (■), reflux and liquid mode experiments with feed B (equimolar (m) composition; ○) and with feed A (x(m) HexOH = 0.63 g/g, xHAc = 0.15 g/g, (m) xHexAc = 0.22 g/g; Δ).

effects on the rate of reaction in this system. This means that the mass transfer within the catalyst, the accessibility of the active sites, and the local composition within the catalyst pores remained unaffected by boiling. Influence of the Water Concentration. In this study, the influence of the water concentration on the performance of the catalyst was investigated. Because these experiments were run in flash mode (i.e., under boiling conditions without reflux), the concentration of water in the reaction mixture was reduced to 0.002 g/g or 0.01 mol/mol, which is similar to the water concentrations present in the reactive section of an HCRD column.5 Figure 7 shows the rate of reaction as a function of the activity term A (cf. eq 1) observed for CSTR experiments carried out at approximately 121 °C in liquid mode (CL4− CL6, CL13, CL14, CL16, CL22), which corresponds to high

parity plot of the observed rates of reaction determined in the present work and the rates of reaction calculated with the model of Schmitt and Hasse.3 Obviously, the rates of reaction measured in the CSTR are in very good agreement with the rates of reaction measured in the PFR for feed A and for the temperature range of 80−120 °C. This feed composition and this temperature range are similar to the feed composition and temperature range used in the PFR experiments carried out by 632



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Schmitt and Hasse.3 Thus, the rates of reaction of Schmitt and Hasse3 were independently confirmed by the measurements carried out in this work. The CSTR and the PFR, although substantially different in the setup and in the method of measuring, give similar results, just as expected from theory. When the composition of the reaction mixture in the CSTR, however, was in a concentration range that was not covered by Schmitt and Hasse3 and the temperature also deviated strongly from that in the experiments of Schmitt and Hasse,3 the model of Schmitt and Hasse3 overestimated the rate of reaction (cf. Figure 8). For that reason, a global parameter estimation was carried out using all of the data from the CSTR experiments. Because the results presented in the two previous sections confirmed the assumptions on which the pseudohomogeneous model is based, this model was chosen for the parameter estimation. The global parameters of the kinetic model were estimated by employing the weighted least-squares method. In this case, the errors are defined as the differences between the observed rate of reaction robs and the rate of reaction described by the kinetic model rmodel. Mathematically, this can be expressed as Mobs

SSE(θ ⃗) =

(14)

Table 6. Results of the Estimation of the Reaction Kinetic Parameters Using the Data from the CSTR Experiments parameter

value

k0f (mol·molH+−1·s−1) EA,f (kJ·mol−1)

5.996 × 105 50.0

The accuracy of the employed model is illustrated by the parity plot in Figure 9. Obviously, the model represents the

!

(10)

Figure 9. Parity plot of the observed rate of reaction and of the rate of reaction given by the model of this work. Symbols: Flash mode experiments with concentrations of water below 0.050 mol/mol (■), reflux and liquid mode experiments with feed B (equimolar (m) composition; ○) and with feed A (x(m) HexOH = 0.63 g/g, xHAc = 0.15 g/g, x(m) HexAc = 0.22 g/g; Δ).

observed data well. Only the data from the experiments in flash mode show a larger deviation compared to the other experiments, but the data are randomly scattered and shows no significant trend. These larger deviations were expected because the data of the experiments in flash mode were influenced more strongly by experimental errors because of the higher experimental complexity. The temperature dependency of the rate constant is illustrated by the Arrhenius plot in Figure 10. Obviously, the model represents the temperature dependency of the rate constant well, and the apparent activation energy is constant, indicating that the rate-limiting step remains the same in this temperature range. To illustrate the deviations between model and observations, the liquid product composition of a CSTR experiment was predicted by means of the new model. For this prediction, a CSTR experiment was chosen that was carried out in flash mode and that showed a large deviation from the bisecting line in Figure 9. The results presented in Table 7 demonstrate the accuracy of the model developed in this work. In addition, the model developed in this work was used to predict the concentration profile of a PFR reactor experiment carried out

⎧ ⎫ ⎡ ⎛1 ⎛1 ⎪ 1 ⎞ 1 ⎞⎤⎪ ⎥⎬ ⎢θ1⎜ − − θ − k f (T ) = exp⎨ c ⎜ ⎟ ⎟ 2 ⎪ Tmin ⎠ Tmax ⎠⎥⎦⎪ ⎝T ⎭ ⎩ ⎢⎣ ⎝ T (11)

with 1 −

EA,f = Rc(θ2 − θ1)

Using the reparameterized formulation of the Arrhenius equation, the dependency of the two parameters (now θ1 and θ2) on their initial guess was significantly reduced. The small absolute value of the correlation matrix (Cθ1,θ2 = −0.29) demonstrate the benefit of the reparameterization of the Arrhenius equation. The results of the parameter estimation are summarized in Table 6.

