Chemical Equilibrium and Reaction Kinetics of Heterogeneously

Pöpken, T.; Götze, L.; Gmehling, J. Reaction Kinetics and Chemical Equilibrium of Homogeneously and ..... Jan-Oliver Drunsel , Mario Renner , Hans H...
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Ind. Eng. Chem. Res. 2006, 45, 4123-4132

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Chemical Equilibrium and Reaction Kinetics of Heterogeneously Catalyzed n-Hexyl Acetate Esterification Markus Schmitt and Hans Hasse* Institute of Thermodynamics and Thermal Process Engineering, UniVersity of Stuttgart, D-70550 Stuttgart, Germany

In the framework of a project on reactive distillation, reaction equilibrium and kinetics of the esterification of n-hexanol and acetic acid, yielding n-hexyl acetate and water, were investigated. Chemical equilibrium and auto-catalyzed reaction kinetics were measured using batch reactors whereas a plug flow reactor was chosen to study the heterogeneously catalyzed reaction. The catalyst was Amberlyst CSP2. Dihexyl ether and hexene were observed as byproducts. The study covers temperatures between 20 and 130 °C, with a focus on the technically important range of 80-120 °C. Feed compositions were varied so that the entire concentration range relevant for reactive distillation was covered. On the basis of the experimental results, a thermodynamically consistent reaction model is developed. Two model types are tested, a pseudo-homogeneous and an adsorption-based model, for which the adsorption constants were determined from independent adsorption experiments of the immersion type carried out in the present work. Despite its simplicity, the pseudo-homogeneous model gives better results and is recommended for further use. 1. Introduction The economic potential of heterogeneously catalyzed reactive distillation is well-known. Taylor and Krishna1 identified in their review the lack of reliable and comprehensive experimental data as an obstacle for the validation of simulation tools and for a growth of trust into the reactive distillation technology. Years of intensive studies strongly improved this situation as can be seen from recent literature.2-8 It has now become clear that the main challenges in the development of these processes lie in mastering the reaction side rather than the separation side of the process. Obtaining reliable reaction data, both on the main and on side reactions, is often the bottleneck in the process development. The heterogeneously catalyzed reactive distillation of nhexanol with acetic acid to n-hexyl acetate and water was chosen as a test system for studying design and scale-up as well as modeling and simulation of reactive distillation in the framework of a European Community project.9 In the present work, within that project, comprehensive experimental studies of reaction equilibrium and kinetics were carried out with special attention to cover the temperature and concentration range relevant for reactive distillation. Auto-catalyzed reaction and chemical equilibrium were studied using batch reactors. For measuring heterogeneously catalyzed reaction kinetics a plug flow reactor was chosen because of the fluid dynamic similarity between the flow through the catalytic internals used in reactive distillation and this reactor type.10 Besides the similar flow pattern, the catalyst concentration is the same as in the catalyst filled channels and the liquid load of the plug flow reactor can be chosen according to that present in reactive distillation. Furthermore, steady-state operation allows excluding dynamic changes of the catalyst properties due to its concentration dependent adsorption and swelling. Side reactions are of special importance in reactive distillation as not only the conversion of the main reaction but also that of * To whom correspondence should be addressed. Phone: +49-711685-6103. Fax: +49-711-685-6140. E-mail: [email protected].

side reactions can be enhanced.11,12 Thus the formation of the byproducts dihexyl ether and hexene was included in the present study. On the basis of the experimental results, both a pseudohomogeneous and an adsorption-based reaction kinetic model were developed. The adsorption constants were determined in independent experiments. The results of these models are compared with the experimental data. 2. Chemical System n-Hexyl acetate (HexAc) is formed by the reaction of n-hexanol (HexOH) and acetic acid (AC) with water (W) as an additional product; see eq I. This reaction is a typical acid catalyzed, equilibrium limited esterification. As n-hexyl acetate and water are the heaviest and respectively the lightest boiling substances in the quaternary system, they can be continuously removed from the reaction zone in a reactive distillation column so that high conversions can be achieved, thus making reactive distillation an attractive process for producing n-hexyl acetate. H+

n-hexanol + acetic acid y\z n-hexyl acetate + water (I) Reaction I is slow in the absence of strongly acidic catalysts, despite auto-catalysis by acetic acid. In the present work, the strongly acidic ion-exchange resin Amberlyst CSP2 (Rohm and Haas) was used for catalysis. Its most important properties are summarized in Table 1. The particle size of about 1 mm is favorable for its use in catalytic packings such as Katapak-S or + -SP. The determination of the ion exchange capacity cHcat,dry was done according to DIN 54403.16 The swelling properties (cf. Table 1) indicate that the resin selectively adsorbs different species, with an affinity to small, polar, hydrogen bonding molecules. This raises the question of considering these adsorption effects in the reaction modeling. In esterification processes olefin and ether formation must be considered as possible side reactions,11,12 that is, for the n-hexyl acetate production the formation of 1-hexene (HEN) and dihexyl ether (DHE). According to the literature,17,18 dihexyl ether is formed by condensation of two n-hexanol molecules

10.1021/ie0504351 CCC: $33.50 © 2006 American Chemical Society Published on Web 05/10/2006

