thermodynamic and kinetic studies for synthesis of the acetal (1,1-diethoxybutane) catalyzed by...

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Thermodynamic and kinetic studies for synthesis of the acetal(1,1-diethoxybutane) catalyzed by Amberlyst 47 ion-exchange resin

Mehabub Rahaman, Nuno S. Graa, Carla S.M. Pereira, Alrio E. Rodrigues

Laboratory of Separation and Reaction Engineering (LSRE), Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias s/n, 4200-465

Porto, Portugal

h i g h l i g h t s

Synthesis of 1,1-diethoxybutane was studied in a batch reactor.Thermodynamic equilibrium constant was determined in the temperature range of 293.15323.15 K.The standard formation properties of 1,1-diethoxybutane have been determined.Two-parameter kinetic model based on a LangmuirHinshelwood indicates good agreement with the experimental data.

a r t i c l e i n f o

Article history:

Received 5 June 2014Received in revised form 14 November 2014Accepted 15 November 2014Available online 25 November 2014

Keywords:

Synthesis of 1,1-diethoxybutaneBatch reactorAmberlyst 47 catalystKineticsThermodynamics

a b s t r a c t

The synthesis of 1,1-diethoxybutane was carried out in a batch reactor from a liquid phase reactionbetween ethanol and butyraldehyde using Amberlyst 47 as the solid acid catalyst to obtain thermody-namic, kinetic and adsorption parameters. The reaction equilibrium constant was experimentally deter-mined in the temperature range 293.15323.15 K. The standard properties of the reaction at 298.15 Kwere also estimated. The effects of temperature, molar ratio of ethanol to butyraldehyde, stirrer speed,and catalyst loading on the reaction rate were investigated. Kinetic experiments were performed inthe same temperature range at 6 bar. A two-parameter kinetic law based on a LangmuirHinshel-woodHougenWatson rate expression, using activity coefficients from the UNIFAC method, was usedto predict the experimental data of the heterogeneous liquid-phase reaction. The kinetic parameters weredetermined based on the kinetic model. The model predicts the kinetic data very well and it will be usefulfor design and optimization of integrated reactionseparation processes.

2014 Elsevier B.V. All rights reserved.

1. Introduction

In recent years, there has been a growing trend in the develop-ment of sustainable technology for production of environmentfriendly gasoline and diesel fuels. Biodiesels or fatty acid alkylesters are an alternative fuel which is obtained from vegetable oilsor animal fats. Biodiesels have various technical advantages overconventional gasoline or diesel fuels such as the reduction of emis-sions, enhanced lubricity and biodegradability, higher flash pointand lower toxicity[1]. They also show properties such as cetanenumber, heat of combustion and viscosity that are similar to theconventional diesels. However, they are inferior to conventionaldiesel in terms of oxidation stability, nitrogen oxides emissions,energy content and cold weather operability [2]. Employment ofadditives is one of the approaches that can improve the quality

of diesel fuel[3]. A wide variety of additives are added to improvefuel efficiency and reduce harmful emissions. Nowadays, methyltert-butyl ether (MTBE) and ethyl tert-butyl ether (ETBE) are wellknown oxygenated additives for gasoline. However, these ethersare not suitable as they drastically reduce the cetane number indiesel blends[4]. An alternate way to overcome this is to use acetalas oxygenated additive[5,6]. Moreover, acetals find their use inraw materials for perfumes, agricultural chemicals and pharma-ceutical applications.

Acetal can be produced from an acid-catalyzed reaction of 2 molof monohydric alcohol and 1 mol of aldehyde. The aldehydes canbe produced from their corresponding alcohols following a partialoxidation or a dehydrogenation process. In other words, acetals canbe obtained from just renewable raw materials. The synthesis ofacetal was carried using homogeneous catalyst such as strongliquid acids like H2SO4, HF and HCl [79]. But, their use suffersfrom some drawbacks, mainly separation from the products dueto miscibility with the reaction mixture and corrosion of the equip-

http://dx.doi.org/10.1016/j.cej.2014.11.077

1385-8947/2014 Elsevier B.V. All rights reserved.

Corresponding author. Tel.: +351 225 081 671; fax: +351 225 081 674.E-mail address:[email protected](A.E. Rodrigues).

