Ind. Eng. Chem. Res. 2009, 48, 2519–2532
2519
Kinetic Study of Dowex 50 Wx8-Catalyzed Esterification and Hydrolysis of Benzyl Acetate Sami H. Ali* and Sabiha Q. Merchant Chemical Engineering Department, Kuwait UniVersity, P.O. Box 5969, Safat 13060, Kuwait
Dowex 50Wx8-catalyzed reactions occurring in systems containing acetic acid, benzyl alcohol, benzyl acetate, and water were studied over a range of catalyst loadings, temperatures, and feed compositions. The initial esterification rate is found to depend on these reaction conditions. The presence of water rather than ester in the feed is found to exert a more adverse effect on the esterification rate. Water is found to swell the resin significantly more than the other three components present in the system. The swelling and adsorption data indicate that adsorption behavior over Dowex 50Wx8 is complex. Although, the Langmuir-Hinshelwood (LH) model can successfully predict the esterification kinetics, it cannot validate the hydrolysis data. A new form of modified LH model indirectly accounting for changes occurring in the resin phase-component activities during the course of the reaction is presented. This is capable of predicting esterification and hydrolysis kinetics as well as the equilibrium behavior. 1. Introduction A large quantity of acetic acid is formed as a byproduct/ waste in the manufacture of cellulose esters and terephthalic acid and from processes using acetic anhydride either as a reagent or a solvent.1 Recovery of this acid constitutes a major problem for the petrochemical and fine chemical industries. The reactive distillation process for heterogeneously catalyzed esterification of the acid with suitable alcohols resulting in valueadded acetates is a feasible solution.2-5 Acetates are used as solvents for nitrocellulose, lacquers, leather finishes, paints, and plastics. They are also used as flavoring agents and preservatives in the food industry, and as fragrances and solvents in the perfume and cosmetics industries. However, the acetates formed with C1 to C5 alcohols are highly flammable and produce vapors which might form explosive mixtures with air at normal temperatures. They also have adverse health effects. The acetates formed with C6 and C7 alcohols (cyclohexyl, hexyl, heptyl, and benzyl acetate) are less flammable in comparison. Hence, esterifying acetic acid in waste streams with these alcohols appears to be more advantageous. Among these alcohols, esterification with benzyl alcohol appears to be the most attractive as the acetate formed has the highest flash point (flash points of hexyl, cyclohexyl, heptyl, and benzyl acetate are 316, 331, 341, and 363 K, respectively).6 Catalysts are required to speed up the esterification reactions which tend to be slow and equilibrium limited. Cation exchangers, like Amberlyst-36, K2441, Amberlyst-15, Indion-130, Amberlite IR120, and Dowex 50Wx8, are gaining more popularity as they are ecofriendly, noncorrosive, and have good thermal stability.7-16 In the current work, we have studied esterification on the macroreticular catalyst Amberlyst 15 and the microreticular catalysts Amberlite IR 120 and Dowex 50 Wx8, whose salient physical properties are considerably different from those of Amberlyst 15. Optimal functioning of reactive distillation depends largely on a relevant process design, properly selected column internals, feed locations, and placement of catalyst as well as a sufficient understanding of general and particular features of the process * To whom correspondence should be addressed. E-mail:
[email protected]. Tel.: (00965) 24985702. Fax: (00965) 24839498.
behavior. All these factors are generally interrelated and have to be considered simultaneously. Patel and Saha13 have extensively studied the heterogeneous kinetics and residue curve mapping for the esterification of acetic acid with hexyl alcohol. The latter esterification has also been extensively studied under the European Union′s Intelligent Column Internals for Reactive Separations (INTINT) project.2,14 The esterification of acetic acid with benzyl alcohol could also be carried out in a similar fashion, with the ester formed in the reaction zone being purified in the stripping section and leaving the column as the “product” stream. Kinetic studies of the esterification of acetic acid with benzyl alcohol have been reported by some workers.12,15,17,18 However, these workers did not account for nonidealities arising due to differences in size and polarity of the constituent species. This greatly restricts the understanding of the probable reaction mechanism and decreases the scalability of the determined kinetic parameters. This study therefore attempts to study systematically cation exchange resin-catalyzed reactions in systems comprising acetic acid, benzyl alcohol, benzyl acetate, and water, and generate the most representative rate expression for it. The nonideality of the system was accounted for by determining activity coefficients of the component species present with the help of one of the most reliable and extensively studied form of the UNIFAC model, namely the Modified UNIFAC (Dortmund) model.19-27 Furthermore, this model has also been integrated into commercial process simulators such as Aspen Plus and ChemCAD. The kinetic model that best correlates the generated kinetic data is determined. The pseudohomogeneous (PH), Eley-Rideal (ER), LangmuirHinshelwood (LH), and modified Langmuir-Hinshelwood (MLH) models were tested for this purpose. Kinetic parameters were generated based on the model best able to represent all the collected data. The generated mathematical models representing the kinetics of the esterification and hydrolysis reactions will be of interest to both research and industry in applications such as in the design and operation of reactive distillation units. 2. Theory 2.1. Reaction Mechanism. Acetic acid and benzyl alcohol react to give benzyl acetate and water. The product composition
10.1021/ie8006787 CCC: $40.75 2009 American Chemical Society Published on Web 01/26/2009
2520 Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 Table 1. Rate Expressions for Different Rate-Controlling Mechanismsa model no.
a
limiting step
adsorption status of reactants
rate expression
1
surface reaction
non
2
surface reaction
adsorbed acetic acid reacting with benzyl alcohol in the fluid
3
adsorption of acid
4
desorption of ester
5
desorption of water
surface reaction
6
surface reaction
adsorbed benzyl alcohol reacting with acetic acid in the fluid
7
adsorption of alcohol
8
desorption of ester
9
desorption of water
10b
surface reaction
11
adsorption of acid
12
adsorption of alcohol
13
desorption of ester
14
desorption of water
adsorbed acetic acid reacting with adsorbed benzyl alcohol
ri ) Mcat.kf(aacidaalc - (1/Ka) aesterawater) ri ) [Mcat.kfKacid(aacidaalc - (aesterawater/Ka))]/ [1 + Kacidaacid + Kwaterawater] ri ) [mcat.kacid(aacid - (aesterawater/(kaaalc)))]/[1 + (Kacid/Ka) (aesterawater/aalc) + Kwaterawater] ri ) [Mcat.Kakester(aalcaacid/awater - (aester/Ka))]/ [1 + Kacidaacid + KaKester(aalcaacid/awater)] ri ) [Mcat.Kakwater(aalcaacid/aester - (awater/Ka))]/ [1 + Kacidaacid + KaKwater(aalcaacid/aester)] ri ) [Mcat.kfKalc(aacidaalc - (aesterawater/Ka))]/ [1 + Kalcaalc + Kwaterawater] ri ) [Mcat.kalc(aalc - (aesterawater/(Kaaacid)))]/ [1 + (Kalc)/(Ka)(aesterawater/aacid) + Kwaterawater] ri ) [Mcat.Kakester(aalcaacid/awater - (aester/Ka)]/ [1 + Kalcaalc + KaKester(aalcaacid/awater)] ri ) [Mcat.Kakwater(aalcaacid/aester - (awater/Ka)]/ [1 + Kalcaalc + KaKwater(aalcaacid/aester)] ri ) [Mcat.kfKacidKalc(aacidaalc - (aesterawater/Ka)]/ [1 + Kacidaacid + Kalcaalc + Kesteraester + Kwaterawater)2] ri ) [Mcat.kacid(aacid - (aesterawater/(Kaaalc)))]/ [1 + (Kacid)/(Ka)(aesterawater/aalc) + Kalcaalc + Kesteraester + Kwaterawater] ri ) [Mcat.kalc(aalc - (aesterawater/(Kaaacid)))]/ [1 + (Kalc)/(Ka)(aesterawater/aacid) + Kacidaacid + Kesteraester + Kwaterawater] ri ) [Mcat.Kakester(aalcaacid/awater - (aester/Ka)]/ [1 + Kacidaacid + Kalcaalc + KaKester(aalcaacid/awater) + Kwaterawater] ri ) [Mcat.Kakwater(aalcaacid/aester - (awater/Ka)]/ [1 + Kacidaacid + Kalcaalc + Kesteraester + KaKwater(aalcaacid/aester)]
awater ) (xwaterγwater)R. b Model 10, R ) 1; model 10′, R ) 1.9; model 10′′ R ) 1 + 0.38awater.