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Table 1. Properties of the Acidic Ion Exchange Catalyst Amberlyst CSP2 ion exchange capacity (mmol H+/g dry cat.) harmonic mean size (water swollen) dcat,W (mm) bulk density dry catalyst Fcat,dry,bulk (g dry cat./mL bulk dry cat.) polymer density Fpolymer (g dry cat./mL polymer) catalyst internal porosity P,cat,dry (mL pore volume/g dry cat.) catalyst bed porosity P,bed (mL bed void volume/mL catalyst bed) component dependent swelling properties swelling ratio cat,swell,i (mL bulk swollen cat./ mL bulk dry cat.) a

Schmitt.15

b

4.43-4.70a 0.8-1.0b 0.60a,b 1.41c 0.4b 0.37d

W

AC

HexOH

HexAc

1.62a

1.40a

1.58a

1.33a

Product data sheet. c Mazotti et al.13

d

Moritz.14

(reaction II), and 1-hexene can be formed either by cleavage of n-hexanol (reaction ΙII) or by cleavage of n-hexyl acetate (reaction IV). The experiments of the present work show that, under the conditions present in n-hexyl acetate reactive distillation, the side reactions II-IV only take place in the presence of the acid catalyst and that the formation of 1-hexene via reaction IV is dominant over reaction III. H+

2 n-hexanol y\z dihexyl ether + water H+

n-hexanol 98 1-hexene + water H+

n-hexyl acetate y\z 1-hexene + acetic acid

(II) (III) (IV)

The literature gives no clear answer to the question of reversibility of reactions II-IV . Therefore long-term experiments over several weeks were carried out in a batch reactor at 120 °C in the presence of Amberlyst CSP2, with either the lefthand side pure components or the right-hand side mixtures (cf. eqs II-IV) as feed. It appears that reactions II and IV are reversible but with the equilibrium far to the right-hand side, whereas reaction III seems to be irreversible. However, it also became clear from these experiments that the system of side reactions is more complex than indicated from eqs II-IV, with several hexene isomers being formed together with further components starting from 1-hexene. For a more detailed discussion regarding side reactions in the esterification of n-butanol with acetic acid under related conditions, see Blagov et al.19 This complexity makes unambiguous interpretation of the experimental results of the long-term studies difficult. The result for reaction IV is in agreement with the findings of Sashihara and Syverson,20 who studied noncatalyzed n-hexyl acetate pyrolysis and report an estimate for the equilibrium constant (mole fraction basis) of that reaction on the order of 102 to 104. The side reaction system was modeled here on the simplified level indicated by eqs II-IV as any more detailed modeling would have required extensive experimental studies beyond the scope of this work. 3. Experimental Section 3.1. Chemicals and Analysis. Acetic acid (p.a. grade, 0.998 g/g) was purchased from Merck, and n-hexanol (technical grade, 0.988 g/g) was delivered by BASF. Most of the n-hexyl acetate (synthesis grade > 0.985 g/g) was produced at Sulzer Chemtech during pilot-scale reactive distillation experiments.12 Only small amounts were purchased from Merck. Water was bi-distilled.

Analysis was carried out by gas chromatography using a Hewlett-Packard HP6890 gas chromatograph equipped with an autosampler. The method was the same as the one described previously;21 for details see Schmitt.15 As confirmed by 12 test mixtures in the concentration range relevant for the experiments of this work, the average relative error is 0.4 mol % for n-hexanol, 0.3 mol % for n-hexyl acetate, 3.8 mol % for acetic acid, and 4.1 mol % for water. The comparatively high relative errors for acetic acid and water are due to the relatively small mass fractions of these components of typically less than 0.1 g/g and 0.02 g/g, respectively, in connection with the massbased analysis method. Water concentrations of less than 0.005 g/g were analyzed using Karl Fischer titration (Metrohm 701 KF Titrino). The average relative error of water mass fractions obtained with that method is 1.0%. In addition to the test mixtures, 100% tests confirm the quality of the analysis with results for the mass fraction sums of all components between 1.00 and 1.02 g/g. 3.2. Apparatus and Procedures. 3.2.1. Batch Experiments. The studies of auto-catalyzed reaction kinetics, reaction equilibria, and binary adsorption experiments were performed in 20 mL glass vials, which were equipped with PTFE septa caps to allow sampling. They were kept at the desired temperature in a thermostated oven. The temperature was measured with Pt100 resistance thermometers inside two representative vials. The overall accuracy of the temperature measurement is better than (0.1 K. Auto-catalyzed reaction kinetics was examined by filling about 18 mL of reaction mixture into a vial, heating it to the desired temperature, and sampling it from time to time. For studies of chemical equilibria, about 15 mL of reaction mixture were filled into the vials together with about 1 g (dry mass) of Amberlyst CSP2, which had previously been transferred into the appropriate swelling state by thoroughly washing with the reactor feed mixture. The comparatively high catalyst mass was chosen to speed up the experiments. It was assumed that chemical equilibrium was reached, when consecutive analysis showed deviations of less than 0.0003 g/g for all components, which is about the reproducibility of the gas chromatographic analysis. Binary adsorption experiments were performed according to the immersion method described in detail by Dabrowski and Jaroniek.22 In these isothermal experiments, the so-called reduced surface excess on mass basis Γ(m) was determined: i

) Γ(m) i

m0 mcat,dry

(x(m),B - x(m),0 ) i i

(1)

