Xiaoda Wang ,Wenkai Li ,Shiwei Wang ,Qinglian Wang ,Ling Li, *,Hongxing Wang *,Ting Qiu

1 Engineering Research Center of Reactive Distillation,Fujian Province University,School of Chemical Engineering,Fuzhou University,Fuzhou 350108,China

2 College of Chemical Engineering and Materials Science,Tianjin University of Science &Technology,Tianjin 300457,China

Keywords:Kinetics Autocatalysis Kinetic modeling 2-Ethyl-1-hexyl thioglycolate Esterification Ion exchange resin

ABSTRACT Producing 2-ethyl-1-hexyl thioglycolate (ETE) via esterification reaction with thioglycolic acid (TGA)aqueous solution as raw material by reactive-separation coupling technology is a promising process intensification method.To choose suitable reactive-separation coupling strategy,the kinetic studies of the esterification of TGA with 2-ethyl-1-hexanol (EHL) were carried out in a batch system.The commercial ion exchange resin was employed as an eco-friendly catalyst.The effects of temperature,catalyst concentration and molar ratio were determined.It was interesting to observe that the equilibrium conversion of TGA increased with the increase of catalyst mass fraction due to the adsorption of product water onto resin surface.The activity-based pseudo-homogeneous (PH),Eley-Rideal (ER) and Langmuir-Hinshelwood-Ho ugen-Watson(LHHW)models were used to fit the kinetics data of the resin-catalyzed reaction.The models of ER and LHHW performed better than the PH model.The kinetics of the TGA-self-catalyzed reaction was also determined.An activity-based homogeneous kinetics model could well describe this self-catalyzed reaction.These results would be meaningful to the selection and design of an appropriate reactionseparation strategy for the production of ETE,to realize the process intensification.

1.Introduction

2-Ethyl-1-hexyl thioglycolate (ETE) is an important organic intermediate in the field of fine chemicals [1,2].It was mainly applied as raw materials for the synthesis of mercaptan tin and mercaptan antimony,thermal stabilizer for polyolefin and catalyst for the production of bisphenol A [3,4].ETE can be synthesized by the esterification of thioglycolic acid(TGA)with 2-Ethyl-1-hexanol(EHL).The reactant TGA was synthesized by fermentation,resulting in the formation of an aqueous solution with 10% (mass) TGA[5–7].TGA was usually separated from the aqueous solution by distillation or extraction for the subsequent reaction.

From the point of view of industrial application,it is wise to couple the separation and reaction in one equipment with TGA aqueous solution as raw material for the production of ETE,to reduce the operation and equipment costs.There are two classic candidate technologies,reactive distillation and reactive extraction,which have succeeded in the production of carboxylic esters from corresponding carboxylic acid aqueous solution [8–13].Choosing a kind of catalyst suitable and 7accurately modeling the reaction kinetics are essential for the design of an ETE synthesis process.However,to data,there is not related report in any literature.

Esterification is a typical acid-catalyzed reaction.Several homogeneous liquid-acid catalysts such as sulfuric,paratoluenesulfonic,sulphuric hydrofluoric and heteropoly acids were used to catalyze the esterification reaction in industrial processes[14–19].However,these liquid-acid catalysts were highly corrosive to the reactors and difficult to be separated from the reaction mixtures.Heterogeneous solid-acid catalysts such as ion exchange resins,montmorillonite clay,zeolite,metal oxides and supported heteropolyacids were excellent alternatives to homogenous liquid acid catalysts [20–24],since they were readily-separable from reaction mixtures and exhibited excellent thermal stability and high catalytic activity.Due to these significant advantages,heterogeneous solid-acid catalysts have increasingly been applied in esterification reactions in industrial processes.In this work,a commercial resin catalyst was chosen for ETE synthesis.