Chemical Engineering Journal 264 (2015) 258267

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ment. The use of heterogeneous catalytic processes has overcomemost of the problems. Therefore, heterogeneous catalysts such asion-exchange resins, silica-based mesoporous materials and zeo-lites have become the alternate path for acetal production[5,1012]. Among the heterogeneous catalysts, such as zeolites, depictgood performances; however, acid ion-exchange resins have been

shown very effective for this type of reaction and attaining higheryields in short periods of time[5,12,13].Several ion-exchange res-ins such as Amberlyst 15 [5,1316], Amberlyst 36 [15,17,18],Amberlyst 46[19,20], Amberlyst 70 [19,20], and Amberlyst 131[19,21]were tested and studied by numerous researchers in theapplications of alkylation, etherification, esterification, transesteri-fication and acetalization reactions.

Acetalization reactions are typically equilibrium limited reac-tions and the determination of thermodynamic equilibrium isimportant. The probable mechanisms for heterogeneous kineticmodel of equilibrium limited reactions have been investigated bymany researchers. The pseudo-homogeneous model (PH) is widelyused in this kind of systems[22,23]. In the PH model, adsorptionand desorption of all compounds are neglected. On the other hand,

EleyRideal (ER) model can be applied when reaction between oneadsorbed reactant and one non-adsorbed reactant from the bulk

liquid phase occur[24,25]. The LangmuirHinshelwoodHaugenWatson (LHHW) model takes into account the adsorption of allthe compounds on catalyst surface. The LHHW model has alreadybeen used to describe the reaction of acetaldehyde with severallinear chain alcohols[3,6,19,26].

There are some studies about the acetalization reaction

between ethanol and butyraldehyde in the literature. Arisketaand co-workers [27,28] studied the kinetics of the synthesis of1,1-diethoxybutane using Amberlyst 47. They have reported theapparent value of rate constant and did not consider the non-ide-ality of the reaction mixture. The possibility of side reactions wasalso reported in literature[27,28]but it has been found that theamount of byproducts formed using Amberlyst 47 ion-exchangeresin catalyst was negligible.

In the present work, liquid-phase reaction of ethanol and butyr-aldehyde catalyzed by Amberlyst 47 for the synthesis of the acetal1,1-diethoxybutane was studied in a batch reactor to obtain ther-modynamic and kinetic data. Effects of temperature, catalyst load-ing and initial molar ratio of reactants on the reaction kinetics wereinvestigated. An activity based kinetic model was suggested to

describe the mechanism of heterogeneous catalytic liquid-phasereaction.

Nomenclature

a liquid-phase activityap specific particle surface area (cm

1)Ap total external area of particles (cm

2)C concentration (mol cm3)Ca Carberry number

Cb bulk concentration (mol cm3

)Cb0 initial bulk concentration (mol cm3)

Cp concentration inside the particle (mol cm3)

Cp0 initial concentration inside the particle (mol cm3)

Cps concentration on the particle surface (mol cm3)

De,j effective diffusivity (cm2 min1)

Dj;m molecular diffusivity in the mixture (cm2 min1)

D0j;i binary diffusivity of reactant j in component i(cm2 min1)

Ea reaction activation energy (J mol1)

DG0 standard Gibbs free energy (J mol1)DG0f standard Gibbs energy of formation (kJ mol

1)

DHs enthalpy of adsorption of water (J mol1)

DH0 standard enthalpy (J mol1)D

H

0

f standard enthalpy of formation (kJ mol

1

)k0;c pre-exponential constant (mol g1 min1)

kc kinetic constant based on LHHW kinetic model(mol g1 min1)

K0;s constant in Eq.(29)Keq equilibrium reaction constant (dimensionless)kL extraparticle mass transfer coefficient (cm min

1)Kc equilibrium constants based on activity coefficients

(dimensionless)Ks adsorption constant (dimensionless)KX equilibrium constants based on the molar fractions

(dimensionless)MRD mean relative deviationN total number of measurementsNE number of experiments performed

NMi number of measurements of variable in theith experi-mentS0 standard entropy of formation (J mol1 K1)DS0 standard entropy of reaction (J mol1 K1)r radial position (cm)rA=B initial ratio of reactantsrobs observed reaction rate (mol g

1 min1)

rp particle radius (cm)R universal gas constant (J mol1 K1)Rc ratio of catalyst volume to catalyst external surface areaR reaction rate (mol g1 min1)Rp rate of reaction relative to the local concentration

(mol g1 min1)t time coordinate (min)

T temperature (K)V molar volume (mol cm3)Vliq volume of liquid inside the reactor (cm

3)Vp total volume of particles (cm

3)x molar fractionsXexp model predicted conversionXmodel measured value of conversionzik kth model predicted value of variable in experimenti~zik kth measured value of variable in experimenti

Greek lettersc activity coefficientseb bulk porosityep porosity of catalyst particleh set of model parameters to be estimated

l viscosity (cp)m stoichiometric coefficientq dimensionless radial coordinateqp catalyst/particle density (g cm