The rate of reaction rmodel is described by the pseudohomogeneous model given in eq 1. Because the reactor behaved as an ideal CSTR, the pseudohomogeneous model was calculated on the basis of the measured temperature of the reaction mixture and the composition of the liquid product. The weights wj in eq 10 were introduced to avoid the overweighting of the numerous experiments carried out at temperatures of approximately 120 °C compared to the few results of experiments carried out at temperatures of 80 and 100 °C. The parameter estimation procedure described in eq 10, however, encounters serious difficulties when it is based on the Arrhenius equation (cf. eq 2). The obtained parameters are then strongly dependent on the initial guesses. The 95% confidence interval of the pre-exponential factor k0f was found to have the same order of magnitude as the parameter itself. As indicated by the values of the correlation matrix being close to 1, the intrinsic mathematical structure of the Arrhenius equation (see eq 2) introduces a high correlation between the two parameters k0f and EA,f.23,24 Thus, it is likely that the obtained parameters would be inaccurate. To overcome these difficulties, the Arrhenius equation was reparameterized by introducing two reference temperatures as recommended by Buzzi-Ferraris and Manenti25

1 Tmin

(13)

∑ wj(robs,j − rmodel,j)2 = min j=1

c=

⎡⎛ θ θ ⎞⎤ k f0 = exp⎢c ⎜ 2 − 1 ⎟⎥ ⎢⎣ ⎝ Tmax Tmin ⎠⎥⎦

1 Tmax

(12)

The combination of eqs 11 and 12 with eq 2 resulted in the following expressions used to calculate the pre-exponential factor and the activation energy 633



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Comparison of the Three Reactor Types. Regarding the determination of the rate of reaction of a heterogeneously catalyzed esterification, all three reactor types mentioned in this article have different advantages and disadvantages. A batch reactor has the advantage that the experimental setup is comparably simple. The consumption of chemicals per experiment is considerably lower than that for a PFR or CSTR. With one experimental run in a batch reactor, a whole concentration profile beginning at the starting composition and ending at the composition at chemical equilibrium can be obtained. A disadvantage is that the measurements in batch reactors are disturbed by the sampling. Furthermore, as the reactants and the catalyst cannot be heated together without reacting immediately, they have to be mixed after having reached the desired temperature. This makes it difficult to achieve isothermal conditions. Of course, an elaborate reactor setup and starting strategy can improve the operation of a batch reactor but would make the batch reactor experiment very complex. The main disadvantage of using a batch reactor for reaction kinetics studies of the present type, however, is that reaction and adsorption are superimposed. As a result, the molar conversions calculated from the change in the bulk-phase composition can deviate significantly for different components. Furthermore, the determined rate constant can depend strongly on the pretreatment of the catalyst and the mass of catalyst. Even though a set of batch reactor experiments was performed in the present work that resulted in the same rate constant as measured in a PFR and in a CSTR, if no independent data from other reactor types are available, it is impossible to judge beforehand whether the rate of reactions determined with a batch reactor are acceptable. The experimental setup of a PFR is more complex compared to that of a batch reactor, but the experimental procedure is simpler, in particular because the measurements of the concentration are started when the reactor is in steady state. The filling procedure of the reactor tubes with catalyst, however, has to be done very carefully to avoid channelling and bypassing of the catalyst bed as well as compression of the catalyst due to swelling. For that reason, it is time-consuming to change the catalyst, and PFRs are less suitable for screening studies with different types of catalyst. For studies of the rate of reaction for a given catalyst under nonboiling conditions, a PFR is a good choice. It has the advantage that a complete concentration profile can be obtained within one experimental run. CSTRs have the disadvantage that the expenditure of time is higher compared to that for batch reactors or PFRs. The consumption of chemicals is typically higher than with a PFR and much higher than with a batch reactor. Using a batch reactor or PFR, a complete concentration profile can typically be measured within a single experiment. In contrast, using a CSTR, only one measurement (composition, temperature, and rate of reaction) can be obtained within a single experiment. On the other hand, this single experiment can be optimized with respect to the sensitivity of the measurement. A CSTR has the advantage that the composition and temperature are constant within the reactor and, thus, the rate of reaction can be directly determined from the component mass balances. Furthermore, with regard to the impact of the bulk composition on the swelling state of the catalyst and thus on the catalyst performance, a well-defined steady state can be achieved. In contrast, batch reactor and PFRs have the disadvantage that the rate of reaction can be determined only indirectly by evaluating