A binary mixture (total initial mass m0 of about 13 g) with was filled in the vial together known initial mass fraction x(m),0 i with dried catalyst (mass mcat,dry of about 5 g). Then the vial was sealed and brought to the desired temperature. After equilibration, the bulk equilibrium mass fraction x(m),B was i determined. The catalyst drying procedure started with predrying at 90 °C and ambient pressure for 1 day, followed by 2 days at 110 °C and 5 kPa. In a general statement on adsorption experiments Dabrowski and Jaroniek22 talk of typical equilibration times between one and several tens of hours. Song et al.,23 who used Amberlyst 15 as the adsorbent, state that 10 min are sufficient for equilibration; Po¨pken et al.24 and Noeres et al.25 do not specify the equilibration times they have used. In this work, long-term equilibration experiments were made in all binary systems and

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Figure 1. Adsorption isotherms for Amberlyst CSP 2 with water + acetic acid at 25 °C. Experimental results for different equilibration times: 4 days (b), 9 days (O), 14 days (9), 22 days (0), 37 days (2), 46 days (4), and 53 days (+, not discernible from 4).

at all studied temperatures. A typical result is shown in Figure 1, using the experiments in the system water + acetic acid at 20 °C as example. It appears that, after a fast initial uptake in the first hours (not shown in Figure 1), equilibration is a slow process with the final adsorption equilibration reached only after 5-6 weeks. Because of enhanced transport processes, this time reduces to about 2 weeks at 70 °C and a few days at 120 °C. It is very likely that the diffusion into the catalyst microparticles is the reason for the long-term effects. These micropores, however, are not relevant for the catalyst performance, which is dominated by the easily accessible active sites located on the surface of the microparticles, as shown by Blagov et al.19 Adsorption “constants” that could be used for describing that process would have to depend on the equilibration time. To avoid such ambiguity, in the present work long-term experiments were used for the determination of the adsorption constants (for a discussion see the section Modeling and Discussion). 3.2.2. Plug Flow Reactor. For the studies of heterogeneously catalyzed reactions, a plug flow reactor was used, Figure 2. It consists of nine tubes in series (inner diameter di of 10.3 mm) that were filled with the catalyst. The active length of the catalyst bed in the tubes varies from 128 mm (tubes 1-4) over 257 mm (tubes 5 and 6) to 385 mm (tubes 7-9). To avoid corrosion problems, the reactor is made from nickel-based alloy NiChroFer 2.4605 supplied by F. W. Hempel & Co, Special Metals Group. Other tested materials such as stainless steel 1.4571 showed corrosion at the contact points between the catalysts beads and the reactor wall, leading to a loss of catalyst activity due to corrosion products. The extent of deactivation is important in the case of the laboratory plug flow reactor, because of its high ratio of contact area to catalyst volume. At the reactor in- and outlets as well as between all tubes sample ports are located, so that a concentration profile with 10 data points along the reactor can be determined. The whole setup is immersed in a thermostated bath. The temperature is measured at seven points inside the reactor with Pt100 resistance thermometers to check isothermal operation. The overall accuracy of the temperature measurement is better than 0.1 K. Each sample port is equipped with a liquid-thermostated cooler that ensures quick cooling of the samples to room temperature before they are filled in sample vials. A piston feed pump (HPD pump multitherm 200, Bischoff) is used for the reactor feed, which can supply a maximum liquid load of 35 m3/(m2 h) (reference area πdi2/4). The feed is pre-thermostated in the feed line, which is also immersed in the thermostated bath. For adjusting the desired reactor pressure, a back-pressure valve is used. The reactor can

Figure 2. Flowsheet of plug flow reactor (D, drum; X, sample withdrawal; TI, temperature measurement; PI, pressure measurement).

be operated at pressures up to 1 MPa and temperatures up to 130 °C. The experimental procedure started with heating the reactor to the desired temperature. During this time only a small feed flow was pumped through the reactor to allow setting the reactor pressure. The pressure was set to about 0.5 MPa in all experiments to avoid partial evaporation. After the desired temperature was reached, the feed flow was set to its final value. The reactor was left undisturbed for at least 150 min, which is sufficient to attain steady state as confirmed by consecutive analysis of the reactor outlet composition in each experiment and reproductions with durations from 120 to 240 min. Then, samples were taken from the sampling ports and analyzed by gas chromatography and Karl Fischer titration to determine the concentration profile. 3.3. Experimental Program. 3.3.1. Chemical Reaction. As explained in the introduction the studies of the present work were carried out in the framework of a project on reactive distillation.6,12 Temperatures and initial compositions of the reaction equilibrium and kinetic experiments were, therefore, chosen in the range relevant for that application. For the temperature, the main focus was on the range between 80 and 120 °C. At lower temperatures the reaction is too slow whereas at higher temperature the stability of the ion-exchange resin is not sufficient and side products are formed in larger amounts. The initial compositions of the reaction experiments cover the whole range that is of interest for reactive distillation as shown in Figure 3.

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Figure 3. Double-triangular diagram of the system n-hexanol + acetic acid + n-hexyl acetate + water in reduced mole fractions (cf. eq 2). Shaded area: range of compositions observed in the reaction zone of reactive distillation columns.6,12,15 Symbols: feed mixtures of experiments from the present work on chemical equilibrium (4), auto-catalyzed reaction kinetics (0), and heterogeneously catalyzed reaction kinetics (O; experiments with results given below, .).