3)s tortuosity factor/wp WeiszPrater parameterU parameter in Eq.(26)

SubscriptsA ethanolB butyraldehydeC DEBD waterexp experimentali relative to componentij relative to componentjliq liquid phasem mixturemodel predicted from modelp particles relative to the surface of the particle

M. Rahaman et al. / Chemical Engineering Journal 264 (2015) 258267 259
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2. Material and methods

2.1. Chemicals and catalyst

Ethanol (99.5% purity) was obtained from Panreac. Butyralde-hyde and 1,1-diethoxybutane (97% purity) were obtained fromAcros Organics. Acetone (99.98% purity) was obtained from Fisher

Chemical and used as the internal standard in gas chromatograph.Deionized water was used for calibration purpose in gas chromato-graph. A commercial strong acid ion-exchange resin namedAmberlyst 47 was used as the catalyst. The catalyst was providedby Rohm and Haas (USA) in an opaque spherical bead-form.Amberlyst 47 has a macroporous cross-linked polystyrene polymermatrix with sulfonic groups according to the datasheet provided bythe manufacture. No information was available for the crosslinkingdegree; however, it has a less to moderate swelling property inmethanol and water which means higher cross-linking degreeand rigid polymer structures. It has a surface area of 50 m2/g withan average pore diameter of 240 .

2.2. Reactor setup

The experimentsof reaction betweenethanol and butyraldehydewere carried out in a closed glass-jacketed1 dm3 autoclave reactor(Bchi, Switzerland). The reactor was mechanically stirred and it isequipped with pressure and temperature sensors, and with ablow-off valve. The reactor was operated in a batch mode and itstemperature was controlled by thermostated silicon oil(Lauda, Ger-many) that flows through the jacket. The reactor was pressurizedwith helium to maintain the reaction mixture in liquid phase overthe entire temperature range. The reactants were charged into thereactor and heated to achieve the desired reaction temperature.The dry catalyst was placed in a basket at the top of the stirrer shaft.Thebasketfallsdowninthereactionsolutionassoonastheagitationstarts. In this way, the starting time of the reaction was accuratelydefined. Samples were collected through one of the outlets of the

reactor in definite time interval and then analyzed.

2.3. Analytical method

All the samples were analyzed in a gas chromatograph (GC-2010 Plus, Shimadzu) using a fused silica capillary column (CP-Wax 57 CB, 25 m0.53 mm ID, df = 22.0 lm) to separate the com-pounds. The column was connected with a flame ionization detec-tor (FID) and a thermal conductivity detector (TCD) to identify andquantify the compounds present in the sample. Water wasdetected in the TCD whereas the other compounds were identifiedin FID. Helium N50 was used as the carrier gas. The injector anddetector temperature was maintained at 250 C. The column tem-perature program of gas chromatographic analysis was given as

follows: 7.5 min initial hold at 50 C; heating from 50 to 100 Cat a rate of 50 C/min and holding for 2 min. The reproducibilityof peaks was found to be good for all of the compounds in gaschromatograph.

3. Thermodynamic analysis for the synthesis of 1,1-

diethoxybutane

The acetal, 1,1-diethoxybutane (DEB), is produced from thehomogeneous liquid phase reaction of ethanol and butyraldehydein a batch reactor described in the previous section. The reactionis catalyzed by sulfonic acid ion exchange resin (Amberlyst 47)according to the following stoichiometry.

2 Ethanol A ButyraldehydeB H

DEBC Water D 1

3.1. Determination of equilibrium constant and reaction enthalpy

It is very important to determine the equilibrium constant forequilibrium limited reactions such as esterification, transesterifica-tion, acetalization, etc. To calculate the equilibrium constant,experiments were undertaken to determine the equilibrium molefractions of ethanol, butyraldehyde, DEB and water. Experimental

runs were carried out in the temperature range 293.15323.15 K,at 6.0 bar pressure, and initial molar ratio of ethanol to butyralde-hyde of 2.1, and a catalyst loading of 1 wt.%. Experiments were per-formed at least three times to minimize the experimental errors.All the experiments were performed for enough time so that thereaction reached the equilibrium. Then, the equilibrium constant,Keq, at different temperatures, for synthesis of DEB, was calculatedusing the experimentally obtained data according to the followingformula:

KeqaCaD

a2AaBxCxD

x2AxBcCcDc2AcB

KXKc 2

where,aare respective activity of the compounds,xare molar frac-tions of the compounds and c are the activity coefficients of thecompounds at the equilibrium. KXand Kcare the equilibrium con-

stants based on the molar fractions and activity coefficients, respec-tively. Due to strong non-ideality of the reaction mixture, activitycoefficients of compounds in the liquid phase were used to calculatethe equilibrium constant. The activity coefficients of compoundswere computed by the UNIFAC method [29,30]. The parametersneeded for UNIFAC method were taken from literature [31] andthey are presented inAppendix A. The average experimentally mea-sured equilibrium compositions and the corresponding equilibriumconstant at each temperature are shown in Table 1.