at equilibrium will depend on the reaction conditions. In general, the probable mechanisms for esterification reactions are available in the literature.28,29 For a homogeneously catalyzed system, this results in a rate expression for the esterification reaction of the form given below: n dxi ri ) Mcat.kf(aacidaalc - aesterawater /Ka) ) νi νi dt
(1)
where ri is the rate of the reaction defined as the number of moles of component i reacting per unit time, mol/s; n is the total number of moles; νi is the stoichiometric coefficient of the ith component; Mcat. is the mass of the catalyst, g; ai is the activity of the ith component in the bulk liquid phase (ai ) xiγi); xi is mole fraction of the ith component; t is the reaction time in s; γi is the activity coefficient of the ith component; kf is the forward reaction rate constant, mol/s/g; and Ka is the activity reaction equilibrium constant. For the heterogeneously catalyzed esterification system, many probable scenarios exist depending on the species adsorbed on the catalyst surfaces. The resultant rate expressions involving single or double sites have been extensively discussed by earlier authors;30 the common ones are shown in Table 1. The hydrolysis of ester involves the breaking down of the ester into its constituent carboxylic acid and alcohol by water. It is reversible. The reaction under conditions similar to those being studied in the current work, i.e., acidic conditions, proceeds via the AAC2 (acid-catalyzed acyl cleavage secondorder reaction) mechanism.31 Furthermore, earlier workers have hypothesized that two water molecules are involved in the hydrolysis and they act as a proton donor and a nucleophile.32-35 A recent study36 on the hydrolysis of methyl acetate under acidic conditions based on the molecular orbital theory also shows that it is necessary to include two water molecules as reactants to obtain a tetrahedral intermediate. The decomposition of this
tetrahedral intermediate is the rate-determining step of the hydrolysis. This could be one of the reasons why the water activity coefficient needs to be adjusted to arrive at a successful kinetic model, as will be shown in the section 4. 2.2. Diffusion. Meaningful kinetic studies cannot be carried out in the presence of either external or internal diffusion limitations. Carrying out the kinetic runs at sufficiently high, experimentally determined optimum agitation rates ensure the absence of external diffusion limitations for heterogeneous solid-liquid catalytic systems. The Weisz-Prater criterion,37 Cwp, is usually used29,38-42 to determine the effect of internal diffusion on the overall reaction rate. Cwp values significantly smaller than unity indicate the absence of internal diffusion limitations in the system.37 2.3. Predicting Real Behavior of the System Components. The behavior of liquid mixtures in liquid-phase reactions may deviate greatly from that of an ideal solution. The nonideality is particularly significant for aqueous mixtures, as are encountered in the present study. The group contribution methods UNIFAC43 and modified UNIFAC (Dortmund)19 methods can account for system nonidealities and have been integrated into commercially available simulators, such as Aspen Plus, CHEMCAD, Pro/II, HYSIM, etc. A comparison of the accuracy of prediction shows that the Modified UNIFAC (Dortmund) rather than the UNIFAC does a better job at predicting vapor-liquid equilibria, liquid-liquid equilibria, solid-liquid equilibria, excess enthalpies, and other thermodynamic properties.20,25,27,44 The former model is recommended for predicting activity coefficients at infinite dilution and for predicting activity coefficients of systems with components very different in size (as is the case in this study). The recently recalculated Modified UNIFAC (Dortmund) interaction parameters for the waterCH3COO group, which is present in benzyl acetate and is a subgroup of the main group CCOO, are available in the open literature.27 Steinigeweg and Gmehling45 have successfully used
Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 2521
Figure 1. Change in esterification rate with time for different catalysts at 333.15 K, acid to alcohol ratio of 1:1, catalyst loading of 30 g of dry cat./ L, and agitation speed 900 rpm.
Figure 2. Change in conversion of acetic acid with time for different catalysts for esterification at 333.15 K, acid to alcohol ratio of 1:1, catalyst loading of 30 g of dry cat./L, and agitation speed 900 rpm.
the Modified UNIFAC (Dortmund) model with the parameters supplied by Gmehling et al.25 to obtain the components activity coefficients for the esterification of decanoic acid with methanol. 3. Experimental Section 3.1. Catalysts. Ion-exchange resins, Dowex 50Wx8-400, Amberlite IR 120, and Amberlyst 15, were procured from Sigma-Aldrich. Some important property values reported by the suppliers of these catalysts appear in our earlier work.29 These catalysts were dried under relatively mild conditions, 343.15 K in a vacuum oven, for 48 h to prevent loss of activity. The BET surface area and porosity of these dried catalysts were measured using automatic ASAP 2010 Micromeritics sorptiometer at liquid nitrogen temperature of 77 K. 3.2. Reactants. Benzyl alcohol (purity g99%), acetic acid (purity g99%), and benzyl acetate (purity of g99%) were supplied by Sigma-Aldrich. For titration purposes, a standard 0.1024 N NaOH solution was used. This solution was supplied by Aldrich. The concentration of the alkali solution was confirmed by back-titrating with a freshly prepared solution of potassium hydrogen phthalate (purity >99.9%) of known concentration. 3.3. Kinetic Runs. A liter glass Lab-Max reactor system was used for carrying out the kinetic runs. Details of the reactor set up can be obtained from our previous papers.29,41 A measured amount of acid (for esterification runs) or ester (for hydrolysis runs) and catalyst were added to the reactor, and the temperature was raised to the desired reaction temperature. The required amount of preheated alcohol (for esterification runs) or water (for hydrolysis runs) was added to the reactor. Details of the conditions under which the experiments were carried and their corresponding run numbers are shown in Figures 1-4, 6, 8, 10, and 12. Each experimental run was repeated three times. The concentration was recorded as a function of time. Samples of the reaction mixture were withdrawn at zero-time (the time corresponding to the addition of preheated alcohol or water to the reactor) and at predetermined time intervals for the next 4 h. The sample was titrated with a standard NaOH solution. The reproducibility of the titration results was found to be ( 1.5%. 3.4. Swelling Ratio Measurements. The different extents to which the catalyst swells in the presence of the reactants and products present in the benzyl alcohol-acetic acid esterification system were determined by equilibrating separately 100 mL of benzyl alcohol, acetic acid, benzyl acetate, and water with known weights of Dowex catalyst (corresponding to 30 g/100
Figure 3. Effect of agitation speed on acetic acid conversion for esterification at 333.15 K, acid to alcohol ratio of 1:1, and catalyst (dried Dowex) loading of 30 g/L.
Figure 4. Experimental and model 10′′ predicted effect of catalyst (dried Dowex) loading on acetic acid conversion for esterification at 333.15 K, acid to alcohol ratio of 1:1, agitation speed 900 rpm.
mL of liquid) in a 250 mL stoppered graduated cylinder at room temperature (298.15 K). The liquid and the catalyst in the cylinder were uniformly mixed for 20 min after which the cylinder was allowed to stand so as to attain equilibrium separation. The wet volume of the catalyst was noted every 15 min. The absence of change in catalyst wet volume with time indicates the attainment of equilibrium and the volume ratio of wet catalyst to dry catalyst at this stage corresponds to the swelling ratio. 3.5. Adsorption Measurements. The adsorption behavior of the components present in the benzyl alcohol-acetic acid
2522 Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009
Figure 5. Effect of catalyst loading on initial esterification rate at 333.15 K, acid to alcohol ratio of 1:1, and agitation speed 900 rpm.