The coordinate transformation used for the representation in Figure 3 is

νi x with (νi/νk)xk ) min!; νk k i ) W, AC, HexOH, and HexAc; and k ) W and HexAc (2)

Xi* ) xi -

It is similar to the transformation proposed by Ung and Doherty,26 with the main difference concerning the choice of the reference component k. The reduced mole fractions Xi* can directly be used for planning the experiments. The chemical interpretation of the transformation (eq 2) is the following: the transformed concentrations are those that would be found if the reaction would proceed in the backward direction until one of the products, n-hexyl acetate or water (namely, the one with the lower mole fraction), is completely converted, thus reducing the initially quaternary mixture to a ternary one (with only two degrees of freedom, easy to represent graphically). In other words, the resulting three-component mixture in reduced mole fractions is exactly the composition of a feed, which would react to the original four-component mixture composition. The obtained ternary mixtures can be represented in triangular diagrams. To get a comprehensive picture, two of these need to be used, one for n-hexanol + acetic acid + water and one for n-hexanol + acetic acid + n-hexyl acetate. It is convenient to draw these two triangles so that they have a common side representing the system n-hexanol + acetic acid. Chemical equilibrium experiments (4) were carried out at 18 different initial compositions covering the entire upright triangle displayed in Figure 3. The examined temperatures were 80, 90, 100, 110, and 120 °C. Thus, in total 90 chemical equilibrium experiments were made. The auto-catalyzed reaction (0) was only examined at five different initial compositions (see Figure 3) due to its lower importance for the present work. Experiments were carried out at 80, 100, and 120 °C and, to obtain information for sample handling, also at 25 °C. Heterogeneously catalyzed reaction kinetics of the main reaction I (O, .) was investigated in the plug flow reactor for

the initial compositions shown in Figure 3. All in all 36 experiments were carried out at temperatures between 60 and 120 °C. The experiments include studies in which the influence of the mass flow on the results was studied. Typical liquid loads in reactive distillation experiments6,12 are between 3 and 7 m3/ (m2 h) (reference: column diameter). Depending on the catalyst volume fraction of the catalytic internal and assuming that all the liquid flows only through the catalyst-filled channels of the internal, this results in catalyst liquid loads and thereby plug flow reactor liquid loads in the range from 15 to 40 m3/(m2 h) (reference: reactor diameter). Taking bypass in a real reactive distillation internal into account, the liquid load range of interest in the plug flow reactor experiments is somewhat lower, ranging from 5 to 30 m3/(m2 h). In addition to the main reaction, heterogeneously catalyzed kinetics of the side reactions II-IV were examined. Four experiments starting from pure n-hexanol or pure n-hexyl acetate at temperatures of 120 and 130 °C were carried out. Clearly, that small data basis only allows the determination of preliminary side reaction kinetics. 3.3.2. Adsorption Experiments. As adsorption experiments of the immersion type may take up to a few weeks (see above, section Apparatus and Procedures) and high adsorbent (here, catalyst) concentrations are used, only nonreactive systems can be examined. Because, furthermore, the system water + n-hexanol has a large miscibility gap, only adsorption in the binary systems water + acetic acid, n-hexanol + n-hexyl acetate, and acetic acid + n-hexyl acetate was studied. The system water + acetic acid was studied at 20, 70, and 120 °C, whereas the systems n-hexanol + n-hexyl acetate and acetic acid + n-hexyl acetate were examined only at 20 °C, as at higher temperatures side reactions II-IV lead to non-negligible formation of byproducts from n-hexanol and n-hexyl acetate. 3.4. Experimental Results. Typical results of the adsorption experiments, chemical equilibria, auto-catalyzed reaction kinetics, and heterogeneously catalyzed reaction kinetics of the main reaction I and the side reactions II-IV are presented together with the modeling results in the section Modeling and Discussion. The full information on experimental primary data is given by Schmitt.15 Only some results of general importance regarding the studies of the heterogeneously catalyzed reaction kinetics of the main reaction in the plug flow reactor are discussed in the present section. The quality of the plug flow reactor experiments was checked with a total of eight reproductions at three different concentrations. A typical example is presented in Figure 4. To quantify the reproduction quality, reaction kinetic constants were fitted individually to each single experiment and compared with the corresponding mean value. The reaction kinetic constants showed deviations from their mean value of less than (5%, proving the good reproduction quality. In addition to the reproductions, the reaction extent calculated individually for each component deviates from its mean value always by less than 6% for all experiments, again confirming their quality. An important question to be answered is the presence or absence of external mass transport limitations. This question was examined at 120 °C with three mass flow studies at different feed compositions. Figure 5 shows as a typical example the n-hexyl acetate concentrations observed in four experiments with liquid loads ranging from 5 to 30 m3/(m2 h) plotted over residence time in the reactor. Because the curves coincide within the quality of a reproduction experiment, it can be concluded that external mass transfer limitations are negligible in the relevant liquid load range. Po¨pken et al.24 and Gonza´lez and

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(

K(T) ) exp -

)

∆Rµ(T) RT

)

∏i aiν

i

(3)