The temperature dependence of equilibrium constant, Keq, isgiven by,

lnKeqDS

0

R

DH0

R

1

T 3

where, DS0 and DH0 are the standard entropy and standard enthalpyof the reaction, respectively, and R is the universal gas constant.From the values of Keq at different temperatures, the standardentropy and standard enthalpy of the reaction were determinedby plotting ln Keq vs. 1/T. The plot of ln Keq vs. 1/T is shown inFig. 1.The data was fitted well by a straight line. The slope of thisstraight line gives the value of the standard enthalpy of the reactionwhile the standard entropy was calculated from the intercept of thestraight line. From the values of DS0 and DH0, Eq. (3) can beexpressed as,

lnKeq1036:80

T 2:56 4

Table 1

Experimental equilibrium compositions and equilibrium constants.

Temperature

293.15 K 303.15 K 313.15 K 323.15 K

xA 0.3772 0.3856 0.3960 0.4076xB 0.1966 0.2016 0.2030 0.2054xC 0.2131 0.2064 0.2005 0.1935xD 0.2131 0.2064 0.2005 0.1935

KX 1.6235 1.4212 1.2628 1.0972

cA 1.1106 1.1156 1.1186 1.1198cB 1.2768 1.2799 1.2831 1.2853cC 1.3652 1.3687 1.3755 1.3830cD 1.8863 1.9372 1.9809 2.0228

Kc 1.6352 1.6646 1.6970 1.7357

Keq=KXKc 2.6547 2.3657 2.1430 1.9044

260 M. Rahaman et al. / Chemical Engineering Journal 264 (2015) 258267


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Therefore, the values ofDH0 8619:96 287:22 J mol1 andDS0 21:28 0:93 J mol1 K1 were obtained. The error wasdetermined through least square method. The value of DH0 isreported in the literature[27,28]as 31,098 J mol1. The experi-

mentally determined value ofDH0 in this present study is quiteless than the value reported in the literature. This may be due topurely computation method employed in their work. On the otherhand, there was no data available for DS0 in any literatures. Thestandard free energy change for the liquid phase reaction is relatedto the standard enthalpy and entropy changes by,

DG0 DH0 TDS

0 5

From the Eq.(5),the value of standard free energy change wasobtained as DG0 2275:33 J mol1. Based on the experimentalvalues ofDH0, DS0 and DG0, the standard formation properties ofDEB were calculated and presented in Table 2[32]. The value ofstandard enthalpy of formation of DEB given in literature as540.46 kJ mol1 [27].

4. Kinetic studies

The experimental results of the reaction kinetics of the produc-tion of DEB from the reaction of ethanol and butyraldehyde cata-lyzed by the Amberlyst 47 resin are presented in this section.The effect of various conditions, such as catalyst loading, initialmolar ratio between ethanol and butyraldehyde, and reaction tem-perature, on the conversion of butyraldehyde as a function of timewas studied. These studies were performed varying the conditionunder evaluation and keeping constant the remaining conditions.

4.1. Mass transfer limitation

To accomplish the true kinetic study for heterogeneous catalyticsystem, it is necessary to evaluate both external and internal masstransfer resistances. The external and internal mass transfer resis-tances of the reaction of ethanol with butyraldehyde over Amber-

lyst 47 in a batch reactor are directly related to the stirrer speedand the particle size of the catalyst, respectively.

4.1.1. External mass transfer resistance

In order to determine the influence of external mass transferresistance, experiments at different stirring speeds were carriedout. These experiments were performed at the temperature of

323 K, initial molar ratio of ethanol to butyraldehyde of 2.1, cata-lyst loading of 1 wt.% and different stirring speeds to evaluate thelimits at which external diffusion limitations will not exist. Theeffect of stirring speeds is shown inFig. 2. It was found that therewas no limitation due to external resistance above 500 rpm, whichis also in agreement with the results reported in the literature [28].Furthermore, existence of external mass transfer resistance wasinvestigated by Carberry number. The Carberry number Cagivesthe ratio between the observed reaction rate and maximum exter-nal mass transfer and is expressed by[33,34]:

CarobsqpkLapCb

CbCpsCb

6

whererobsis the observed reaction rate,qpis the particle density,

kLis the external mass transfer coefficient, apis the specific particlesurface area,Cb is the bulk concentration of butyraldehyde and Cpsis the concentration of butyraldehyde on the particle surface. Thecriteria for negligible external mass transfer resistance the valueof Ca should be less than 0.05[34]. In this study the value of Cawas found to be in an order of 103 for the experiment conductedat 500 rpm. Therefore, all further experiments were performed at500 rpm to ensure that the external mass transfer resistance doesnot exist. Usually the rate of reaction in ion exchange catalyzed pro-cesses do not depend on the external mass transfer resistanceunless the viscosity of the reactant mixture is very high or the speedof agitation is very low[14].