Figure 6. Experimental and model 10′′ predicted effect of temperature on acetic acid conversion for esterification at acid to alcohol ratio of 1:1, catalyst (dried Dowex) loading of 30 g/L, and agitation speed 900 rpm.
esterification system was studied systematically at 333.15 K (the temperature at which the majority of the kinetic runs were carried out). To this effect, the adsorption of three nonreactive systems, namely, benzyl acetate/benzyl alcohol, benzyl acetate/ acetic acid, and acetic acid/water systems, were studied separately in the Lab-Max reactor in which the kinetic studies were also carried out. For each system the adsorption studies were conducted for three different molar ratios, approximating 1:3, 1:1, 3:1. The binary components, having known (determined by GC) initial compositions, were mixed at a stirrer speed of 900 rpm with 30 g of dried Dowex 50 Wx800/L for 30 min. Stirring was then stopped and after another 30 min, a liquidphase sample was withdrawn and its composition also determined using the GC. A Porapak S column (packed column 3 m × 3.2 mm × 2 mm SS) at 250 °C, with helium at 10 cm3/min as the carrier gas, coupled to a TCD detector was capable of separating and quantifying the components of the binary mixtures studied. 4. Results and Discussion 4.1. Characterization of Catalysts Used for Kinetic Studies. The catalysts used in this study are strongly acidic ion exchange resins. They all have an insoluble polymeric matrix containing labile ions capable of exchanging with ions in the surrounding medium. The backbone of the three catalysts studied is polystyrene cross-linked with divinylbenzene (the crosslinker). Amberlite IR 120 and Dowex 50 Wx8 are gel-type
resins. BET analysis showed an average pore diameter of 3.8 and 2.6 nm for Amberlite IR 120 and Dowex 50 Wx8, respectively. The degree of cross-linking is 8% for both these catalysts. Their pore volumes determined by N2 BET analysis were found to be very small (0.001 cm3/g). The low values are expected since gel type resins are known to have no measurable porosity when dry.46 The total exchange capacity values, which are a measure of all the functional groups on a resin, were comparable, 4.4 and 4.8 mequiv/g, for Amberlite and Dowex, respectively.47 The particle size range of Amberlite IR 120 is 16-50 mesh47 while that of Dowex is much smaller, namely, 200-400 mesh. Amberlyst 15, the third catalyst studied, is a macroreticular ion-exchange resin. The internal surface area by N2 BET analysis was found to be 45 m2/g. This value is comparable with the value of 53 m2/g reported by the manufacturers46 and is significantly higher than the values obtained for Amberlite IR 120 and Dowex 50 Wx8 (1 and 2.4 m2/g, respectively). The average pore diameter and pore volume (28 nm and 0.4 cm3/g) of Amberlyst 15 were also found to be significantly higher than that of Amberlite (3.8 nm and 0.001 cm3/g) and Dowex (2.6 nm and 0.001 cm3/g), respectively. Moreover, this catalyst is highly cross-linked (20%) as compared to Amberlite IR 120 (8%) and Dowex 50 Wx8 (8%). The particle size range of Amberlyst (16-50 mesh) is the same as that of Amberlite IR 120. 4.2. Selection of Catalyst. The common cation exchange catalysts, Amberlyst 15, Amberlite IR 120, and Dowex 50 Wx8, were tested for their effectiveness in catalyzing the esterification of acetic acid with benzyl alcohol at 333.15 K. An acid alcohol ratio of 1:1 and catalyst loading of 30 g of dry cat./L were employed. The rates of these reactions were followed for several hours; the comparison is shown in Figure 1. The initial reaction rates show that Dowex catalyzes the reaction faster than the other two catalysts. The rate of the Dowex-catalyzed system becomes less than that of the Amberlyst-catalyzed system after approximately 1 h and less than the Amberlite-catalyzed system after approximately 11/2 h of reaction time. This behavior is to be expected since with time the concentration of both reactants decreases much faster for the Dowex-catalyzed system than for the other two catalysts. Figure 1 also shows that the Dowexcatalyzed system moves toward a zero rate (corresponding to the equilibrium state) much faster than the other two systems. Figure 2, which is a plot of the conversion of acetic acid with time for these three catalysts, shows that throughout the course of the reaction the highest conversions are achieved using Dowex as the catalyst. This figure also shows that for the time period studied Amberlyst gives higher conversions than Amberlite. Earlier workers have associated better catalytic activity for esterification reactions with macroreticular rather than gel type catalysts mainly due to the former’s ability to function even in negligible-swelling (nonpolar) solvents, such as hexane and benzene.12,48,49 However, in the current study, it is found that Amberlyst performs better than the gel resin Amberlite, but not Dowex. This might be due to the fact that each component present in the system studied is considerably more polar than hexane and benzene. The dipole moments of acetic acid, benzyl alcohol, benzyl acetate, and water are 1.74, 1.71, 1.80, and 1.85 D, while those of hexane and benzene are both 0 D. Dowex is also found to perform better than Amberlyst for other systems29,41 containing components with nonzero dipole moments. Figures 1 and 2 and the above discussion clearly show that, despite the fact that all the three catalysts studied are strongly acidic cation exchangers, differences exist in their kinetic behavior. These
Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 2523
Figure 7. Initial esterification rate or kf values versus 1/T, at acid to alcohol ratio of 1:1, catalyst (dried Dowex) loading of 30 g of cat./L, agitation speed 900 rpm.
figures also establish the superior performance of Dowex 50 W x8 for the studied reaction. This catalyst was therefore used to catalyze the remainder of the kinetic experiments studied. 4.3. Absence of Mass Transfer Resistance. Prior to the kinetic studies, experiments were conducted and calculations performed to establish the absence of mass transfer limitations (both external and internal) during esterification. 4.3.1. External Mass Transfer Resistance. Preliminary experiments were carried out at 333.15 K, initial acid to alcohol ratio of 1:1, catalyst loading of 30 g of dry catalyst/L of reaction mixture, and stirrer speeds of 100, 300, 500, 700, 900, and 1100 rpm to determine the limits beyond which diffusion limitations will not exist. Figure 3 shows the percent conversion of acetic acid with time. It can be seen that, in the range of 100-700 rpm, the percent conversion at any point of time is higher at higher stirrer speeds. However, in the range 700-1100 rpm there was no effect of agitation speed on the conversion. Hence, all further experiments were conducted at a stirrer speed of 900 rpm to ensure the absence of external mass transfer resistances. Roy and Bhatia12 also found that the stirrer speed did not affect the rate of reaction above 700 rpm, while studying the esterification of acetic acid over benzyl alcohol over Amberlyst 15, at 351.15 K. The work of Chakrabarti and Sharma50 has established that esterification of less viscous reactant mixtures can be studied at lower agitation speeds without encountering external diffusion limitations. For instance, Xu and Chuang51 were able to work at stirrer speeds as low as 160 rpm without encountering external diffusion limitations in the Amberlyst 15 catalyzed esterification of methanol with dilute acetic acid. Hence, in the current work, the absence of external diffusion limitations for the esterification (forward) reaction, at stirrer speeds of 900 rpm, implies the absence of these limitations for the hydrolysis (backward) reaction also. This is because the viscosity of the hydrolysis reaction mixture is lower: at 333.15 K, the viscosities of benzyl acetate, water, acetic acid, and benzyl alcohol are 1.04, 0.47, 0.70, and 2.02 cP (DIPRO), respectively. 4.3.2. Internal Mass Transfer Resistance. The Weisz-Prater parameter, Cwp37 was determined for runs 3, and 9-28. The Cwp values range from 3.61E-5 (for run 16) to 1.51E-2 (run 20). Since, the Cwp values of all the runs are much less than 1, internal diffusion limitation can be safely considered to be absent under the conditions studied for the given system catalyzed by Dowex 50 Wx8. It is interesting to note that our group29,41 has also found internal diffusion limitations to be absent for other esterifications (acetic acid with 2-propanol and propanoic acid with propanol, respectively) catalyzed by the same catalyst. The
