Kinetics of esterification of methanol and acetic acid with mineral homogeneous acid catalyst

Mallaiah Mekala*,Venkat Reddy Goli

Department of Chemical Engineering,National Institute of Technology,Warangal 506004,India

Keywords:Esterification Homogeneous catalyst Kinetic rate-equation Simulation

ABSTRACT In this work,esterification of acetic acid and methanol to synthesize methyl acetate in a batch stirred reactor is studied in the temperature range of 305.15-333.15 K.Sulfuric acid is used as the homogeneous catalyst with concentrations ranging from 0.0633 mol·L?1 to 0.3268 mol·L?1.The feed molar ratio of acetic acid to methanol is varied from 1:1 to 1:4.The influences of temperature,catalyst concentration and reactant concentration on the reaction rate are investigated.A second order kinetic rate equation is used to correlate the experimental data.The forward and backward reaction rate constants and activation energies are determined from the Arrhenius plot.The developed kinetic model is compared with the models in literature.The developed kinetic equation is useful for the simulation of reactive distillation column for the synthesis of methyl acetate.

1.Introduction

Carboxylic acid esters constitute major components of numerous natural products and synthetic compounds.They are widely used as softeners,emulsifiers,dispersants,detergents,surfactants,solvents and biodiesel fuels.Several synthetic routes are available to obtain carboxylic acid esters.A comprehensive review of ester synthesis route is available[1].

The kinetics of esterification reaction between acetic acid and methanol in alcoholic and non-hydroxylic media was investigated earlier by Rolfe and Hinsshelwood[2].They proposed a kinetic model based on the theory of molecular statistics of esterification reaction by using hydrochloric acid as the catalyst.The kinetics of esterification of acetic acid with methanol using a homogeneous hydrogen iodide catalyst was investigated by Ronnback et al.[3],where the protonation of carboxylic acid was considered as the rate-initiating step in the reaction mechanism.They observed that hydrogen iodide was esterified by methanol and produced methyl iodide as a by-product.Hilton and Smith[4]found that the kinetics of acid catalyzed esterification of n-aliphatic acid with methanol is influenced by the length of carbon chains with different buffer solutions.

Agreda et al.[5]proposed a rate expression foresterification reaction using homogeneous sulfuric acid as a catalyst while carrying out the reaction in a reactive distillation unit.The kinetic model shows nonlinear dependence on the catalyst concentration without the kinetic parameters reported.Engell and Fernholz[6]and Kruel et al.[7]modified the kinetic modelproposed by Agreda et al.[5]for the esterification reaction using heterogeneous sulfonic ion exchange resin as the catalyst.Liu et al.[8]developed a rate expression for the esterification reaction of methanol with acetic acid using homogeneous sulfuric acid catalyst,presenting a linear kinetics on catalyst concentration.Elgue et al.[9]also proposed a linear kinetics on catalyst concentration and applied it for intensification of methyl acetate production in a continuous reactor.The catalytic esterification reaction between methanol and acetic acid for the synthesis of methyl acetate with Amberlyst-15(dry)as heterogeneous catalyst was studied by Is mail et al.[10]in the temperature range of 318-338 K.The similarities and differences between heterogeneous and homogeneous catalyzed esterification reactions of acetic acid with methanol were described by Liu et al.[11].They presented the kinetics using a commercial nafion/silica nano composite catalyst(SAC-13)and H2SO4separately,reported that heterogeneous and homogeneous catalysts show similar reaction inhibition by water formation,and suggested a common reaction mode based on Bronsted acid sites.

The kinetics of reversible liquid-phase esterification of acetic acid with methanolusing sulfuric acid catalyst in an isothermal batch reactor was investigated by Ganesh et al.[12].They observed that the rate constant is influenced by the concentration of catalyst and the reaction rate increases with the catalyst concentration.They also observed that the catalyst activity is slightly inhibited by the formation of water in the reaction mixture.The reaction kinetics and chemical equilibrium of the reversible catalytic esterification of acetic acid with methanol were investigated by Popken et al.[13].The reaction was catalyzed homogeneously by acetic acid itself and heterogeneously by an acidic ion-exchange resin.

Without catalyst it requires very long time to reach equilibrium[13].Although acetic acid itself may act as a catalyst,its activity for reaction is very low due to its weak acidic nature.The addition of catalyst improves the acidic nature of the reaction mixture by providing more H+ions for the reaction.Homogeneous catalysts such as hydrochloric acid,hydrogen iodide,hydrogen bromide and sulfuric acid have been used for the esterification reaction between acetic acid and methanol.It is reported that sulfuric acid is a better catalyst due to its greater density of acid sites per gram and it can prevent the side reactions[11].It is more effective than the heterogeneous catalyst for the esterification reaction,so it is selected for the present study.