In addition to the thermodynamic data,the accurate reaction kinetic data and models were required to design an industrial reactor for the solid-acid-catalyzed esterification reaction[24–37].The kinetics for the heterogeneously solid-acid-catalyzed esterification reactions could be described by different models,including pseudo-homogeneous (PH),Eley-Rideal (ER) and Langmuir-Hin shelwood-Hougen-Watson (LHHW) models [26–30].Although the self-catalyzed esterification reaction was very slow due to the low acidity of carboxylic acid,it remained non-negligible in the industrial design [36–39].In industry,the hydrolysis conversion of methyl acetate was not higher than 95%in the reactive distillation column due to the self-catalyzed esterification of acetic acid and methanol.Our group developed a reactive dividing-wall distillation process for the hydrolysis of methyl acetate,to suppress the self-catalyzed reaction by the in-situ separation of methanol,realizing the complete conversion of methyl acetate[40].To describe the self-catalyzed esterification reaction,P?pken et al.[37] provided two different kinetic models based on two different catalytic mechanisms.Both of these two models performed well in describing the self-catalyzed esterification of acetic acid with methanol.Therefore,not only the heterogeneously solidacid-catalyzed,but also the homogeneously self-catalyzed reaction kinetics should be studied for the industrial design.

In this work,the reaction kinetics for the heterogeneous-resinand homogeneous-self-catalyzed esterification of TGA with EHL to synthesize ETE were determined in a batch reactor.The activitybased PH,ER and LHHW models were used to describe the kinetics of the heterogeneously catalyzed reaction,and the models proposed by P?pken et al.[37] were applied to describe the kinetics of the homogeneously self-catalyzed reaction.These results would be meaningful to the selection and design of an appropriate reaction-separation strategy for the production of ETE,to realize the process intensification.

2.Experimental

2.1.Chemicals

TGA(mass purity ≥90.0%)and EHL(mass purity ≥99.5%)were purchased from Shanghai Aladdin Bio-chem Technology Co.,Ltd.(Shanghai,China).TGA was used without purification,since the major impurity was water (mass purity ≈10.0%),which was the product of the esterification reaction of TGA with EHL.ETE (2-Ethyl-1-hexyl thioglycolate,mass purity ≥98.0%) were purchased from Adamas Reagent,Ltd.(Shanghai,China).The specifications of the chemicals used were presented in Table 1.The strong acid action exchange resin A46 supplied by Jiangsu Success Resin Company (Jiangsu,China) was used as catalyst for the heterogeneous reaction.The physicochemical properties of A-46 were presented in Table 2.

Table1 Specifications of the chemicals used

Table2 Physicochemical properties of the strong acid action exchange resin A46

2.2.Analytical method

The gas chromatography (TRACE 1300,Thermo Fisher Scientific) equipped with a hydrogen flame ionization detector and a weak polar capillary column (30 m × 0.32 mm × 0.25 μm) was used to analyze EHL and ETE with Nitrogen gas as carrier gas.The internal standard method was adopted to quantitatively determine the mass fraction of EHL and ITA with cyclohexanone as internal standard substance.The concentration of TGA was detected by acid-base titration method.The water was measured by a Karl Fischer titration (KLS-411,INESA Scientific Instrument Co.,Ltd.).