Cwp value for run 23, corresponding to a Dowex 50 W x8 loading of 40 g/L, temperature of 323.15 K and acid to alcohol molar ratio of 1:2 was found to be 5.54E-3. This value is higher than the corresponding values obtained while esterifying acetic acid with 2-propanol (Cwp)1.12E-4; estimated after 1/4 h of reaction time)41 and while esterifying propanoic acid with propanol (Cwp ) 8.03E-4; estimated after 1/2 h of reaction time).29 The observed differences are apparently due to the significant difference in the viscosity of the alcohol involved (2.54, 1.05, and 1.12 cP for benzyl alcohol, 2-propanol, and propanol, at 323.15 K, respectively) and the reaction time at which the Weisz-Prater criterion is evaluated. Note that the viscosity values of acetic (0.794 cP) and propanoic (0.744 cP) acids are close to each other at 323.15 K. Since the reaction rate for any given run is fastest at the start of the reaction, evaluating the criterion at this stage (as has been done in the current study) constitutes a more stringent test of the absence of internal diffusion limitations. 4.4. Batch Kinetic Results. The Dowex 50 Wx8-catalyzed esterification of acetic acid with benzyl alcohol was studied over a temperature range of 303.15-353.15 K, acid to alcohol ratios of 1:3, 1:2, 1:1, 2:1, and 3:1 and catalyst loadings of 10, 30, 50, and 60 g of dry catalyst/L of reactant mixture. Some esterification runs with water or ester being present in the feed and the backward (hydrolysis) reaction over a temperature range of 313.15-353.15 K have also been studied. The reaction kinetics under the different conditions employed is followed with the help of the initial reaction rate and conversion of the limiting reactant. Benzyl alcohol is the limiting component for runs 24 and 25 (it is present in less than stoichiometric ratios relative to acetic acid in the feed) while acetic acid is the limiting component for runs 20-22. For the remainder of the esterification runs, though both acetic acid and benzyl alcohol in the feed are present in stoichiometric ratios, for the sake of convenience and uniformity, acetic acid is designated as the limiting component. Similarly for the hydrolysis runs (runs 16-19), ester is designated as the limiting component, though both ester and water are present in stoichiometric ratios in the respective feeds. The reaction rate is determined by differentiation of a polynomial fit of the concentration versus time data.52 The conversion of the limiting component, ζexp, is calculated using the following equation: ζexp )
moles of limiting component reacted × 100 (2) moles of limiting component initially present
4.4.1. Effect of Catalyst Loading on Esterification. The catalyst loading was varied from 10 to 60 g of dry cat./L of reactant mixture at a temperature of 333.15 K, acid to alcohol feed mole ratio of 1:1, and stirrer speed of 900 rpm (runs 3, 9, 10, and 11). Figure 4 shows that at each catalyst loading the percent conversion of limiting component (ζexp) increases with time. As found by previous workers,12,29,38,39,41,53 the conversion increases with catalyst loading, also. After 1/4 h of reaction time 5.4, 14.8, 24.2, and 24.6% conversion has been achieved at catalyst loadings of 10, 30, 50, and 60 g of dry cat./L, respectively, while 37.9, 53.5, 57.7, and 60.1% conversions are achieved at the end of 4 h. This shows that the relative differences in the percent conversion change with time. Comparing the conversions at the end of 4 h, it can be seen that a 20 g of dry cat./L increase in catalyst loading, from 10 to 30 g of dry cat./L raises the conversion from 37.9 to 53.5, an increase of 41%; in contrast, a further 20 g of dry cat./L increase in catalyst loading from 30 to 50 g of dry cat./L raises the percent
2524 Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009
Figure 9. Initial hydrolysis rate and kb values versus 1/T at ester to water ratio of 1:1, catalyst (dried Dowex) loading of 30 g of dry cat./L, and agitation speed 900 rpm.
Figure 8. Experimental and predicted effect of temperature on conversion for hydrolysis at ester to water ratio of 1:1, catalyst (dried Dowex) loading of 30 g of cat./L, and agitation speed 900 rpm.
conversion from 53.5 to 57.7, an increase of just 8%. Hence, at 333.15 K, the use of catalyst loadings greater than 30 g of dry cat./L does not appear attractive. All further kinetic studies were therefore conducted at this apparently optimum catalyst loading. The initial rates of the reactions catalyzed by different amounts of catalyst are plotted against the catalyst concentration in Figure 5. The rate is found to increase with loading. This fits well with the description of the proton mechanism, proposed by Tsvetkova and Kovemev,54 in which an increase in the number of resin functional groups increases the concentration of the carbonium ion formed. 4.4.2. Effect of Reaction Temperature. 4.4.2.1. On Esterification. Runs 3, 12, 13, 14, and 15 study the effect of temperature on esterification. As can be seen from Figure 6, increasing the temperature increases the conversion of acetic acid. This behavior is to be expected and has been observed by previous workers.9,18,29,38-41,51,53 The initial rates in terms of moles of products formed per g of dry catalyst per second (ri′) at the five temperatures studied are plotted against 1/T (Figure 7) and are found to be well correlated (R2 ) 0.99) by an exponential relationship of the Arrhenius type, as shown below. ri′ ) 10685 × exp(-6555/T)
(3)
This equation results in an apparent activation energy (54.50 kJ/mol) higher than that for a diffusion limited process. This behavior strongly indicates the absence of mass transfer limitations52 as has also been established in section 4.3. 4.4.2.2. On Hydrolysis. The kinetics of the hydrolysis of benzyl acetate was studied at 313.15, 333.15, 343.15, and 353.15 K at a catalyst loading of 30 g of dry cat./L and at ester to water molar ratio of 1. For these runs, the equimolar reactant feed composition corresponds to a benzyl acetate composition of 89% (by volume) in the feed. This composition increases further due to the preferential uptake of water in the resin catalyst (swelling ratio of 2 as compared to 1.5 for the ester). Moreover, the density of water (985.195 kg/m3 at 333 K) is not significantly different from the density of the ester (1009 kg/m3 at 333 K). At a stirrer speed of 900 rpm, the four-bladed
Figure 10. Experimental and model 10′′ predicted effect of initial acid to alcohol ratio on conversion for esterification at 333.15 K, catalyst (dried Dowex) loading of 30 g/L, and agitation speed 900 rpm.
glass impeller used was able to keep the reacting mass in a visibly uniform suspension. This ensures uniform mixing (of the reactants, products, and the catalyst used) throughout the kinetic run. Increasing the temperature results in higher conversions of ester during the entire course of the reaction studied as can be seen from Figure 8. This is a plot of percent conversion of ester versus reaction time for the four temperatures studied. The highest conversions obtained at the end of 4 h of reaction time were 1.5, 5.0, 8.7, and 17.4%, at 313.15, 333.15, 343.15, and 353.15 K, respectively. These values are significantly lower than the corresponding values (30.6, 53.5, 59.8, and 65.3%) for the forward reaction, clearly indicating that the forward (esterification) reaction is significantly faster than the backward (hydrolysis) reaction. The initial rates of hydrolysis at these four temperatures are shown in Figure 9. As temperature increases, the initial rate is found to increase. Moreover, as was observed in the esterification reaction, the initial hydrolysis rates and corresponding 1/T values could be well correlated (R2 ) 0.99) with an exponential relationship of the Arrhenius type. Moreover, the
Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 2525
Figure 11. Effect of acid mole fraction on initial esterification rate at 333.15 K, catalyst (dried Dowex) loading of 30 g of cat./L, and agitation speed 900 rpm.
strong influence of temperature, as evidenced by the high value of apparent activation energy obtained (56.1 kJ/mol), again indicates the absence of diffusion limitations. Moreover, the apparent activation energy obtained from the initial hydrolysis rates is comparable to that obtained from the initial esterification rates (54.8 kJ/mol). 4.4.3. Effect of Initial Reactant Ratio on Esterification. The kinetics of this esterification was studied at acid to alcohol molar ratios of 1:3, 1:2, 1:1, 2:1, and 3:1. The catalyst loading was maintained constant at 30 g of dry cat./L and the temperature at 333.15 K. Figure 10 is a plot of the conversion of the limiting component with time at these molar ratios. It should be noted that the limiting component is acetic acid for the runs at initial acid to alcohol ratios of 1:3 and 1:2 and benzyl alcohol for the runs at initial acid to alcohol ratios of 2:1 and 3:1. At an equimolar feed ratio of 1:1 either the acid or the alcohol can be considered to be the limiting component. At the end of 4 h of reaction, conversions of 78.0, 69.3, 53.5, 74.1, and 85.9% were obtained at acid to alcohol molar ratios of 1:3, 1:2, 1:1, 2:1, and 3:1, respectively. This shows that an initial excess of either acid or alcohol increases the product yield as compared to that which is obtained when equal moles of both reactants are present. An initial excess of acid rather than alcohol appears (from Figure 10) to be more beneficial. It is worth mentioning that Roy and Bhatia,12 while catalyzing the same esterification with 28 g of Amberlyst 15/L of reaction mixture with an acid to alcohol molar ratio of 1.6:1 and a slightly higher temperature of 335 K, obtained a limiting component conversion of ∼31% at the end of 1 h. This value is lower than the corresponding value obtained in the current study (42.9%) at 333.15 K with an acid to alcohol ratio of 2:1 using 30 g of Dowex 50 Wx8/L of reaction mixture. This trend conforms to the trend observed (using different catalysts) when the esterification was carried out with an initial acid to alcohol ratio of one (section 4.2). Because of the large relative difference in the molecular weights of acetic acid (60 g/mol) and benzyl alcohol (108 g/mol), these runs also differ in the mass of catalyst available per mole of reactant. The systems containing 1:3, 1:2, 1:1, 2:1, and 3:1 moles acid to alcohol actually have 2.77, 2.65, 2.45, 2.22, and 2.10 g of catalyst per mole of reactant. Hence, a clearer picture arises while considering the influence of molar ratio on the initial reaction rate per unit mass of catalyst (Figure 11). The initial rate with a feed ratio of 1:3 (initial mole fraction of acid, 0.25) is lower than that observed with a feed ratio of 3:1 (initial mole fraction of acid, 0.75). It can be seen that, as the acid to alcohol molar ratio increases, the initial rate increases.