∆Rµ(T) is the liquid chemical potential of the reaction at temperature T, ai is the activity, and νi is the stoichiometric coefficient of component i. The function K(T) can be determined from a fit to experimental data. Here, the integrated form of the van’t Hoff equation was used for that purpose

ln K(T) ) a +

Figure 4. Reproduction (4) of a heterogeneously catalyzed plug flow reactor experiment (O; feed composition, 0.605 mol/mol n-hexanol, 0.235 mol/mol acetic acid, 0.155 mol/mol n-hexyl acetate, 0.005 mol/mol water; liquid load, 25.9 m3/(m2 h); T ) 393.4 K).

b T

with

a ) ln K(T*) +

and

b)-

∆Rh R

∆Rh RT* (4)

In this equation a and b are the fitted parameters, from which the reaction enthalpy ∆Rh (which is assumed to be constant in the temperature range of interest) and the equilibrium constant K(T*) at reference temperature T* ) 393.15 K can be calculated. Alternatively to a correlation, numbers for the chemical equilibrium constant K in the liquid phase can also be predicted at any temperature, starting from eq 3, with data on standard enthalpy of formation, standard entropy, and caloric data to calculate ∆Rµ(T). This was done here using published standard state data28 (or where such data were missing a correlation29) and heat capacity data.30

Figure 5. Study of the influence of mass flow on the heterogeneously catalyzed reaction (feed composition for all experiments, 0.605 mol/mol n-hexanol, 0.235 mol/mol acetic acid, 0.155 mol/mol n-hexyl acetate, 0.005 mol/mol water; T ) 393.4 K). Experimental n-hexyl acetate concentrations at liquid loads of 5.15 m3/(m2 h) (0), 10.54 m3/(m2 h) (O), 20.79 m3/(m2 h) (]), and 31.09 m3/(m2 h) (4).

Fair27 report for related problems that intraparticle mass transfer resistance is negligible as well; hence, it can be concluded that the reaction kinetic data measured in this work is intrinsic reaction data. 4. Modeling and Discussion The new experimental data on reaction equilibrium, kinetics, and adsorption from the present study was correlated with thermodynamically consistent models. The influence of pressure on the results is neglected as only liquid and solid phases are present. The nonideality of the liquid phase is described with activity coefficients γi calculated with the NRTL model. NRTL parameters were adopted from Schmitt and Hasse21 and are based on a comprehensive study on vapor-liquid and liquidliquid equilibria in binary and ternary systems containing water + n-hexanol + acetic acid + n-hexyl acetate as well as some data on the quaternary system. The parameter-set used here is the one recommended by Schmitt and Hasse21 for the description of vapor-liquid equilibria, because in reactive distillation the reaction takes place with simultaneous vapor-liquid mass transport. 4.1. Chemical Equilibrium. The thermodynamically consistent chemical equilibrium constant K derived from thermodynamics, neglecting pressure dependence, is

The experimental values of the chemical equilibrium constant K were obtained from composition data according to eq 3, applying activity coefficients determined as described above. They are plotted against the inverse temperature in Figure 6, together with their correlation by eq 4 and their prediction on basis of standard thermodynamic data. The experimental data on chemical equilibrium show a comparatively large standard deviation of 18.5%. This is largely due to a systematic influence of composition on the experimental number for K (the higher the initial n-hexyl acetate concentration, the higher K) that should in theory not be observed. This finding is not unexpected and shows that the NRTL model cannot fully predict the influence of activity coefficients on the compositions in chemical equilibria. For a detailed recent discussion of that subject, see Grob and Hasse31 and Grob.32 The experimental chemical equilibrium constant data can be correlated using eq 4. The results are given in Table 2, indicating a weakly endothermic reaction. The observed large deviations between the prediction based on standard thermodynamic data and the experimental results underline the need for experimental studies. 4.2. Auto-Catalyzed Reaction Kinetics. Po¨pken et al.24 successfully used a rate equation to describe auto-catalyzed reaction kinetics of methyl acetate esterification, which assumes catalysis by molecular acetic acid. This approach was also used in the present work to describe auto-catalysis of reaction I:

1 dxi auto ) rauto ) aAC(kauto I f,I (T)aHexOHaAC - kb,I (T)aHexAcaW) νi dt (5) ) As in chemical equilibrium the reaction rate vanishes rauto I 0, eq 5 yields the thermodynamically consistent relationship between the rate constants kauto f/b,I(T) of forward and backward

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Figure 6. Chemical equilibrium constants of the esterification of n-hexanol and acetic acid: experimental data, this work (O), fit of the data with eq 4 (solid line), prediction from standard state and caloric data (dashed line). Table 2. Chemical Equilibrium Correlation Parameters Fitted to the Experimental Data a

b (K)

K(T* ) 393.15 K)

∆Rh (kJ/mol)

4.218

-335.0

29.0

+2.9

Figure 7. Auto-catalyzed reaction kinetics of the esterification of n-hexanol with acetic acid, exemplified for n-hexanol concentration courses at different temperatures (feed composition for all experiments about 0.20 mol/mol n-hexanol, 0.325 mol/mol acetic acid, 0.475 mol/mol n-hexyl acetate). Experimental data, this work: 298.3 K (0), 351.8 K (O), 373.88 K (]), and 394.1 K (4). Simulation: solid lines.