4.1.2. Internal mass transfer resistance

Different particle sizes of Amberlyst 47 resin are not commer-cially available, so it was not possible to investigate the internalmass transfer limitation experimentally and thus, the WeiszPrater criterion was employed. The WeiszPrater equation forheterogeneous catalytic reaction can be expressed as in[35]:

/wp robsqPR

2c

De;jCj7

where /wp is the WeiszPrater parameter, Rc(=rp/3) is the ratio ofthe catalyst volume to the catalyst external surface area where rp

Fig. 1. Linearization of the experimental equilibrium constants.

Table 2

Standard formation properties at 298.15 K.

Component DH0f kJ mol1 DG0f kJ mol

1 S0 J mol1K1

Ethanol[17] 277.6 174.8 160.7Butyraldehyde[17] 239.2 119.5 246.6DEB* 517.2 234.3 476.7Water[17] 285.8 237.1 70.0

* Calculated from this work. Fig. 2. Effect of stirring speeds on conversion of butyraldehyde (rA/B= 2.1,

catalyst = 1 wt.%, P= 6 bar, T= 323 K).

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(=0.05 cm) is the particle radius[27],Cjis the concentration of lim-iting reactant in the mixture, and De,jis the effective diffusivity. Thevalue ofqPis taken as 0.5508 g/cm

3 [27]. The WeiszPrater crite-rion states that diffusion does not limit the reaction if the value of/wp is less than 1. On the other hand, strong diffusion limitationsexist if/wp > 10. The expression for determination of effective dif-fusivity is given as,

De;j epDj;ms

8

whereep0:5is the porosity of catalyst particle [27], Dj;m is themolecular diffusivity of limiting reactant in the mixture and s isthe tortuosity factor of catalyst. Estimation of the tortuosity wasperformed using the correlation given by Wakao and Smith [36].Dj;m was calculated using Perkin and Geankoplis [37] method formulticomponent system

Dj;ml0:8m

Xni1ij

xiD0j;il

0:8i 9

where x i is the mole fraction of the component i , D0

j;i is the binarydiffusivity of reactantjin component i, and liand lmare the viscos-

ities of component i and the mixture, respectively. The viscosity ofthe liquid mixture, lm, was calculated by the Grunberg-Nisaanmethod[38]. D0j;i was estimated by the following Scheibel correla-tion, which is the modified WilkeChang equation in order to elim-inate the association factor[39]

D0j;i 8:2 10

8T

liV1=3j

1 3ViVj

2=3" # 10

whereVis the molar volume of the respective compounds and Tisthe temperature.

The WeiszPrater parameters, /wp, were estimated from someof the experimental data and are presented inTable 3. The valuesof/wp from the table indicate that the reaction of ethanol withbutyraldehyde using the ion exchange resin was limited by theinternal diffusion to some extent. Therefore, the effect of internaldiffusion was taken into account in further analysis of reactionkinetics.

4.2. Kinetic model

It is evident from the values presented inTable 3that the kinet-ics of the reaction is affected by the internal diffusion. Therefore, anisothermally operated batch reactor model that considers diffusionof the components inside the catalyst particle was used in thisstudy[16,40].

The mass balance in the bulk fluid of batch reactor in the liquidphase at constant temperature is given by,

dCb;jdt ApVliq

De;j@Cp;j@rrrp

j AD 11

with

Ap3

rpVp 12

whereCb;j is the bulk concentration of component j,Cp;j is the con-centration of componentjinside the particle pore,Vliqis the volumeof liquid inside the reactor, rp is the particle radius, Ap is the totalexternal area of particles, Vp is the total volume of particles, r isthe radial position and tis the time coordinate.

Similarly, mass balance inside the catalyst particle at constanttemperature is given by,

ep @Cp;j

@t 1r2

@@r De;jr

2@Cp;j@r

1 epmjqpRp 13

wheremjis the stoichiometric coefficient of the component jand Rpis the rate of reaction relative to the local concentration.