It reaches a maximum somewhere around an acid mole fraction of 0.6 (1.61:1) and then decreases. Similar behavior has also been observed by other workers9,38,55,56 while studying different cation-exchange-catalyzed esterifications. These workers9,38,55,56 also found the esterification rate to be surface-reaction limited. This coincidence suggests the possibility of surface reaction being the limiting step for the studied esterification. 4.4.4. Effect of Presence of Ester or Water in the Reactant Mixture on Esterification. Esterification runs having acid:alcohol:ester:water feed compositions of 2:2:1:0 (run 26) and 2:2:0:1 (run 28) were studied at 333 K and a catalyst loading of 30 g of dry cat./L of the feed. The presence of product in the feed is expected to favor the backward reaction and lower the conversion of the acid. Figure 12, which compares the conversion of acetic acid with time for these runs, shows that adding both water as well as ester decreases the percent conversion but the presence of water rather than ester in the feed exerts a more detrimental effect. At the end of 4 h, the percent conversion for runs 26 and 28 are 48.6% and 39.6%, respectively as compared to the value of 53.5% obtained when neither water nor ester is added to the system (run 3). Another esterification (run 27) with a feed composition of 2:2:1:0, temperature of 333 K and a lower catalyst loading corresponding to 30 g of dry cat./L of reactants (acid + alcohol) in the feed was also studied. Figure 12 shows that, in spite of the lower catalyst loading, run 27 exhibits higher conversions of acetic acid than run 28. The presence of the same ratio of product (ester or water) in the feed does not inhibit the reaction rate to the same extent. This is faster in ester-rich rather than water-rich mixtures. Similar behavior has been observed by Grob and Hasse57 while studying the sulfuric acid catalyzed esterification of 1-butanol with acetic acid. They attributed this behavior to the presence of water hindering the approach of butanol to the protonated acid. Other workers have also observed the detrimental effect of the presence of water on rates of reactions catalyzed by sulfuric acid58 and PTSA,59 as well as cation exchange resins.29,60-63 The very strong affinity of water for cation exchange resins64,65 appears to be responsible for this behavior. In the current study the detrimental effects of water can also be observed. 4.5. Accounting for Nonideality in the System. The widely used Modified UNIFAC (Dortmund) method, which is based on a wide database, has been employed in this study to account for system nonidealities. The UNIFAC groups of the different components and their Rk and Qk values are shown in Table 2. The thermodynamic model used predicted the reported vaporliquid equilibria data66 of binary and ternary systems containing acetic acid, benzyl alcohol, benzyl acetate, and water with high accuracy (root-mean-square error of 0.04). For the kinetic run at 333.15 K, an equimolar acid to alcohol feed ratio and a catalyst loading of 30 g of dry cat./L (run 3), the activity coefficients of acetic acid, benzyl alcohol, benzyl acetate and water change from 1.198, 1.049, 1.684, and 4.874 at the beginning of the run to 1.108, 1.129, 1.754, and 4.826, respectively, when 25% of acetic acid is converted. As the reaction progresses, the thermodynamic model predicts an increase in the activity coefficients of benzyl alcohol and ester and a decrease in the activity coefficients of acetic acid and water. The result shows a gradual increase in the Πγ value (ratio of the product of activity coefficients of the products (ester and water) to that of the reactants (acid and alcohol)) from 6.531 to 6.767 with increase in reaction time. At a higher temperature of 343.15 K (run 14), the activity coefficients of each component at the beginning of the run
2526 Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 Table 2. Modified UNIFAC (Dortmund) Groups Present in the Different Components and Their Rk and Qk Values group
CH3
ACH
ACCH2
OH
H2O
CH3COO
COOH
acetic acid benzyl alcohol benzyl acetate water Rk Qk
1 0 0 0 0.6325 1.0608
0 5 5 0 0.3763 0.4321
0 1 1 0 0.91 0.7962
0 1 0 0 1.2302 0.8927
0 0 0 1 1.7334 2.4561
0 0 1 0 1.27 1.6286
1 0 0 0 0.8 0.9215
Table 3. Swelling Ratio for Dried DOWEX 50 Wx8 water
acetic acid
benzyl alcohol
benzyl acetate
density (g/mL) at 333.15 K 0.985 1.005 1.014 1.010 MW (g/mol) 18.00 60.05 108.14 150.19 weight of catalyst (g) 2.53 2.53 2.53 2.53 volume of catalyst (mL) 3 3 3 3 volume of catalyst + solvent (ml) 6 5 5.2 4.5 swelling ratio (mL/mL) 2.00 1.67 1.73 1.50 adsorbed volume (mL/g) 1.19 0.79 0.87 0.59 adsorbed mass (g/g) 1.17 0.79 0.88 0.60 adsorbed amount (mmol/g) 64.90 13.22 8.16 4.00
(1.183, 1.036, 1.657, and 4.758 for acid, alcohol, ester, and water, respectively) are found to be lower than those at 333.15 K. The net result of the decrease in activity coefficients of all the components at the higher temperature is a decrease in the Πγ value (from 6.531 at 333.15 K to 6.433 at 343.15 K). This shows that the activity coefficient of the products decreases more significantly than that of the reactants as temperature increases. At 323.15 K, the component activity coefficients for the equimolar system at the start of the reaction are in the sequence of alcohol (1.060) < acid (1.211) < ester (1.719) < water (4.973). It is interesting to note that a similar sequence was observed in the esterification of acetic acid with methanol (Maki-Arvela et al.67 using UNIQUAC), though the activity coefficient model used is different. 4.6. Catalyst Swelling and Adsorption Studies. The results obtained from the swelling tests are shown in Table 3. All the components swell the resin appreciably. The swelling ratio is found to decrease in the order of water, benzyl alcohol, acetic acid, benzyl acetate. The values of neither the volume nor the moles nor the mass of the component adsorbed per unit mass of Dowex 50 Wx8 was found to be a constant for the different components present in the system. Interestingly, earlier workers65 while studying the swelling behavior of acetic acid, methanol, methyl acetate, and water over Amberlyst 15, found the mass of different components adsorbed per gram of catalyst to be almost constant. Using this assumption these workers65 generated Kads values from adsorption experiments and successfully used them to predict the kinetic behavior. The work of Pietrzyk48 has shown that solvent uptake properties of macroreticular (like Amberlyst 15) and gel-type (Dowex 50 W x8) resins differ from one another. The former is rigid and porous in structure and this enables it to take up all types of solvents while the latter, which depends on swelling of the resin matrix, is not able to take up the nonpolar solvents significantly. In polar solvents, gel-type resins swell and usually contain 5-50 Å48 channel widths depending on the degree of cross-linking. If they are in the dry state or not swollen, the channels are practically nonexistent and the resins will remain in this condition when placed in a nonpolar solvent. It is interesting to note that Pietrzyk48 obtained a comparable solvent uptake value (1.16 as compared to 1.17 g/g of dry resin obtained in this study) for water while working with Dowex 50 Wx8. However, he obtained lower values for acetic acid uptake (0.57 as compared to 0.79 g/g of dry resin obtained in this study). This difference could be due to the different mesh size of the
Table 4. Change in Composition of Binary-Component Systems Using Dried Dowex 50Wx8 at 333.15 K mole fraction of component 1 component 1/component 2 (approx ratio)
overall (xoverall ) 1
liquid (xliquid ) 1
xliquid / 1 xoverall 1
water/acetic acid (1:1) water/acetic acid (1:3) water/acetic acid (3:1) alcohol/ester (1:1) alcohol/ester (1:3) alcohol/ester (3:1) ester/acetic acid (1:1) ester/acetic acid (1:3) ester/acetic acid (3:1)
0.4453 0.2850 0.7534 0.4980 0.2340 0.7353 0.4905 0.2724 0.7159
0.4358 0.2620 0.7421 0.4627 0.2393 0.7423 0.4975 0.2412 0.7358
0.979 0.919 0.985 0.929 1.022 1.010 1.014 0.886 1.028