Figure 10. Arrhenius plot. Symbols: Observed rate constants of the flash mode experiments with concentrations of water below 0.050 mol/mol (■) and of the reflux and liquid mode experiments with feed B (equimolar composition; ○) and with feed A (x(m) HexOH = 0.63 g/g, (m) x(m) HAc = 0.15 g/g, xHexAc = 0.22 g/g; Δ). Line: Rate constant given by the model of this work.

Table 7. Comparison of the Measured (Reconciled) and Predicted Liquid Product Composition of CSTR Experiment CF10 Carried Out in Flash Mode mole fraction product

experiment

model

HexOH HAc HexAc W

0.579 0.172 0.212 0.037

0.573 0.166 0.218 0.043

by Schmitt and Hasse.3 The good agreement between the measurements and the model predictions (see Figure 11) shows again that the PFR and the CSTR give similar results concerning the rate of reaction.

Figure 11. Concentration profile of PFR experiment 2A:6 Measured concentrations of hexanol (○), acetic acid (□), hexyl acetate (▽), and water (Δ). Model predictions () using the kinetic model of this work.

In the next step, all 39 concentration profiles of the PFR experiments carried out by Schmitt and Hasse3 were predicted with the new model developed in this work and compared with the predictions of the model developed by Schmitt and Hasse.3 The mean relative error (MRE) was 4% when the new model was used and 3% when the model given by Schmitt and Hasse3 was used. As expected, the model given by Schmitt and Hasse3 was slightly better in predicting the concentration profiles of the PFR because it was fitted to these data only and it contains one additional parameter (cf. eq 4). 634



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demonstrated by Harbou et al.,32 the model developed in the present work is able to predict the rate of reaction over a broad range of concentrations including those present in HCRD processes.

the gradient of the concentration profile or by integrating an assumed kinetic model and fitting the results to the concentration profile (as was done in the present work). As only a finite number of points in the concentration profile are measured with a batch reactor or PFR, the determined rate of reaction can be correlated only to an average composition and thus also an average catalyst performance. As the reaction kinetics determined in the present work with a CSTR are in good agreement with those from the PFR, this effect was, at least in the present case, negligible. A major advantage of CSTRs, however, is the scope of design. As illustrated in this work, a CSTR can be operated in different modes such as reactive flash or under boiling conditions. This offers the unique opportunity to measure sensitively the rate of reaction under conditions close to the conditions of the process for which the kinetic model will be used.

■

APPENDIX

Data Reconciliation Procedure

In the present work, the weighted least-squares method was applied to the objective function for the constrained optimization problem of the data reconciliation procedure, as expressed in the equation Nmeas

Ω=

!

∑ wi(zi − zĩ )2 = min i=1

■

(15)

where zi is the reconciled value, z̃i is the value measured in the experiment, wi represents the weights, and Nmeas is the total number of measurements. Different approaches exist to choose the values z̃i, the weights wi, and the physical constraints (for details, see, e.g., Narasimhan33). In the present work, the measured component mass flows were reconciled, resulting in the four component mass balances (cf. eq 7) as constraints. The weights in eq 15 are important for reflecting the accuracy of the respective measurements and making the least-squares procedure independent of the dimensions of the measurements. The weights were defined here based on the experimental standard error SE