Although a large number of studies are available in literature,some uncertainties remain in the reported kinetic models.In the present paper,the esterification reaction of acetic acid with methanol to produce methylacetate using homogeneous sulfuric acid catalyst is studied at different temperatures,catalyst concentrations and feed molar ratios.The kinetic models based on concentration as well as activity are developed and the model predictions are compared with experimental data.The model predictions are also compared with the models in literature.

2.Experimental

2.1.Chemicals

Acetic acid(99.95%,by mass),methanol(99%,by mass),and sulfuric acid(98%,by mass)were purchased from SD Fine Chemicals Ltd.(Mumbai,India)and used without any further purification.

2.2.Experimental setup

The esterification reaction was carried out in a 500 ml three neck round-bottom flask placed in a heating rota mantle,which contains a heating knob and a speed control knob.The rota-mantle was maintained at constant temperature by adjusting the heating knob.The minimum stirring speed was maintained at 240rpm for uniform mixing of catalyst in the reaction mixture using the speed control knob.A glass thermometer inserted into the reactor was used to measure the reaction mixture temperature inside the flask.A spiral condenser was connected vertically to the reaction flask to reduce the vapor losses from the reactor.

2.3.Experimental procedure

In the experiment,equimolar quantities of methanol(32 g)and acetic acid(60 g)were charged to the reactor.The desired amount or concentration of sulfuric acid was added to initiate the reaction.When the reaction mixture reached the desired reaction temperature,the time was noted.The samples were withdrawn at regular intervals of time and analyzed for the acetic acid concentration.The reaction was carried out for sufficient time to reach equilibrium conversion or without further decrease in acetic acid concentration.

2.4.Analysis

The acetic acid concentration was determined by titration of reaction mixture sample with standard solution of NaOH using phenolphthalein as the indicator.To prepare the standard solution of NaOH,pure water was obtained from an ultra-pure water purifier system(Millipore-Synergy UV system)with a resistance of 18.2 MΩ.

3.Results and Discussion

The present esterification reaction with homogeneous catalyst is investigated at1:1 mole ratio of acetic acid to methanol,with the temperature varied from 305.15 to 333.15 K and the catalyst concentration varied from 0.0633 mol·L?1to 0.3268 mol·L?1.

3.1.Effect of different factors on the reaction

3.1.1.Effect of temperature

The experimental results for conversion of acetic acid at different temperatures with fixed catalyst concentration(0.1288 mol·L?1)are shown in Fig.1.The rate of conversion of acetic acid increases with temperature.At the lowest temperature(305.15 K),the reaction reaches equilibrium after 400 min and at higher temperature,and the time required for the reaction to reach equilibrium reduces drastically.At 333.15 K the time needed is only 100 min.The higher the reaction temperature,the shorter the time required to reach equilibrium.At equilibrium,the acetic conversion is 0.69 or 69%.

Fig.1.Effect of temperature on reaction kinetics at0.1288 mol·L?1 catalyst concentration.?305.15 K;■313.15 K;▲323.15 K;●333.15 K.

3.1.2.Effect of catalyst concentration

Fig.2 shows the effect of catalyst concentration on the conversion of acetic acid at a fixed temperature of 323.15 K.As the catalyst concentration increases the reaction reaches equilibrium faster.At 0.3268 mol·L?1catalyst concentration the reaction takes about 70 min to reach equilibrium whereas at 0.0633 mol·L?1it only takes about 150 min.The effect of catalyst concentration on the acetic acid conversion is similar to that of the effect of temperature.

Fig.2.Effect of catalyst concentration on reaction kinetics at 323.15 K.? 0.0633 mol·L?1;■ 0.1288 mol·L?1;▲ 0.1923 mol·L?1;Δ 0.2576 mol·L?1;● 0.3268 mol·L?1.

3.1.3.Effect of initial reactant mole ratio

Fig.3 shows the effect of initial molar ratio of acetic acid to methanol on the acetic acid conversion at fixed catalyst concentration of 0.1288 mol·L?1and reaction temperature of 333.15 K.The equilibrium conversion of acetic acid increases with mole ratio due to the availability of excess methanol.With an increase in mole ratio of acetic acid to methanol from 1:1 to 1:4,the equilibrium conversion of acetic acid increases from 69%to 91.7%.

Fig.3.Effect of reactant initial mole ratio on the acetic acid conversion at 0.1288 mol·L?1 catalyst concentration and reaction temperature 333.15 K.? 1:1;■ 1:2;▲ 1:3;● 1:4.