catalyst used by Pietrzyk48 (100-200 mesh as compared to 200-400 mesh used in this study). The adsorption of the binary components water/acetic acid, alcohol/ester and ester/acetic acid was studied at the approximate component molar ratios of 1:3, 1:1 and 3:1 while keeping the catalyst concentration the same as used for the kinetic runs. The mole fraction of component 1 in the binary-component feed (x1overall) and that obtained after equilibrium adsorption (x1liquid) are shown in Table 4. For each binary component system the ratio x1liquid to x1overall (also shown in Table 4) is found to change with composition. It is found to be less than 1 for the water/ acetic acid system. For the alcohol/ester and ester/acid systems, this ratio is found to fluctuate between greater than and less than one depending on the composition. The nonuniform trends being observed for the alcohol/ester and ester/acid system indicates that the composition of the binary system greatly affects the affinity between the bulk phase and the resin and that considerable differences might exist during esterification and hydrolysis. While studying etherification catalyzed by the macroporous resin Bayer K2631, Fite et al.68 also concluded that the affinity between the bulk phase and the resin depends on the composition of the reaction medium and it plays an important role in the catalyst activity. These experiments show that the adsorption behavior on Dowex 50 Wx8 is appreciably different from that on macroreticular catalysts like Amberlyst 15 and 39 reported in the literature.64,65,69 4.7. Elucidation of the Reaction Mechanism. 4.7.1. Correlating Kinetics during the Initial Stage of the Reaction. The rate expressions of the probable models, shown in Table 1, were simplified to correspond to initial stage conditions. These expressions were then linearized and fitted to the initial rates of runs 3, 9-11, 20, 22, 24, and 25. The fitted parameter values and the coefficient of determination (R2) of the different models are shown in Table 5. Negative constant values are obtained for models 2, 10, 11, and 12, indicating their inability to predict initial kinetics of the studied system. Among the remaining models, model 6 shows the highest degree of fit (R2 ) 0.948). The pseudohomogeneous (PH) model (model 1) does not predict the initial rate efficiently (R2 ) 0.49), indicating that contrary to what has been found by earlier workers,65 the reaction within Dowex cannot be treated as homogeneous during the start of the reaction. The inability of the simple PH model to predict the kinetic data reasonably well in the current study
Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 2527 Table 5. Reaction Constants and Errors Obtained by Fitting Initial Rates at 333.15 K to Different Models model no.
kf (mol/s/g)
Kacid
kacid
1 2 3 4 5 6 7 8 9 10 11 12 13 14
8.95E-05 -1.15E-04
-4.90E-01
Kalc
kalc
kester/Kester
kwater/Kwater
4.19E–05 2.38E–05 2.38E–05 9.95E-05
1.37E+00 4.51E–05 2.38E–05
5.72E-05
-2.77E+00 -1.00E+00
2.38E–05
-4.36E+00 -6.25E-01
2.72E–05
1.70–05 2.38E–05 2.38E–05
R2 0.494 0.394 0.812 0.812 0.948 0.380 0.812 0.812 0.812 0.812
Table 6. Reaction Constants Generated for Correlating Kinetic Data during the Course of the Reaction kf (mol/s/g) model no. 1 2 6 10 10′ 10′′
adsorption equilibrium constants
Af (mol/g/s)
Ef (J/mol)
313.15 K
333.15 K
343.15 K
353.15 K
Kacid
Kalc
Kester
Kwater
7.00E+04 7.01E+04 6.90E+04 5.00E+05 5.06E+05 5.00E+05
57000 56890 57100 57000 57010 57000
2.17E-05 2.27E-05 2.06E-05 1.55E-04 1.56E-04 1.55E-04
8.09E-05 8.43E-05 7.69E-05 5.78E-04 5.82E-04 5.78E-04
1.47E-04 1.53E-04 1.40E-04 1.05E-03 1.06E-03 1.05E-03
2.59E-04 2.70E-04 2.47E-04 1.85E-03 1.87E-03 1.85E-03
1.95 2.15 2.27 2.03
1.13 1.21 0.95 0.98
0.10 0.13 0.11
5.00 2.83 3.25 2.55 3.00
may be partly due to the difference in the nature of the catalyst used (earlier workers used Amberlyst 15) and partly due to the differences in polarity of the components. Model 6 corresponding to a reaction mechanism wherein the rate-limiting step is the surface reaction between the adsorbed alcohol and the acid in the bulk is found to predict the initial kinetics successfully as evidenced by the R2 value (0.948) obtained. The kf and Kalc values at 333.15 predicted by this model were found to be 9.95E-5 mol/g/s and 1.37, respectively. Keeping the latter value constant, the kf values at 303.15, 313.15, 343.15, and 353.15 K back calculated from corresponding initial rates by this model were found to be 1.82E-5, 2.96E-5, 2.04E-4, and 4.13E-4 mol/g/s, respectively. These values can be correlated with the Arrhenius relationship shown below with a high degree of fit (R2 ) 0.99) as can be seen from Figure 7:
( -6661.4 ) T
kf ) 55770 × exp
(4)
The activation energy from the above relationship was found to be 55.4 kJ/mol. This value is close to the apparent activation energy predicted by exponentially fitting the initial rates to 1/T (54.5 kJ/mol) (section 4.4.2.1). It has to be mentioned that the kinetic data generated in this study were obtained by adding alcohol to acid and catalyst already present in the reactor. To determine the effect of the sequence of addition on reaction kinetics, a run at 333.15 K, acid to alcohol ratio of 1:3, and catalyst loading of 30 g of dry cat./L was performed with acid being added to the alcohol and catalyst (run 21). The results are plotted in Figure 10. The initial reaction rate for this run was found to be higher (1.86E-5 as compared to 1.71E-5 mol/g/s). This indicates that reaction kinetics, especially initial reaction rates, depend somewhat on the addition sequence of the reactants, which appears to camouflage the role of the acid adsorption in the rate-limiting step. However, as the reaction proceeds, the acid adsorption term might have to be introduced and in such an event the reaction kinetics would be represented by a dual site mechanistic model, like model 10, rather than a single-site one, like model 6.
The above discussion strongly suggests that a mechanism, with surface reaction being the limiting step, will continue to be efficient in correlating the reaction kinetics after the initial stage. However, the number of sites involved might change as the reaction proceeds. 4.7.2. Correlating Kinetics during the Course of the Reaction. Besides being prejudiced by the addition sequence of the reactants and the catalyst, as seen above, development of a complete rate equation from the initial rates only would result in a kinetic model that does not account for the changes occurring with time in the swelling and adsorption behavior of the components present in the system. The kinetic data during the course of the reaction was analyzed by the method of nonlinear least-squares regression. Experimental data was fitted to different mathematical models (Table 1) using the statistics “NonlinearFit” function of Mathematica software. Estimates of the model parameters which minimized the merit function given by the sum of squared residuals (∑all data samples (ri,corr - ri,exp)2) were determined. The optimization method used by NonlinearFit is iterative, so starting values were required for the parameter estimate search. Careful choice of starting values is necessary, as the parameter estimates found may represent a local minimum in the merit function. The Kalc (1.37) and activation energy (55.4 kJ/mol) values generated by model 6 in the previous section can serve as good initial guesses for analyzing the kinetic data. The activity equilibrium constant Ka expression occurring in the rate equations of Table 1 is substituted by the following temperature-dependent Dowex 50 Wx8 catalyzed reaction equilibrium constant relationship (eq 5) generated by our group in another study.70 ln(Ka,Dowex(T)) )
+ 6.810 ( -1279 T )
(5)
The PH, the two ER, and LH models in which the surface reaction is the controlling step were systematically fitted to the kinetic data of runs 3, 9-15, 20-22, and 24-28. The values of the parameters generated are shown in Table 6. The standard errors of estimate in correlating the conversion of limiting components of these runs are shown in Table 7.