Table 3. Model Parameters for Describing the Auto-Catalyzed Reaction Kinetics of the Esterification Reaction I kauto,0 (s-1) f,I 5.40 ×

Eauto f,I (kJ/mol)

104

61.6

reaction and the chemical equilibrium constant K(T) (see eq 3):

kauto f,I (T) kauto b,I (T)

)

aHexAcaW ) K(T) aHexOHaAC

(6)

Consequently, eq 5 can be reformulated using eq 6 to substitute kauto b,I (T) and using independent chemical equilibrium information instead, thus reducing the number of adjustable reaction kinetic parameters:

(

) aAC kauto rauto I f,I (T) aHexOHaAC -

1 a a K(T) HexAc W

)

(7)

Figure 8. Adsorption isotherms for Amberlyst CSP2 with water + acetic acid. Experimental results at 20 °C (O), 70 °C (0), and 120 °C (4). Solid line: temperature independent correlation.

4.3. Adsorption. Binary adsorption on the solid catalyst is modeled here using the Langmuir isotherm: B mads Kads mads i i ai ) mcat,dry mcat,dry 1 + KadsaB + KadsaB 1

The temperature dependence of the forward reaction kinetic constants kauto f,I is modeled with Arrhenius’ law

( )

auto,0 kauto exp f,I (T) ) kf,I

Eauto f,I RT

(8)

The kinetic model described by eqs 7 and 8 has two parameters, the pre-exponential factor kauto,0 and the activation f,I energy Eauto f,I of the forward reaction. These parameters were determined from a fit to the experimental data of the present work and are given in Table 3. The mean relative deviation between simulation and experimental data is 5.3%, which is acceptable for the purpose of this work. Losses of light boiling components into the relatively big gas phase led to deviations in the reaction extents of the individual components in the liquid phase of up to 20%. Figure 7 shows a comparison between experimental data and the reaction kinetic model for the example of a temperature study. At ambient temperature, it takes many hours until the reaction progress of the auto-catalyzed reaction leads to concentration shifts beyond the analytical uncertainty. Even at 120 °C, it takes about 50 h until the reaction approaches equilibrium. Comparison with the heterogeneously catalyzed reaction kinetics determined later shows that in reactive distillation the auto-catalyzed reaction may safely be neglected.

1

2

(9)

2

mads i /mcat,dry is the adsorbed mass of component i per unit mass of dry catalyst from a liquid bulk mixture with the bulk phase activities aBi . Here the formulation of the Langmuir isotherm on a mass basis is chosen, because the assumption of constant, composition independent, total adsorbed mass per unit mass of dry catalyst mads/mcat,dry, though still crude, is much better met than the assumption of constant adsorbed amount. This is in agreement with the work of Po¨pken et al.24 For more details see Schmitt.15 An important question is whether the adsorption constants depend on temperature. The temperature range important Kads i for reactive distillation is near 120 °C. At that temperature, longterm adsorption experiments with mixtures containing n-hexanol or n-hexyl acetate in the presence of catalyst are not possible because of the occurrence of side reactions, even in systems in which the main reaction does not take place. Therefore, adsorption experiments over the whole temperature range were carried out only for the nonreactive system water + acetic acid; see Figure 8. They show only a weak influence of temperature, so that it was decided to neglect that dependence in modeling of the adsorption constants not only for the system water + acetic acid but also for the other studied systems as well. and the constant ratio mads/mcat,dry Adsorption constants Kads i (see eq 9) can be determined by means of fitting these

Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006 4129 +

mcat,drycHcat,dry (product of dry catalyst mass mcat,dry and ion + exchange capacity cHcat,dry) is then given by

dni dt

+

IV

) mcat,drycHcat,dry

νm,irhet ∑ m m)I

(11)

When eq 11 is used, the component material balance of an ideal plug flow reactor can be derived:

dn˘ i Figure 9. Adsorption isotherms for Amberlyst CSP2 at 20 °C. Experimental results: n-hexanol + n-hexyl acetate (O), acetic acid + n-hexyl acetate (0). Solid line: temperature independent correlation.

parameters to the information obtained from the binary adsorption experiments, namely, the data of the reduced surface excess on mass basis Γ(m) and bulk equilibrium mass fractions x(m),B . i i The necessary relation between the individually adsorbed masses (m) mads can be obtained without further assumpi /mcat,dry and Γi tions using the definition of Γ(m) from eq 1 together with the i overall mass balance of the binary adsorption process (see Kipling33). This results in

mads mads 2 1 (m),B (m),B Γ(m) ) x x 1 1 2 mcat,dry mcat,dry

(10)

The determination of the model parameters was done here using a simultaneous fit of all binary adsorption experiments at 20 °C. The resulting parameters are summarized in Table 4.

dmcat,dry

Kads AC

ads KHexOH

ads KHexAc

8.1

1.7

10.4

0.5

mads/m

cat,dry

IV

∑νm,irhet m m)I

(12)

where n˘ i refers to the component mole flow. The rates of reaction rhet m are modeled with the pseudohomogeneous approach, that is, assuming the catalyst to be homogeneously distributed in the bulk phase. This is done thermodynamically, consistent on the basis of activities ai. For the main reaction, this results in

(

het rhet I ) kf,I (T) aHexOHaAC -

1 a a K(T) HexAc W

)

(13)

Here again the chemical equilibrium information has been taken into account to substitute the backward reaction kinetic constant, thus reducing the number of adjustable reaction kinetic parameters (see modeling of auto-catalyzed reaction kinetics above). As discussed in the Chemical System section, the side reactions are either irreversible or have large chemical equilibrium constants. As a result of the limited amount of available information, these reactions were treated as simple as possible and, hence, modeled as irreversible reactions, which leads to