Initial conditions:

t 0 Cb;j Cb0;j; Cp;j Cp0;j 14

Considering negligible external mass transfer resistance, theboundary conditions are,

r 0 @Cp;j

@t 0 15

r rp Cp;j Cp;jrrp 16Introducing the dimensionless space variable q r=rp, the

model equations can be expressed as,

dCb;jdt

3

r2p

1 ebeb

De;j@Cp;j@q

q1

17

@Cp;j@t

De;jr2p

1

q2@

@q q2

@Cp;j@q

1 epep

mjqpRp 18

whereeb is the bulk porosity. The boundary conditions for abovemodel equations then become:

q 0 @Cp;j

@t 0 19

q 1 Cp;j Cp;jq1 20

It should be noted that the amount of catalyst was implementedin the kinetic model through the calculation of the total volume ofparticles, Vp, using the value of catalyst density; then the totalinterfacial area fluid/particle Apwas calculated from Eq.(12).

In this study, the LangmuirHinshelwoodHaugenWatsonmodel equation was used. It was considered to be the most appro-priate model for the reaction between ethanol and butyraldehydecatalyzed by Amberlyst 47, following the previous works donewith diethylacetal and dimethylacetal synthesis[16,26,40]. There-fore the present model was developed on the basis of LHHW mech-anism. The mechanism is based on adsorption of the reactantspecies (ethanol and butyraldehyde), the reaction between

adsorbed reactants on the catalyst surface, and desorption of thereaction products (DEB and water). The surface reaction involvesthe following steps:

Surface reaction between adsorbed species of ethanol (A) andbutyraldehyde (B) to give absorbed hemiacetal, I1S:

ASBS I1 SS 21

Surface reaction to obtain absorbed water, D S:

I1SS I2SDS 22

Surface reaction to obtain adsorbed DEB, C S:

I2SASCSS 23

The surface reaction is assumed to be the controlling step and

also multicomponent Langmuir adsorption isotherms are assumedfor describing the adsorption behavior of the compounds of the

Table 3

WeiszPrater parameter for determination of internal

diffu sion (rA/B= 2.1, catalyst = 1 wt.%, stirring

speed = 500 rpm,P= 6 bar).

Temperature (K) /wp

293.15 1.52303.15 1.76313.15 2.18

323.15 3.03



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reaction mixture in the surface of the resin. The model is based onactivities (ai) of the respective compounds. Taking into account theabove considerations, the following rate expression, consideringnonideality of the reaction mixture, is obtained[26]:

R kcaAaB

aCaDaAKeq

1 Ks;AaAKs;BaBKs;CaCKs;DaDKI1aAaBKI2aC=aA2

24

where R is the reaction rate, kcis the kinetic constant based on thekinetic model andKsare the adsorption constant for the respectivecomponents. A detailed derivation of the rate expression isdescribed inAppendix B. In order to reduce the number of optimi-zation parameters, only those compounds which had strongestadsorption were taken into consideration. Water has the strongestadsorption strength on the resin surface as the acidic property ofAmberlyst 47. Thus, the adsorption of the other compounds wasneglected. The simplified rate expression which was used todescribe the experimental data is:

R kcaAaB

aCaDaAKeq

1 Ks;DaD2

25

According to the above kinetic model, there were two parame-ters to be estimated, the kinetic constant kcand the adsorptionconstant of water Ks;D;at each temperature.

4.2.1. Parameter estimation from experimental data

The model equations were solved numerically using the soft-ware gPROMS (general PROcess Modeling System), version 3.3.1which is commercial package from Process System Enterprise.The particle radial domain in batch reactor model was discretizedusing the second-order orthogonal collocation in the finiteelement method (OCFEM). The system of ordinary differentialequation was integrated over time using DASOLV integratorimplemented in gPROMS. For radial discretization, 10 finite

elements with two collocation points were used in each element.For all simulations, tolerance equal to 105 was fixed. Theunknown parameterskc; Ks;Dproposed in the kinetic model wereestimated using Parameter Estimation tool in gPROMS provid-ing the best fit of measured and predicted conversion data usingthe maximum likelihood method. The objective function associ-ated with the parameter estimation is described by the followingequation:

U N

2ln2p

1

2min

h

XNEi1

XNMik1

lnr2ik ~zikzik

2

r2ik

" #( ) 26

whereNis the total number of measurements taken during all theexperiments,his the set of model parameters to be estimated, NE is

the number of experiments performed, NMiis the number of mea-surements of variable in theith experiment, r2ik is the variance ofthekth measurement of variable in experiment i,~zikis thekth mea-sured value of variable in experiment i and zik kth model predictedvalue of variable in experiment i . The quality of the model fit wastested through the mean relative deviation (MRD) between the dataof model predicted conversion Xmodel and the experimental dataXexpusing the following equation.