2528 Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 Table 7. Standard Error of Estimate of Individual Runs model errors (%) run no.
catalyst loading (g of dry cat./L)
3 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
30 10 50 60 30 30 30 30 30 30 30 30 30 30 30 40 30 30 30 21 30
temp (K)
acid:alcohol:ester:water rounded molar ratio
1
2
6
10
10′
10′′
333.15 333.15 333.15 333.15 303.15 313.15 343.15 353.15 313.15 333.15 343.15 353.15 333.15 333.15 333.15 323.15 333.15 333.15 333.15 333.15 333.15
1:1:0:0 1:1:0:0 1:1:0:0 1:1:0:0 1:1:0:0 1:1:0:0 1:1:0:0 1:1:0:0 0:0:1:1 0:0:1:1 0:0:1:1 0:0:1:1 1:3:0:0 1:3:0:0 1:2:0:0 1:2:0:0 2:1:0:0 3:1:0:0 2:2:1:0 2:2:1:0 2:2:0:1
3.78 3.70 5.37 3.78 3.15 2.08 4.50 4.22 4.67 4.73 4.81 4.09 3.92 4.69 3.70 3.60 8.70
3.30 1.52 7.25 7.12 1.48 0.95 7.82 11.44 10.57 13.46 6.38 7.22 23.16 54.96 9.09 6.26 2.99
6.63 2.22 10.68 11.07 2.42 1.31 12.08 16.07 55.20 53.25 27.01 17.84 4.26 4.95 9.92 6.52 13.31
2.84 3.09 6.70 5.46 1.85 1.91 3.59 3.05 2.28 5.82 7.35 5.53 2.66 5.54 3.65 4.01 3.30 4.02 1.58 2.30 1.01
5.54 5.54 2.75 4.73 6.01 8.65 9.56 5.55 0.38 1.20 0.82 2.65 11.86 11.86 9.39 8.97 11.34 17.59 6.56 6.92 3.04
2.19 1.81 5.49 4.96 2.34 3.25 5.30 3.74 0.30 1.28 1.18 1.78 4.65 5.45 4.55 4.27 2.71 5.83 2.08 2.13 1.59
The standard error is calculated by the following equation Sy/x )
(ζexp - ζpred)2 N-f
(6)
where ζexp and ζpred are the percent conversions of the limiting component determined from experimental and predicted values of acid mole fractions, respectively; N is the number of data points, and f is the number of degrees of freedom pertaining to the different models. The incorporation of the degrees of freedom in the error equation enables a realistic comparison of models differing in the number of optimizable parameters. If the degrees of freedom are not accounted for, some models benefit unduly from the advantage of a greater number of optimizable parameters to better correlate the reaction kinetics. For model 1, the errors in correlating the effect of catalyst loading, temperature, reactant molar ratio, and presence of ester or water in the feed on the limiting component were found to be 4.16, 3.55, 4.43, and 5.33, respectively. The average value of the standard error for predicting esterification kinetics using this model was found to be 4.34. The highest error observed is for run 28. This is probably due to the fact that in this run, water, whose swelling and adsorption behavior is significantly different from the other system components, was present initially in the feed and the PH model has no provision to account for these differences. This model is able to predict the kinetics of run 23, with an error of 4.09. Run 23 was carried out at a temperature (323.15 K) and catalyst loading (40 g of dry catalyst/L) different from the runs used for correlating the kinetic model. Model 2, which assumes that alcohol does not get adsorbed and remains in the bulk phase, was found to correlate the effect of catalyst loading, temperature, reactant molar ratio, and presence of ester or water in the feed on the limiting component with errors of 4.80, 5.00, 18.64, and 6.11, respectively. The high error observed for the runs with different feed ratios, especially for runs 24 and 25, which have acid to alcohol molar ratios of 2:1 and 3:1, respectively, indicate that the role of the reactants has not been suitably accounted for by this model. Not only is the average error for this model (10.48) higher than that for the PH model (4.34), but it also predicts the kinetics of run 23 with a higher error (7.22 as compared to 4.09).
Model 6, which assumes that acid does not get adsorbed and remains in the bulk phase, was found to correlate the effect of catalyst loading, temperature, reactant molar ratio and presence of ester or water in the feed on the limiting component with errors of 7.65, 7.70, 25.22, and 9.92, respectively. Like model 2, this model also predicts the effect of changing the initial feed ratio on the reaction kinetics with a very high error. Run 20, which has an initial acid to alcohol molar ratio of 1:3, has the highest error (55.20). The role of the reactants does not appear to have been suitably accounted for by this model either. Although this model was efficient in predicting the kinetics in the initial stage of the reaction (section 4.7.1), when a time span of 0-4 h is considered, the degree of fit is found to be poor. In fact, the average error for this model (14.81) is found to be higher than that for both models 1 (4.34) and 2 (10.48). The dual-site LH mechanism model (model 10), in which the surface reaction between adsorbed acid and alcohol is the rate-limiting step, was found to correlate the kinetics with an average error of 3.28, showing that it is better than the PH model in predicting the effect of changes in reaction conditions on kinetics. The effects of catalyst loading, temperature, reactant molar ratio, and presence of ester or water in the feed were correlated with errors of 4.52, 2.65, 3.67, and 1.63, respectively. This model can predict the kinetics of run 23 with an error of 4.01, a value comparable to that of model 1. The activation energy predicted by the LH model was found to be 57 kJ/mol. This is much higher than the value obtained while carrying out this esterification using sulfuric acid (40.7 kJ /mol)71 or zeolites HB (33.49 kJ/mol),17 HY (45.11 kJ/mol),17 and HZSM5 (40.84 kJ/mol)17 and lower than the value obtained when the reaction is catalyzed by Amberlyst-15 (73.3 kJ/mol).12 The adsorption equilibrium constant was found to be smallest for benzyl acetate and the highest for water. 4.7.3. Predicting the Backward Reaction. Model 10, the LH model, was used to predict the kinetics of the backward (hydrolysis) reaction (runs 16-19). The conversion values predicted by this model are plotted in Figure 8. The LH model predicted higher than experimental conversions for each of the studied temperatures. For a temperature of 333.15 K, it predicted conversions which coincide with those obtained experimentally at 343.15 K. Similarly, at 343.15 K, the model predicted conversions close to those obtained experimentally at 353.15
Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 2529
K. This shows that while the LH model can predict the kinetics of the esterification reaction, it falls short of adequately predicting the kinetics of the backward reaction. This is not surprising. The polarity of the organic reaction media/solvent in the hydrolysis runs differs from that in the esterification runs used to arrive at model 10. Since solvent polarity influences swelling and adsorption behavior, the LH model might not be successful in predicting the kinetics of systems undergoing large changes in the organic solvent polarity. Hence, an attempt is made to make the model predict lower hydrolysis conversions by modifying the water activity term. This is raised to the power of a correction term R, as has been done to good effect in previous work, by ourselves29,41 and other workers.72 The hydrolysis kinetic data is fitted to the resultant mathematical expression, which corresponds to the modified LangmuirHinshelwood model (model 10′). Fitted parameter values are shown in Table 6. The predicted conversions, also plotted in Figure 8, show that this model is able to predict the hydrolysis kinetics successfully. The effects of catalyst loading, temperature, reactant molar ratio and presence of ester or water in the feed were correlated with errors of 4.64, 7.06, 11.26, and 5.51, respectively. The latter three errors are considerably higher than those corresponding to model 10, indicating that model 10′ is not very good at predicting the effect of temperature, reactant molar ratio, and presence of ester or water in the feed. In all probability, the inability of model 10′ to adequately predict the esterification kinetics of the same system is related to polarity differences of the organic components/species in esterification and hydrolysis runs. This implies that, for a better overall fit, the water activity correction term should vary as the reaction proceeds. Previous work with cation exchangers and aqueous organic solvents73-79 has shown that at equilibrium the preferential uptake of water by the resin causes the solution composition in the resin phase to be very different from that in the outer solution. This difference becomes greater with less polar organic solvents. A similar situation is expected to exist in the systems being studied. The polarity of the organic part of the system is continuously changing as acid and alcohol react to give ester and water. The correction term (R) should therefore vary with composition of the organic species present in the system. The R term can therefore be made proportional to the activity of water in the system (values ranging from 1 for the esterification runs to 1.9 for the hydrolysis runs). Since the average awater value during the hydrolysis run at 333.15 K (run 17) is 2.338, the R term of model 10′ can be replaced with the expression 1 + 0.38awater to arrive at a mathematical expression capable of correlating both the esterification as well as the hydrolysis runs. The resultant model, model 10′′ is able to predict the effect of changes in reaction conditions on esterification kinetics very well as can be seen in Figures 4, 6, 10, and 12. The kf values predicted by this model at different temperatures, shown in Figure 7, are found to be higher than the values calculated while considering only the initial-stage kinetics (section 4.7.1). These kf values are also found to follow an Arrhenius relationship with temperature. The parallel nature of the plots, seen in Figure 7, shows that the activation energies for the forward reaction predicted in the three cases are comparable to one another. The values of the backward reaction rate constant for esterification (kb) are back-calculated for different temperatures from the model 10′′-predicted kf and experimentally derived Ka values (kb ) kf/Ka). These values could also be correlated with temperature by an Arrhenius relationship (Figure 9). The errors involved in predicting the effect of catalyst loading, temperature, reactant molar ratio, and
Figure 12. Experimental and model 10′′ predicted effect of presence of ester/water in the feed on acetic acid conversion for esterification at 333.15 K, catalyst (dried Dowex) loading of 30 g/L, and agitation speed 900 rpm.