Table 4. Parameters of the (Mass-Based) Adsorption Model. Kads W

+

) cHcat,dry

het rhet II ) kf,II(T)aHexOHaHexOH

(14)

het rhet III ) kf,III(T)aHexOH

(15)

het rhet IV ) kf,IV(T)aHexAc

(16)

(g/g)

0.44

Figures 8 (water + acetic acid) and 9 (acetic acid + n-hexyl acetate and n-hexanol + n-hexyl acetate) show the correlation results together with all experimental data. Considering the simplicity of the Langmuir model for the liquid-phase adsorpbetween tion, the agreement with a mean relative error in Γ(m) i simulation and experiment of 7% is good. The nature of the adsorption isotherm of water + acetic acid in Figure 8 shows clearly that water is stronger adsorbing than acetic acid. The adsorption isotherms in Figure 9 indicate that adsorption is decreasing in the order n-hexanol, acetic acid, n-hexyl acetate. The adsorption constants given in Table 4 reflect this behavior. It is worthwhile to mention that the higher adsorption constant of n-hexanol compared with that of water is attributed to the formulation of adsorption on a mass basis. 4.4. Heterogeneously Catalyzed Reaction. Both the main reaction I and side reactions II-IV were studied in the present work using a plug flow reactor. In the studies of the main reaction, the slow byproduct formation was not observed. During the investigation of the side reactions, the main reaction did not take place because of the pure n-hexanol or n-hexyl acetate feed, but the side reactions II and III took place simultaneously. Generally up to four simultaneous reactions have to be considered in modeling. The reaction source term for a control volume containing the mole number of catalytically active sites

The temperature dependence of all reaction kinetic constants is modeled using the Arrhenius approach similar to eq 8. As an alternative to the pseudo-homogeneous approach, also an adsorption-based reaction kinetic model was tested. This type of model is preferred by different authors in the literature23-25 as it allows accounting for the concentration differences between the reacting adsorbed phase and the bulk phase. Po¨pken et al.24 give a detailed description of the model equations for a Langmuir-Hinshelwood-Hougen-Watson (LHHW) mechanism, which was also used in the present work. Only the results are therefore summarized here. They are based on the following assumptions: the reaction takes place in the adsorbed phase according to the mole fractions present there; no mass transfer limitations are present; the multiphase adsorption equilibrium can be described with the Langmuir isotherm. The thermodynamically consistent formulation of the reaction rate according to the LHHW adsorption mechanism is

rLHHW I

)

kLHHW (T)a′HexOHa′AC - kLHHW (T)a′HexAca′W f,I b,I (a′HexOH + a′AC + a′HexAc + a′W)2

(17)

where a′i is calculated from the bulk phase activity aBi , the

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Figure 10. Simulations with the adsorption-based model (dashed lines) and the pseudo-homogeneous model (solid lines) in comparison with experimental data (n-hexyl acetate (4) and n-hexanol (O)). Feed composition: 0.605 mol/mol n-hexanol, 0.235 mol/mol acetic acid, 0.155 mol/mol n-hexyl acetate, 0.005 mol/mol water; liquid load, 25.9 m3/(m2 h); T ) 393.4 K.

Figure 12. Results from studies of heterogeneously catalyzed n-hexyl acetate formation (reaction I). Symbols: experimental n-hexanol concentration courses. Lines: model predictions. Feed compositions: see dots (.) in Figure 3; liquid load ∼25 m3/(m2 h); T ) 393.4 K. Table 5. Parameters for the Pseudo-Homogeneous Model of the Heterogeneously Catalyzed Esterification Reaction Ι (Model Equations 13 and 19 with an Arrhenius Term Similar to Equation 8)

Figure 11. Reaction kinetic constants of experiments with varying initial composition (compare Figure 3) at T ) 393.15 K determined from individual fits (O). Solid line: result from kinetic model (cf. eq 19).

molecular mass Mi, and adsorption constant Kads i :

a′i )

B Kads i ai Mi

(18)

The adsorption constants were not treated as adjustable reaction kinetic parameters but were adopted from Table 4 and are, hence, based on independent experimental data. Similar to eq 13, the two kinetic constants are coupled by the equilibrium constant so that only one of them was adjusted in the fit to the experimental data. Figure 10 shows a typical result for an individual fit of both reaction kinetic models to experimental data of a single experiment. The adsorption based model is unable to give an adequate description whereas the pseudo-homogeneous model nicely describes the reaction progress. This observation holds for all experiments carried out in the present work. In the simultaneous fit of both models to all experimental data from this work the mean relative deviation of the mole fractions predicted by the adsorption-based model is 6.6% compared to 4.2% for the pseudo-homogeneous model. The unsatisfactory results for the adsorption-based model can be explained by the questionable significance of the adsorption constants from the (long-term) equilibrium experiments for the reactive distillation process; see above. Consequently, the adsorption based model is not recommended for use and not discussed any further in the following. Figure 11 shows results from reaction kinetic constants obtained from individual fits of the pseudo-homogeneous model to each experiment of the concentration study, in which only the initial composition was varied (see Figure 3 for those

het,0 kf,I,a [mol/(molH+‚s)]