MRD% 1

N

X XmodelXexpXexp

100 27

4.3. Modeling and discussion of results

Experiments were performed at different temperatures(293.15 K323.15 K), at various initial mole ratio of ethanol to

butyraldehyde (2.14.1), and also at various catalyst loading(0.51.5%). For the proposed kinetic model, the unknown parame-ters kc; Ks;Dwere estimated from the conversion data along timefor the reaction between ethanol and butyraldehyde using Amber-lyst 47 resin as catalyst. The optimized values of these parameters,at each temperature, are presented inTable 4.

The temperature dependence of kinetic and adsorption con-

stants were described by the Arrhenius and Vant Hoff equations,respectively:

kc k0;c EaRT

28

Ks;D K0;s DHsRT

29

whereEa is the reaction activation energy, k0;cis the pre-exponen-tial constant, R is the universal gas constant, K0;s is a constant,DHsis the enthalpy of adsorption of water and Tis the temperature.

The plot ofkcandKs;D fitted in Arrhenius and Vant Hoff equa-tion, respectively, are shown inFig. 3. The data were fitted well

by the straight lines. The slopes of these lines give the values ofthe activation energy Ea and enthalpy of adsorption DHs. Thecorresponding values were obtained as Ea 37:92 2:58 kJ=moland DHs 24:28 1:8 kJ=mol, respectively. A value ofEa= 35.50 kJ/mol was obtained by Arisketa and co-workers[27,28]. This may be due to consideration of a non-ideal mixtureand a simple kinetic model to describe the acetalization reaction.A summary of the proposed kinetic model and their parametersis presented inTable 5. In order to validate the existence of internaldiffusion resistance; by simulation it is possible to observe the con-centration gradient inside the catalyst particle. Fig. 4shows theinternal concentration profile of butyraldehyde at different tem-peratures after 10 min. The presence of concentration gradientbetween the surface and the center of the catalyst indicates the

presence of internal mass transfer resistance.

Table 4

Estimated model parameters at different temperatures.

Temperature (K)

293.15 303.15 313.15 323.15

kc mol g1min1 0.06196 0.08603 0.15584 0.25050

Ks;D 2.9385 2.2377 1.6991 1.1566

Fig. 3. Arrhenius and Vant Hoff plots for kc and Ks,D, respectively, at differenttemperatures.

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4.3.1. Effect of reaction temperature

The effect of temperature on the conversion of butyraldehyde isshown inFig. 5. It is evident from the figure that the rate of reac-tion increases with temperature while the equilibrium conversionof butyraldehyde decreases due to the exothermic nature of thisreaction. It is also observed from the figure that the experimentsare well predicted by the model.

4.3.2. Effect of catalyst loading

Fig. 6shows the effect of the catalyst loading on the conversionof butyraldehyde at 303.15 K, where it can be seen that the reac-tion rate increases with increase in catalyst loading. This is dueto the fact that the increase in catalyst loading results in highernumber of active catalytic sites available for reaction. Once again,

the model was able to predict the experimental conversion datafor various catalyst loadings.

4.3.3. Effect of initial molar ratio of reactants

As mentioned above, the effect of initial mole ratio of ethanol tobutyraldehyde was studied by varying it from 2.1 to 4.1. Theobtained results are presented inFig. 7. It is observed in this figurethat, as expected, the equilibrium conversion increases for higher

values of initial mole ratio. This behavior is well described bythe developed model. However, a small overestimation of model

Table 5

Kinetic law and parameters from proposed kinetic model.

Kinetic law R kcfaAaB aCaD=aAKeqg=1 Ks;DaD 2

Equilibrium constant(dimensionless)

Keq 7:73 102 exp1036:80=TK

Kinetic constant(mol g1 min1)

kc 3:21 105 exp4561:06=TK

Adsorption constant of water

(dimensionless)

Ks;D 1:454 104 exp2920:68=TK

Fig. 4. Internal concentration profile of butyraldehyde after 10 min.

Fig. 5. Effect of reaction temperature on conversion of butyraldehyde (rA/B= 2.1,catalyst = 1 wt.%, stirring speed = 500 rpm,P= 6 bar).

Fig. 6. Effect of catalyst loading on conversion of butyraldehyde (rA/B= 2.1, stirringspeed = 500 rpm, P= 6 bar, T= 303 K).

Fig. 7. Effect of initial molar ratio of ethanol and butyraldehyde on conversion ofbutyraldehyde (catalyst = 1 wt.%, stirring speed = 500 rpm, P= 6 bar, T= 303 K).

Fig. 8. Parity plot comparing experimental and calculated conversions.