Figure 13. Parity between model 10′′ predicted and experimental limiting reactant mole fractions under different conditions.
presence of ester or water in the feed (3.61, 3.36, 4.23, and 1.93, respectively) are comparable to the corresponding values of model 10. Furthermore, model 10′′ gave an average error for the esterification runs of 3.43, a value which is also comparable to that obtained using model 10 (3.28). Model 10′′ also predicts the kinetics of run 23 with an error value (4.27) comparable to that predicted by model 10 (4.01). This model is also successful in predicting the kinetics of the hydrolysis reaction, as can be seen from Figure 8. The introduction of a variable rather than a fixed R term appears to have effectively addressed the simplifications on which the LH model is based, and the anomalous swelling and adsorption behavior observed in this study. Thus, model 10′′ is the most successful for predicting both esterification as well as hydrolysis kinetics. The overall success of model 10′′ in expressing the kinetics of the studied system can also be seen easily from Figure 13, which is a plot of model 10′′ predicted versus experimental limiting component mole fractions for all the studied kinetic runs. Furthermore, the average relative error in predicting the equilibrium conversion with model 10′′ is found to have a value of around 3% only. Hence, model 10′′ is considered as the most suitable model to represent the kinetics associated with the system comprising acetic acid-benzyl alcohol-benzyl acetatewater over a wide range of conditions. Since, model 10′′ relates (indirectly) the reaction kinetics to the composition and polarity
2530 Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009
of the organic reacting media, it can be applied for processes such as the reactive distillation of acetic acid waste streams with benzyl alcohol, where the composition and polarity of the system might vary across different theoretical plates. 5. Conclusions For the heterogeneously catalyzed esterification of acetic acid with benzyl alcohol, Dowex was found to be better than Amberlite IR 120 and Amberlyst 15. A stirrer speed of g700 rpm was found to be effective in eliminating external diffusion limitations. Hence, further kinetic studies were carried out at a stirrer speed of 900 rpm. Internal diffusion limitations were assessed by the Weisz-Prater criterion and found to be absent at all conditions studied. The initial rate of esterification was found to increase linearly with catalyst loading at 333.15 K and 1:1 acid to alcohol ratio. Under reaction conditions implemented in this study, a catalyst loading of 30 g of dry cat./L was found to be optimum, since increasing the amount of catalyst added beyond this value does not result in substantially higher conversions. Raising the temperature from 303.15 to 353.15 K increases reaction conversion. The initial esterification as well as hydrolysis rate follows an Arrhenius type of relationship with temperature. Increasing the mole fraction of acid was found to increase and then decrease the initial rate; i.e., an unsymmetrical polynomial behavior is observed, with a maximum rate value corresponding approximately to an acid to alcohol molar ratio of 1.61:1. Although the presence of both water and ester in the feed exerted a detrimental effect on the extent of conversion, the presence of water was found to exert a more adverse effect. The swelling ratio was found to decrease in the order of water, benzyl alcohol, acetic acid, benzyl acetate. Neither the mass nor the moles nor the volume of the component adsorbed per gram of the catalyst was constant for the different components for the Dowex system. Water appears to be preferentially adsorbed by the catalyst from a binary solution of acetic acid and water, while the preferential adsorption of ester from the ester/acid and ester/alcohol system depends heavily on the initial ratio of ester present. The ER model, in which the surface reaction between adsorbed alcohol and acid in the bulk is the rate-limiting step, appears to best represent the esterification mechanism when the initial kinetic data were analyzed. However, least-squares regression based on the entire range of kinetic data generated shows the LH model to be efficient in predicting the esterification but not the hydrolysis behavior, while the MLH model with a correction term for the activity of water (R) having a value of 1.9 is good at predicting the hydrolysis but not the esterification behavior. To arrive at a mathematical expression with a wide range of applicability, which completely describes the kinetics of both the forward and backward reactions involving acetic acid, benzyl alcohol, benzyl acetate, and water, the composition and polarity of the organic reaction media have to be accounted for. This was done by correcting for the water activity with a variable power term (R ) 1 + 0.38awater). The resultant model was found to predict efficiently esterification and hydrolysis along with equilibrium composition.
Nomenclature AAC2 ) acid-catalyzed acyl cleavage second order reaction mechanism aacid ) activity of acetic acid in the liquid phase aalc ) activity of the alcohol in the liquid phase aester ) activity of the ester in the liquid phase Af ) pre-exponential factor for the forward reaction leading to ester formation, mol/s/g ai ) activity of the ith component in the bulk liquid phase awater ) activity of the water in the liquid phase Cwp ) Weisz Prater parameter Ef ) activation energy for the forward reaction leading to ester formation, kJ/mol ER ) Eley-Rideal model f ) number of degrees of freedom available for a model Ka ) activity reaction equilibrium constant kb ) backward reaction rate constant for esterification, mol/g/s kf ) forward reaction rate constant for esterification, mol/g/s Kacid ) adsorption equilibrium constant for acetic acid present in the system Kalc ) adsorption equilibrium constant for the alcohol present in the system Kester ) adsorption equilibrium constant for the ester present in the system Kwater ) adsorption equilibrium constant for the water present in the system LH ) Langmuir-Hinshelwood model Mcat. ) mass of the catalyst, g MLH ) modified Langmuir-Hinshelwood model n ) total number of moles in the system N ) number of data points PH ) pseudohomogeneous model Qk ) the area parameter of the UNIFAC group k R2 ) coefficient of determination of the fitted values ri ) reaction rate in mol/s ri,corr ) correlated reaction rate in mol/s ri,exp ) experimental reaction rate obtained by differential method in mol/s Rk ) volume parameter of the UNIFAC group k Sy/x ) standard error T ) temperature, K t ) time, s xi ) mole fraction of component i x1liquid ) mole fraction of component 1 in the liquid phase at equilibrium x1overall ) mole fraction of component 1 in the binary component feed ζexp ) percent conversion of the limiting component determined experimentally ζpred ) predicted percent conversion of the limiting component Πγ ) ratio of the product of activity coefficients of the products (ester and water) to that of the reactants (acid and alcohol) during the reaction R ) exponential term to account for water affinity for the resin γi ) activity coefficient of the ith component νi ) stoichiometric coefficient of component i
Literature Cited Acknowledgment This work was supported by Kuwait University, Research Grant No. [EC 04/03]. The excellent technical assistance found at Sorptiometry units of SAF (GS 01/01) of Faculty of Science, Kuwait University, is also acknowledged.
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ReceiVed for reView April 27, 2008 ReVised manuscript receiVed December 3, 2008 Accepted December 17, 2008 IE8006787