2.3.Apparatus and procedure

The kinetic experiments were performed in a 500 ml glass three-necked flask at atmosphere pressure,as shown in Fig.1.The middle neck was connected to a glass condenser to avoid the mass loss of most volatile component water,which was one product of TGA-EHL esterification reaction.In the all the experimental runs,the mass fraction of water was lower than 8%.The slight loss of water might lead to the shift of chemical equilibrium.The other two necks of the flask were used to measure reaction temperature with a mercury thermometer and sampling with a syringe,respectively.The reaction temperature was maintained by immersing the flask into a thermostat-controlled oil bath with an accuracy of±0.3 K.The oil bath was equipped with a magnetic stirring apparatus to ensure the uniform mixing of reactive mixture.To ensure the reaction occurred at desired temperature,the mixture of reactant ITA and catalyst A46 was heated in the glass flask by the oil bath,while the reactant TGA was heated in a preheater.After the desired reaction temperature was reached,we added TGA into the glass flask and defined this moment as the beginning of the esterification reaction.During each run of the kinetic experiment,about 0.5 mL liquid was withdrawn from the flask at regular time intervals by a syringe to determine the variation of TGA conversion with time.The samples were cooled rapidly to 263.15 K in a refrigerator to avoid any further reaction and analyzed within 30 min.Each experimental run was continued until the chemical equilibrium was achieved.Similar apparatus and procedures was applied in our group to accurately determine the kinetics of other reactions,manifesting their reliabilities [41].

3.Results and Discussion

3.1.Reaction kinetics

3.1.1.Heterogeneous A46-catalyzed reaction

3.1.1.1.Elimination of mass-transfer resistance.To accurately measure the kinetics of TGA-EHL esterification reaction catalyzed by A46,the mass-transfer resistances inside and outside the catalyst particle should be eliminated.External mass-transfer resistance could be reduced by increasing the stirring speed.The effect of stirring speed on conversion was determined at the temperature of 363.15 K,TGA-EHL molar ratio of 1:2 and catalyst mass fraction of 5%.Fig.2 illustrated the variation of TGA conversion with time at three different stirring speeds.At the same reaction time,TGA conversion increased with stirring speed increased from 200 r.min-1to 300 r.min-1.The agitation speed had no appreciable effect on TGA conversion over 300 r.min-1,indicating the external mass-transfer resistance could not be reduced above this agitation speed.Agitation speed higher than 300 r.min-1contributed little to the reduction of external mass transfer resistance,and would lead to the fragmentation of catalyst particles.Therefore,all further experiments were carried out at the agitation speed of 300 r.min-1.The internal mass-transfer resistance of catalyst particle could be decreased by reducing the size of catalyst particle.Several researches concluded that the particle size had little effect on the reaction rate as it was less than 0.68 mm[25,42–44].Since the particle size of A46 was in the range of 0.25–0.5 mm,the effect of internal mass-transfer could be ignored for A46.

3.1.1.2.Effect of reaction temperature.Fig.3 showed the variation of TGA conversion with time at different reaction temperatures 333.15,343.15,353.15 and 363.15 K with the initial TGA-EHL molar ratio of 1:2 and catalyst mass fraction of 5%.It was interesting to find that the equilibrium conversion of TGA-EHL esterification reached up to 0.9310 at 333.13 K at very low molar ratio.With the reaction temperature rose sharply by 30 K from 333.15 to 363.15 K,the equilibrium conversion increased marginally from 0.9310 to 0.9421,indicating that this was a slight endothermic reaction.Reaction temperature also had an effect on reaction rate.Higher temperature resulted in faster reaction rate due to the greater collision probability of reactant moles.The esterification of TGA and EHL also followed such law.As shown in Fig.3,TGA reached its equilibrium conversion of 0.9421 at 363.15 K at the reaction time of 1300 min,but only about 78% of TGA was converted at 333.15 K at the same reaction time.Additionally,the equilibrium conversion could be reached in 1300 min at 363.15 K,but the reaction time of 6000 min was required at 333.15 K to reach the chemical equilibrium.Therefore,although increasing temperature had slight effects on the equilibrium conversion of TGA-EHL esterification,it was helpful to reduce the reaction time due to its significant acceleration to this reaction.The experiment was not conducted at the temperature higher than 363.15 K,since some of the water would volatilize and escape from the reaction system at atmospheric pressure.The volatilization of product water would give rise to the shift of chemical equilibrium,which was not conducive to the accurate measurement of the reaction kinetics.

Fig.1.Apparatus for the kinetics experiments.1-Thermostatic oil bath with stirrer,2-flask,3-thermometer,4-condenser,5-sampling device.