3.2.The kinetic model

3.2.1.Concentration based model

A second-order elementary kinetic model is assumed since the reaction is carried out with a molar ratio of 1:1 of acetic acid to methanol.The reaction rate expression for the homogeneous reaction[14]is

where CA,CB,CCand CDare the acetic acid,methanol,methylacetate and water concentrations,respectively,kfand kbare the forward and backward reaction rate constants,respectively,and Keqis the equilibrium constant of the reaction.It is assumed that products water and methyl acetate are not present at the beginning of the reaction.The reaction volume during the reaction remains constant.Eq.(1)is rearranged in terms of acetic acid conversion,XA=1?CA/CA0.The rate equation is modified as

Eq.(2)is integrated and re-arranged to a linear form to find the forward reaction rate constant.The equation is

From Eq.(3),the forward reaction rate constants at different temperatures and at 0.1288 mol·L?1catalyst concentration are calculated.The temperature dependency of the reaction rate constants is expressed by the Arrhenius equation.

where kf0and kb0are the pre-exponential factors,Efand Ebare the activation energies for forward and backward reactions,respectively,R is the gas constant,and T is the temperature.

The influence of temperature on the reaction rate constant is determined by fitting kfand kbto the Arrhenius Eqs.(4a)and(4b).Fig.4 shows the Arrhenius plot of ln kfvs.1/T and ln kbvs.1/T.The forward and backward activation energies are found to be 62,721 and 62,670 J·mol?1,respectively.Because the two activation energies are nearly equal,it can be concluded that the equilibrium constant(Keq)for this reaction is nearly independent of temperature[5],and is approximately equal to 5.07.The equilibrium constant can be determined experimentally from the equilibrium conversion XAeof acetic acid as follows

Fig.4.Arrhenius diagram for reaction rate constants.

Fig.2 shows the effect of catalyst concentration on the reaction kinetics for five different catalyst concentrations at fixed temperature of 323.15 K.With similar experiments conducted for various catalyst concentrations at different temperatures to the rate constant kf,and the pre-exponential factor kf0are determined.The pre-exponential factor(kf0)is plotted as a function of catalyst concentration as shown in Fig.5.A mathematical expression is proposed from the linear fitting of data,where WCis the concentration of catalyst(mol·L?1)in the initial reaction mixture.

Fig.5.Relation between pre-exponential factor and catalyst concentration.

Fig.6 shows the comparison of acetic acid conversion from experimental results with that from the concentration based model for different catalyst concentrations at 323.15 K.As the catalyst concentration increases,the conversion of acetic acid increases.At lower catalyst concentrations,the model predictions are in close agreement with experimental results.The predictions are a little lower than experimental values at the early stages but as the time proceeds they are in good agreement.At higher catalyst concentration the predictions are lower in magnitude in the initial stage then they tend to approach the experimental results closely.One of the reasons for the mismatch is the formation of water,which may inhibit the rate of reaction until reaching the equilibrium.

Fig.6.Comparison of experimental results with concentration based model results for the conversion of acetic acid at different catalyst concentrations at 323.15 K.?0.0635 mol·L?1;▲0.1288 mol·L?1;● 0.3268 mol·L?1;0.0635 mol·L?1;0.1288 mol·L?1;0.3268 mol·L?1(symbols represent experimental data and lines represents concentration based model results).

3.2.2.Activity model

The activity model accounts for the non-ideality of the solution.It can be developed from the concentration-based model by defining the activity as

The reaction rate equation in terms of the activities is given by

with

Based on the equilibrium conversion,the activities and mole fractions are computed and substituted into Eq.(9)to find the equilibrium constant based on activity.kfactis related to the temperature through an Arrhenius relation

with

where kf0is calculated from the concentration-based model.The nonideality of the reaction mixture is calculated by the UNIQUAC equation.The UNIQUAC riand qivalues and the interaction parameters are given in Tables 1 and 2,respectively[12].

Table 1 UNIQUAC ri and qi values

Table 2 UNIQUAC interaction parameters

Fig.7 shows the comparison for the conversion of acetic acid from experimental results with that predicted from the activity based model at different catalyst concentrations at 323.15 K.The deviation is little between the experimental and predicted results,except at lower catalyst concentrations.

Fig.7.Comparison of experimental results with activity-based model results for the conversion of acetic acid at different catalyst concentrations at323.15 K.? 0.0635 mol·L?1;▲0.1288 mol·L?1; ● 0.3268 mol·L?1;0.0635 mol·L?1;0.1288 mol·L?1;0.3268 mol·L?1(symbols represent experimental data and lines represents activity based model results).

The experimental results and the activity-based model predicted values are plotted for acetic acid conversion with constant catalyst concentration of 0.1288 mol·L?1and different reaction temperatures as shown Fig.8.The predicted and experimental values match well except at lower temperature.As the temperature increases the reaction rate also increases,which may be due to the increase in the kinetic energies resulting in more inter-molecular collisions.