CONCLUSIONS In this work, the rate of reaction of the esterification reaction of hexanol and acetic acid to hexyl acetate and water catalyzed by the ion-exchange resin Amberlyst CSP2 was investigated in two different types of reactor: batch reactor and CSTR. The measured rates of reaction were compared to measurements by Schmitt and Hasse3 carried out in a PFR. Because reaction and adsorption on the catalyst are superimposed in a batch reactor, the measured rate constant depends on the pretreatment of the catalyst and the mass of catalyst. Thus, batch reactors are not recommended for measurements of the kinetics of reactions that are heterogeneously catalyzed by ion-exchange resin and that produce a component, such as water, that is strongly adsorbed by the resin. To investigate the influence of boiling on the performance of the catalyst, CSTR experiments were carried out in which the liquid reaction mixture was subcooled and in which it was boiling. It was shown that boiling has no effect on the rate of reaction in this system. The liquid phase concentrations present in an HCRD column were emulated by operating the CSTR as a reactive flash. The lowering of the concentration of the lowboiling components (i.e., water in the hexyl acetate system) did not result in a significantly change in the performance of the catalyst or in the rate constant. The rate of reaction measured with the CSTR and with a PFR were found to be in good agreement when the CSTR experiments were carried out in the same concentration and temperature ranges as used for the PFR experiments. Compared with a PFR, a CSTR has the advantage that the rate of reaction can be measured sensitively at the conditions of interest. The data from the CSTR experiments were used to estimate the parameters of the pseudohomogeneous model. In the present work, the Arrhenius equation was reparameterized to reduce the correlation between the parameters. This reparameterization led to significant improvement in the parameter estimation procedure. The model prediction with the parameters obtained in the present work was in very good agreement with the data from the CSTR experiments. Even though the PFR experiments of Schmitt and Hasse3 were not included in the parameter estimation procedure, they were predicted with almost the same quality with our model as with the model of Schmitt and Hasse.3 All in all, reaction kinetics measurements carried out in the liquid phase under nonboiling conditions using a CSTR or a PFR are well suited for determining reaction kinetic models that can be used in models of HCRD processes. As

wi =

1 SEṁ i 2

(16)

As the component mass flows were not directly measured, the standard error was derived by the propagation of error, as in the equation SEṁ i 2 = [ṁ SE xi(m)]2 + [xi(m)SEṁ ]2

(17)

The standard errors of the mass flow SEṁ and the standard errors of the mass fraction SEx(m) were set according to the i estimations of the errors, resulting in 0.05 g/min for the mass flows of the feed and product, 0.075 g/min for the mass flow of the distillate, 0.001 g/g for the mass fraction of water, and 0.002 g/g for the mass fractions of the remaining components. To avoid infeasible values such as negative concentrations, the values zi were bounded. The boundaries were calculated according to the equations max(ṁ i − Δṁ i , 0) ≤ ṁ i ≤ (ṁ i + Δṁ i)

(18)

with Δṁ i = ṁ Δxi(m) + xi(m)Δṁ

(19)

The maximum allowed adjustment of the mass fraction Δx(m) i and the maximum allowed adjustment of the mass flow Δṁ were set to 0.01 g/g and 0.1 g/min, respectively. Assuming that the measurement errors were only random errors and not gross errors (i.e., the measured values z̃i were not biased), the reconciliation process yields a consistent and statistically most probable data set. A global test for gross errors was applied to verify this assumption. When the minimum objective function value Ωmin exceeds the 95% quantile of the χ2 distribution with the difference of the total number of measured values and the number of constraints as degrees of freedom, a gross error is detected.33 In this case, the reconciliation would 635



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lead to large adjustments being made to the measured values, and it is most likely that the measurements are biased. Thus, all such data sets detected by the global test were rejected and not used for the parameter estimation procedure. The data reconciliation problem as defined in eqs 15−19 was implemented in Matlab (MathWorks, Natick, MA) and was solved for the unknown reconciled component mass flows ṁ i and the unknown extent of reaction ξ̇ using the solver fmincon.

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ASSOCIATED CONTENT

* Supporting Information S

Most important properties of the catalyst Amberlyst CSP2, chemical equilibrium and kinetic parameters determined by Schmitt and Hasse3 using PFR experiments, and data from each batch and CSTR experiment described in this work. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +49 (0)631 205 3497. Fax: +49 (0)631 205 3835. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge funding of the present work by BASF SE, Ludwigshafen, Germany. We thank Rohm and Haas, Chauny, France, for providing the catalyst Amberlyst CSP2 and Ralf Böhling, BASF, for fruitful discussions.

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REFERENCES

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(32) von Harbou, E.; Schmitt, M.; Großmann, C.; Hasse, H. A Novel Type of Equipment for Reactive Distillation: Model Development, Simulation, Sensitivity and Error Analysis. AIChE J., published online Nov 15, 2012, http://dx.doi.org/10.1002/aic.13947. (33) Narasimhan, S. Data Reconciliation & Gross Error Detection: An Intelligent Use of Process Data; Gulf Publishing Co.: Houston, TX, 2000.

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