Fig.2.Effect of stirring speed on TGA conversion for the A46-catalyzed TGA-EHL esterification reaction.Reaction conditions:TGA-EHL molar ratio of 1:2,reaction temperature of 363.15 K,and catalyst mass fraction of 5%.

Fig.3.Effect of reaction temperature on TGA conversion for the A46-catalyzed TGA-EHL esterification reaction.Reaction conditions:stirring speed of 300 rpm,TGA-EHL molar ratio of 1:2,and catalyst mass fraction of 5%.Solid point:experimental data,line:simulation data.

3.1.1.3.Effect of catalyst mass fraction.The effect of catalyst mass fraction on TGA conversion was tested at 363.15 K and TGA-EHL molar ratio of 1:2.Higher catalyst mass fraction meant higher concentration of catalytic active site in the liquid,resulting faster conversion rate of TGA.As shown in Fig.4,TGA conversion increased from 0.8531 to 0.9421 with the improvement of catalyst mass fraction from 1% to 5% at about 1300 min.It was very interesting to observe that the equilibrium conversion of TGA increased from 0.9351 to 0.9421 with the catalyst mass fraction increased from 1% to 5%.The water-adsorbing quality of the resin catalyst could give a reasonable explain for this result.The molar fraction of water was 30% at the initial TGA-EHL molar ratio of 1:2 with the TGA conversion of 0.9,while its mass fraction was only 5.16%because of the large molecular weight of TGA and EHL.Since this was on the same order of magnitude with that of catalyst and the sulfonic acid ion-exchange resin had strong hydrophilicity to water,some of the water generated would be adsorbed onto the surface of A46 catalyst,driving the reaction forward to improve the equilibrium conversion.The water-adsorbing quality of the resin catalyst was also utilized by Oh et al.[45]to enhance the synthesis of propylene glycol methyl ether acetate via the esterification of acetic acid with 1-methoxy-2-propanol in a reactive chromatography.

3.1.1.4.Effect of reactant initial molar ratio.The effect of initial TGAEHL molar ratio was studied at 363.15 K with catalyst mass fraction of 5.0%,as shown in Fig.5.The TGA conversion grows significantly with initial TGA-EHL molar ratio increased from 1:1 to 1:2,which should be attributed to the increase of EHL concentration.The TGA conversion arisen slightly with the molar ratio further improved from 1:2 to 1:6,which suggested that the molar ratio of 1:2 was an economical operation condition for the esterification of TGA and EHL.

3.1.1.5.Reusability of A46.The reusability of A46 was evaluated at the TGA-EHL molar ratio of 1:2,reaction temperature of 363.15 K and catalyst mass fraction of 5%.As shown in Fig.6,the TGA conversion kept constant after 4 runs,which demonstrated that A46 had a great industrial application potential for the esterification of TGA and EHL.

Fig.4.Effect of catalyst mass fraction on the TGA conversion for the A46-catalyzed TGA-EHL esterification reaction.Reaction conditions:stirring speed of 300 r.min-1,TGA-EHL molar ratio of 1:2,and reaction temperature of 363.15 K.Solid point:experimental data,line:simulation data.

Fig.5.Effect of initial TGA-EHL molar ratio on the TGA conversion for the A46-catalyzed TGA-EHL esterification reaction.Reaction conditions:stirring speed of 300 r.min-1,reaction temperature of 363.15 K,and catalyst mass fraction of 5%.Solid point:experimental data,line:simulation data.

Fig.6.Reusability of A46 in catalyzing the TGA-EHL esterification reaction.Reaction conditions:stirring speed of 300 r.min-1,TGA-EHL molar ratio of 1:2,reaction temperature of 363.15 K and catalyst mass fraction of 5%.