+ khet,0 f,I,b [mol/(molH ‚s)]

Ehet f,I (kJ/mol)

1.0697 × 106

1.0447 × 106

49.0

compositions). If the reaction kinetic model is capable of describing the reaction rate in the composition space correctly, these fits should yield similar numbers for the kinetic constants. Instead of plotting the results three-dimensionally over the reduced composition plane (cf. Figure 3), they are plotted here two-dimensionally as a function of the reduced n-hexanol concentration only, as the influence of the reduced acetic acid concentration is only small. As can be seen in Figure 11, the reaction kinetic constants from the individual fits depend strongly on the reduced n-hexanol concentration. Increasing the reduced n-hexanol concentration from 0.1 to 0.7 mol/mol reduces the rate by about a factor of 2.5. This means that although the pseudo-homogeneous reaction kinetic model nicely describes the reaction for a given initial composition (see Figure 10), it exhibits a weakness to describe concentration dependence over the composition space, due to catalyst-reactant interactions. This is in agreement with the findings of Grob32 for the butyl acetate esterification. To provide a good reaction kinetic model, the dependence of the kinetic constants on the composition needs to be accounted for. This was done here by empirically introducing a simple linear dependence of the pre-exponential factor khet,0 f,I from the reduced n-hexanol mole fraction XHexOH* according to the insight obtained from Figure 11: het,0 het,0 khet,0 f,I ) kf,I,a - kf,I,b XHexOH*

(19)

The parameters of the empirically extended pseudo-homohet,0 het geneous model, with khet,0 f,I,a , kf,I,b , and Ef,I fitted to the entire set of available experiments, are summarized in Table 5. The resulting concentration dependence of the reaction kinetic constant at T ) 393.15 K is included in Figure 11, showing a good representation of the individual fit results. The mean relative error of this model is only 2.8%, which is much smaller compared with 4.2% of the model that does not consider the concentration dependence according to eq 19. Figure 12 illustrates the quality of the model by comparing model prediction to typical results of experimental reaction kinetic

Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006 4131

Figure 13. Results from studies of heterogeneously catalyzed side reactions II and III. Symbols: concentration courses of n-hexanol (]), water (O), hexene (4), and dihexyl ether (0). Solid lines: model predictions. The feed was pure n-hexanol (technical grade); liquid load, 24.9 m3/(m2 h); T ) 403.3 K.

chemical equilibrium and kinetics of the main and side reactions. In the present work, a comprehensive study of the esterification of n-hexanol with acetic acid was carried out to provide such information. Heterogeneously catalyzed reaction kinetics were studied using a plug flow reactor. The catalyst was Amberlyst CSP2. Dihexyl ether and hexene were observed as side products. The reaction kinetic study of the main and side reactions covers the technically important range with temperatures between 60 and 130 °C and the initial compositions according to those present in the reaction zone of reactive distillation. In addition, chemical equilibrium and auto-catalyzed reaction kinetics were examined in batch reactors, the latter being of negligible rate compared with heterogeneous catalysis. On the basis of the experimental results, a thermodynamically consistent reaction model was developed employing chemical equilibrium information for parameter reduction. The adsorption-based model, for which the adsorption constants were determined from independent adsorption experiments of the immersion type, fails to correctly describe reaction kinetics. This is probably due to the character of the experiments for determination of adsorption constants, causing discrepancies with the locus of the chemical reaction in the catalyst. Despite its simplicity, the pseudo-homogeneous model gives better results and is recommended for use. Acknowledgment

Figure 14. Results from studies of heterogeneously catalyzed side reaction IV. Symbols: concentration courses of n-hexyl acetate (]), acetic acid (O), and hexene (4). Solid lines: model predictions. The feed was pure n-hexyl acetate (synthesis grade); liquid load, 24.7 m3/(m2 h); T ) 403.3 K. Table 6. Parameters for the Kinetic Model of the Heterogeneously Catalyzed Side Reactions II-IV reaction m

+ khet,0 f,m [mol/(molH ‚s)]

Ehet f,m (kJ/mol)

reaction II reaction III reaction IV

1.7115 × 107 2.7102 × 104 2.8184 × 107

85 64 84

studies. It is worthwhile to mention that heterogeneous catalysis increases the reaction rate by about factor 300 compared to autocatalysis. In addition, note that the reaction rates calculated with model parameters from Table 5 differ from the rates obtained using the preliminary model and parameters given in a former paper by Schmitt et al.6 Because the reaction kinetic data base of the work of Schmitt et al.6 was determined at very small liquid loads using a plug flow reactor made of stainless steel 1.4571, mass transfer limitations were present together with corrosion effects, both hampering the reaction. Thus only the reaction kinetic data, model, and parameters given in this work should be used further. Despite the very small data basis of only four experiments, a reaction kinetic model for the side reactions was developed. The results for the parameters of eqs 14-16 (Arrhenius-like temperature dependence similar to eq 8) are shown in Table 6. The mean relative error in the byproduct mole fractions is 9%, which is good, considering the small absolute numbers of these mole fractions in the experiments. Typical examples for all side reactions are shown in Figures 13 and 14. 5. Conclusions The design and simulation of reactive distillation processes requires knowledge of the chemical reaction, namely, of

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ReceiVed for reView April 11, 2005 ReVised manuscript receiVed March 16, 2006 Accepted March 29, 2006 IE0504351