Fig.9 compares the experimental conversion of acetic acid with that predicted by the concentration based model and activity based model at a fixed catalyst concentration of 0.1288 mol·L?1and different temperatures.Both models are in good agreement with the experimental data.

Fig.8.Comparison of experimental results with activity-based model results for the conversion of acetic acid at different reaction temperatures at 0.1288 mol·L?1 catalyst concentration.? 305.15 K;▲313.15 K;● 323.15 K;?333.15 K;305.15 K;313.15 K;323.15 K;333.15 K(symbols represent experimental data lines represents activity based model results).

Fig.9.Comparison of experimental results with respect to concentration and activity based model results for the conversion of acetic acid at different reaction temperatures at 0.1288 mol·L?1 catalyst concentration.? 305.15 K;▲ 313.15 K;● 323.15 K;?333.15 K(symbols represent experimental data);——305.15 K;313.15 K;323.15 K;333.15 K(activity based model);305.15 K;313.15 K;—323.15 K;333.15 K(concentration based model).

3.2.3.Comparison with models in literature

The kinetic models proposed for the esterification of acetic acid with methanol are given in Table 3.Our experimental data and model predictions are compared with these literature models as shown in Figs.10-12.

Fig.10.Comparison of different kinetic models at 313.15 K and 0.3268 mol·L?1 catalyst concentration.?experimental;— —concentration based;activity based;Liu et al.[8];Elugu et al.[9];Bonnaillie et al.[15];Agreda et al.[5].

Fig.10 shows the conversions of acetic acid from the concentration and activity based models and the existing kinetic models in literature at temperature 313.15 K and catalyst concentration of 0.3268 mol·L?1.The experimental results are quite accurately predicted by our models as well as Agreda et al.'s model[5].The accuracy of the predictions decreases in the following order:activity-based model,concentration based model,Agreda et al.'s model[5],Bonnaillie et al.'s model[15],Elgue et al.'s model[9],and Liu et al.'s model[8].

Fig.11 shows the comparison of the experimental results against kinetic models at temperature of 323.15 K and catalyst concentration of 0.3268 mol·L?1.The experimental results are predicted fairly accurately by the activity-based,concentration-based and Agreda et al.'s models.The activity-based model provides a slightly better fit than the concentration-based model.Comparing Fig.11 with Fig.10,we can conclude that even at higher temperatures,while maintaining the catalyst concentration constant,activity-based and concentration-based models predict the results with reasonable accuracy.

Fig.11.Comparison of different kinetic models at 323.15 K and 0.3268 mol·L?1 catalyst concentration.?experimental;— —concentration based;activity based;Liu et al.[8];Elugu et al.[9];Bonnaillie et al.[15];Agreda et al.[5].

Table 3 Kinetic models and parameters in literature

Fig.12 compares the available kinetic models[5,8,9,15],our models and the experimental data at temperature of 323.15 K and catalyst concentration of 0.1288 mol·L?1.The models proposed in the present study,concentration-based and activity-based models,are better than the models available in the literature.Our models provide better fit to the experimental data.

Fig.12.Comparison of different kinetic models at 323.15 K and 0.1288 mol·L?1 catalyst concentration.?experimental;— —concentration based;activity based;Liu et al.[8];Elugu et al.[9];Bonnaillie et al.[15];Agreda et al.[5].

4.Conclusions

The esterification reaction between methanol and acetic is conducted in a batch stirred reactor with sulfuric acid as a catalyst.The experimental results show that as the temperature and catalyst concentration increase the reaction rate increases.The experimental data is expressed with a reversible second order reaction rate equation.The activation energies for forward and backward reactions are obtained using the Arrhenius equation.A mathematical equation is developed to describe the relation between the catalyst concentration and the frequency factor.The kinetic models are developed for the concentration-based and activity-based and compared with literature models.The developed kinetic equation predicts the results accurately.

Nomenclature

aiactivity of component i

CAacetic acid concentration,mol·L?1

CA0initial acetic acid concentration,mol·L?1

CBmethanol concentration,mol·L?1

CCmethyl acetate concentration,mol·L?1

CDwater concentration,mol·L?1

CAe,CBe,

CCeand CDeequilibrium concentration of acetic acid,methanol,methyl acetate and water,mol·L?1

Ebbackward activation energy,J·mol?1

Efforward activation energy,J·mol?1

Keqequilibrium constant

kbbackward reaction rate constant,L·mol?1·min?1

kb0backward frequency factor,L·mol?1·min?1

kfforward reaction rate constant,L·mol?1·min?1

kf0forward frequency factor,L·mol?1·min?1

rAreaction rate of acetic acid,mol·L?1·min?1

R gas constant,J·mol?1·K?1

T absolute temperature,K

t time,min

WCcatalyst concentration,mol·L?1

XAacetic acid conversion

XAeacetic acid equilibrium conversion

γiactivity coefficient of component i