3.1.2.Homogeneous self-catalyzed reaction

3.1.2.1.Effect of reaction temperature.The effect of temperature on the homogeneous self-catalyzed reaction was determined at the temperatures of 333.15,348.15,353.15 and 363.15 K with the TGA-EHL molar ratio of 1:2 and stirring speed of 300 r.min-1.As shown in Fig.7,higher temperature led to faster initial reaction rate and shorter time to reach equilibrium.Without the application of catalyst,the time required to reach equilibrium was about 33,000 min at the reaction temperature of 363.15 K.With the application of catalyst,the time required to reach equilibrium was only 1300 min,as shown in Fig.3.It demonstrated that although the reactant TGA could spontaneously catalyze its esterification with EHL,the application of catalyst was necessary to reduce the reaction time for the industrialization of this reaction due to the low catalytic activity of TGA.Moreover,the equilibrium conversion of reactant improves from 0.9052 to 0.9386 with temperature increased from 333.15 K to 363.15 K due to the fact that the esterification of TGA with EHL was an endothermic reaction.In comparison with the equilibrium conversion of A46-catalyzed esterification reaction,that of self-catalyzed reaction was lower at the same molar ratio and temperature.This was coincident with our conclusion in Section 3.1.1.3 that the water was adsorbed onto the A46 catalyst,driving the reaction forward.

Fig.7.Effect of reaction temperature on TGA conversion for the self-catalyzed TGAEHL esterification reaction.Reaction conditions:stirring speed of 300 r.min-1 and TGA-EHL molar ratio of 1:2.Solid point:experimental data,line:simulation data.

3.1.2.2.Effect of TGA-EHL molar ratio.The effect of TGA-EHL molar ratio on the homogeneous self-catalyzed reaction was determined at the temperatures of 363.15 K and stirring speed of 300 r.min-1,as shown in Fig.8.Similar to the results of the A46-catalyzed reaction,the conversion of TGA increased significantly and slightly with the molar ratio increased from 1:1 to 1:2 and from 1:2 to 1:6,respectively.Compared with the A46-catalyzed reaction,the time required to the reach equilibrium reduced from 14,500 min to 605 min at the molar ratio of 1:6 after the addition of catalyst.

Fig.8.Effect of TGA-EHL molar ratio on TGA conversion for the self-catalyzed TGAEHL esterification reaction.Reaction conditions:stirring speed of 300 r.min-1 and reaction temperature of 363.15 K.Solid point:experimental data,line:simulation.

3.2.Chemical equilibrium

The kinetics were determined at different temperatures until the chemical equilibrium was reached,as illustrated in Figs.3 and 7 for the A46-and self-catalyzed reactions.The selectivity to ETE was considered as 100% since no by-product was detected.

Due to the non-ideality of the reaction system in liquid phase,the chemical equilibrium constant was calculated based on component activity a instead of component mole fraction x:

where γ was the activity coefficient,which was calculated by the UNIFAC model.The information about the UNIFAC model and related parameters were given in theSupplementary Material.Table 3 listed the thermodynamic equilibrium constants and compositions at different temperatures.The dependence of Keqon reaction temperature T was measured by plotting lnKeqvs 1/T in Fig.9,which showed that lnKeqvaried linearly with 1/T for the A46-and self-catalyzed reactions:

Table3 Chemical equilibrium constants and equilibrium compositions for the reaction

Equilibrium constants could be expressed in terms of the standard Gibbs free energy of reaction

3.3.Kinetic models

3.3.1.Heterogeneous A46-catalyzed reaction

The pseudo-homogeneous(PH),Eley-Rideal(ER)and Langmuir-Hinshelwood (LHHW) models were adopted to describe the heterogeneous A46-catalyzed reaction.These models were showed as follows:

PH model:

Fig.9.Dependence of chemical equilibrium constant on reaction temperature.

where riis the reaction rate of component i,the chemical equilibrium constant Keq=k+/k-,k+the forward reaction rate constant,k-the backward reaction rate constant,Kithe adsorption equilibrium constant of component i.The dependence of reaction rate constant on temperature was expressed by the Arrhenius law:

k0,+and k0,-are the pre-exponential factors for the forward and backward reactions,respectively.Ea,+and Ea,-are the activation energies for the forward and backward reactions,respectively.The dependence of adsorption equilibrium constant Kion temperature was measured by plotting lnKivs 1/T:

ΔGad,iwas the adsorption energy of component i.The derivations of ER and LHHW models were given in theSupplementary Material.In these models,the activity was used instead of molar fraction to describe the liquid non-ideality to improve the model accuracy.The activity coefficient of each component was calculated by the UNIFAC model.In Eqs.(3)–(5),ricould be written as:

where n0was the initial total mole numbers of reactants in reaction system (mol),wcatthe catalyst mass concentration (g.ml-1),t the reaction time (min) and υithe stoichiometric coefficient of component i.

3.3.2.Homogeneous self-catalyzed reaction

In this case,the esterification reaction was catalyzed by the reactant TGA.The kinetic model for the self-catalyzed esterification reaction was developed by P?pken et al.[30],and they successfully used it to describe the self-catalyzed esterification reaction of acetic acid with methanol.Their kinetic model,named after PP model in this work,was expressed as follows:

The exponent α in Eq.(11)could be set as 0.5 or 1 under different assumptions.In the first case,we assumed that the esterification reaction occurs with the catalysis of the solvated protons dissociated by TGA and the dissociation equilibrium was described by the Br?nsted equilibrium constant Ka:

As a result,xH+≈Based on this assumption,the exponent α=0.5 with√incorporated into the kinetic constant.In the other case,we assumed that the esterification reaction was catalyzed by the un-dissociated TGA.It means that the reaction between one molecule of TGA and one molecule of EHL catalyzed by one molecule of TGA,leading to α=1.

3.3.3.Kinetic parameter fitting and model validation

Since the kinetic parameters depended on reaction temperature,the kinetic data at different temperatures were used to fit the kinetic parameters.The kinetic data in Figs.3 and 7 showed the dependence of reaction kinetic on temperature for the heterogeneous A46-catalyzed and homogeneous self-catalyzed reactions,respectively.They were used to fit the kinetic parameters of Eqs.(4)–(6)and(11),respectively.The calculation flow chart for the fitting process is as follows.At first,the initial values of kinetic parameters were set.Based on these initial values,the kinetic model,which was a system of ordinary differential equations,were solved by the fourth order Runge-Kutta integration method to calculate the mole fraction of each component at every time point.The sum of squared residuals (SSR) between the experimental and calculated molar composition was applied as objective function:

where nc and nt are the number of component and time point,respectively.The non-linear least square method was applied to search the minimum SSR.The calculation was realized by the functions ode23s and lsqnonlin in the math software MATLAB.The rootmean-square deviation (RMSD) between the experimental and calculated mole fraction were applied to evaluate the accuracy of the kinetic parameters fitted:

The fitted kinetic parameters were listed in Table 4 for all the models used.For the A46-catalyzed reaction,the ER and LHHW models performed better than the PH model at all temperatures,suggesting the necessity of considering the reactant and production adsorption on catalyst particles.For the ER and LHHW models,all the adsorption equilibrium constants decreased with the increase of temperature.Such a variation trend accorded with the physical absorption theory.For the self-catalyzed reaction,the values of RMSD were lower when the PP model with α=1 was used.It suggested that the esterification of TGA and EHL was more probably catalyzed by the un-dissociated TGA.Based on Eqs.(7)–(9),the values of k0,+,k0,-,Ea,+,Ea,-,Aiand ΔGad,iwere calculated with the data in Table 4 by the least square method and listed in Table 5.

Table4 Kinetic parameters and RMSD of PH,ER,LHHW and PP models

Table5 Dependence of kinetic parameters on temperature based on Arrhenius equation (k= and Ki=)

Table5 Dependence of kinetic parameters on temperature based on Arrhenius equation (k= and Ki=)

Note:the units of k+0 and k-0 are mol.g-1.min-1.ml-1 for the PH,ER and LHHW models and are mol.min-1.ml-1 for the PP model,respectively;the units of Ea+,Ea-and ΔHad,i are kJ.mol-1.

The fitted kinetic parameters and models were applied to predict the TGA conversions at different catalyst mass fractions and initial TGA-EHL molar ratios.The comparisons between the calculated and experimental data,which were expressed by RMSD,were given in Table 6.For the A46-catalyzed reaction,the ER and LHHW models performed better than the PH model.For the self-catalyzed reaction,the prediction accuracy was higher at α=1.The prediction deviations of ER,LHHW and PP models were less than 5%,suggesting the well prediction ability of these models.The deviation of PH model was less than 14%,which was acceptable from the point of view of engineering design.Table 6 also illustrates that the prediction deviation increases with the increase of molar ratio.A reasonable explain to this result is that the contribution of selfcatalyzed reaction become weaker at higher TGA-EHL molar ratio because of the decrease of TGA concentration.

Table6 Values of RMSD for the PH,ER,LHHW and PP models

4.Conclusions

In order to select a suitable reactive-separation coupling method to produce 2-Ethyl-1-hexyl thioglycolate(ETE)via esterification reaction with thioglycolic acid (TGA) aqueous solution as raw material by technology,the kinetic studies of the esterification of TGA with 2-ethyl-1-hexanol (EHL) were carried out in a batch system.The commercial ion exchange resin A46 was employed as an eco-friendly catalyst.The effects of temperature,catalyst concentration and molar ratio were determined.More than 90%TGA conversion was realized at low molar ratio,much higher than most of the esterification reaction reported in literatures.The equilibrium conversion improved slightly from 0.9310 to 0.9421 with the great increase of reaction temperature from 333.15 to 363.15 K,indicating that this was a mild endothermic reaction.It was interesting to find that the equilibrium conversion of TGA increased with the increase of catalyst mass fraction due to the adsorption of product water onto the hydrophilic resin surface.The kinetics of the TGA-self-catalyzed reaction was also determined.The activity-based pseudo-homogeneous (PH),Eley-Rideal(ER)and Langmuir-Hinshelwood-Hougen-Watson(LHHW)models were used to fit the kinetics data of the resin-catalyzed reaction.The models of ER and LHHW performed better than the PH model.The activity-based homogeneous kinetics model was used to describe this self-catalyzed reaction and revealed high prediction accuracy.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

We acknowledge the financial support for this work from the National Natural Science Foundation of China (No.21706034),the Guiding Project of Fujian Province (No.2018H0016),the Open Foundation of State Key Laboratory of Chemical Engineering (No.SKL-ChE-18B02),and the Integration of Industry,Education and Research of Fujian Province (No.2018Y4008).

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2020.08.052.

Nomenclature

aiActivity of component i

Ea,+and Ea,-Activity energies for the forward and backward reactions,J.mol-1

KeqActivity-based chemical equilibrium constant

KiAdsorption equilibrium constant of component i on A46

k0,+and k0,-Pre-exponential factors of the Arrhenius equation,mol.g-1.min-1.ml-1or mol.min-1.ml-1

k+and k-Forward and backward reaction rate constants,mol.g-1.min-1.ml-1or mol.min-1.ml-1

n0Initial total mole numbers of reactants in reaction system,mol

R Ideal gas constant,J.mol-1.K-1

riReaction rate of component i,mol.g-1.min-1.ml-1or mol.min-1.ml-1

T Temperature,K

t Reaction time,min

wcatCatalyst mass concentration,g.ml-1

α Exponent in the PP model

γiActivity coefficient of component i

υiStoichiometric coefficient of component i