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predicted conversion over the experimental conversion was foundfor the initial molar ratio of 4.1.

The proposed model describes very well the experimental dataat various temperature, catalyst loading and initial molar ratio ofthe reactants up to the equilibrium conversion and also the equi-librium stage (Figs. 57). A comparison of the experimental dataof conversion of butyraldehyde and those predicted from the

model is shown inFig. 8. The value of MRD between experimentaland model-predicted conversions of 7.7% was obtained.

5. Conclusion

The synthesis of 1,1-diethoxybutane in a liquid phase reactionof ethanol and butyraldehyde catalyzed by Amberlyst 47 was stud-ied in a batch reactor. The thermodynamic equilibrium constantwas determined in the temperature range of 293.15 K323.15 Kand can be expressed as Keq 7:73 10

2 exp1036:80=TK.The standard properties of the reaction at 298.15 K areDH0 8619:96 J mol1, DS0 21:28 J mol1 K1 andDG0 2275:33 J mol1. Due to the strong non-ideality of theliquid reaction mixture, the kinetic model was formulated in termsof activities. A two-parameter kinetic model based on a LangmuirHinshelwoodHaugenWatson rate expression was proposed todescribe the experimental kinetic results. The effects of differentparameters such as temperature, catalyst loading, and ethanol tobutyraldehyde initial mole ratio were studied. The model parame-ters such as experimental rate constant and adsorption coefficientof water were determined. The simulation results were in goodagreement with the experimental results and this model can beused to predict the batch reactor performance for the synthesisof 1,1-diethoxybutane. These data will be useful for the implemen-tation of integrated reactionseparation processes such as fixedbed reactors and simulated moving bed reactors to improve theconversion to 1,1-diethoxybutane.

Acknowledgments

Financial support for this work was provided by project PEst-C/EQB/LA0020/2011, financed by FEDER through COMPETE Progra-ma Operacional Factores de Competitividade and by FCT Fun-daopara a Cincia e a Tecnologia, for which the authors arethankful. This work was also co-financed by QREN, ON2 and FEDER(Project NORTE-07-0124-FEDER-0000007 Multifunctional Reac-tors/Process Intensification). C.S.M. Pereira acknowledges FundoSocial Europeu (European Social Fund) and Programa OperacionalPotencial Humano (Human Potential Operational Programme)(FCT Investigator-IF/01486/2013).This project has been alsofunded with support from the European Commission. This commu-nication reflects the views only of the authors, and the Commissioncannot be held responsible for any use which may be made of the

information contained therein.

Appendix A.

Tables A.1 and A.2present the UNIFAC method parameters usedin this work to calculate the activity coefficients.

Appendix B.

The kinetic model described in this work based on the activityof the respective species and has the following steps:

Step 1 adsorption of ethanol:

2A 2S

k1

k1 2AS B1

where k1 and k1 are the forward and backward rate constant,respectively. The adsorption coefficient can be written as

K0s;A k1k1

a2

AS

a2A

a2S

withKs;A ffiffiffiffiffiffiffiffi

K0s;A

q aAS

aAaS:

Step 2 adsorption of butyraldehyde:

BSk2

k2

BS B2


Ks;B k2k2

aBSaBaS

:

Step 3 surface reaction between the adsorbed species of eth-anol and aldehyde to give adsorbed hemi-acetal:

ASBSk3

k3

I1SS B3


K3 k3k3

aI1 S

aS

aASaBS:

Step 4 surface reaction to obtain adsorbed water:

DS: I1SSk4

k4

I2SDS B4


K4 k4k4

a I2 S

aDS

aI1 SaS

:

Step 5 surface reaction of formation of adsorbed DEB:

CS: I2SASk5

k5

CSS B5


K5 k5k5

aCSaSaI2 S

aAS:

Step 6 desorption of DEB:

CSk6

k6

CS B6


Ks;Ck 6

k6 aCS

aCaS:

Step 7 desorption of water:

DSk7

k7

DS B7

where k7 and k7 are the forward and backward rate constant,respectively. The adsorption coefficient can be written asKs;D

k 7k7

aDSaD aS

:

Assuming the surface reaction (i.e., Step 4) is the ratedetermining step, the rate expression for LangmuirHinshel-woodHaugenWatson (LHHW) kinetic model is:

R

k4hI1 S

hSk4

hI2 S

hDS k4

hI1 S

hS

k4

k4 h

I2 ShDS

k4 hI1 ShS

1

K4

hI2 ShDS

B8

where h I1 S; hI2Sand hDSare the fractions of catalyst sites occupiedbyI1S,I2SandD S, respectively,hSis the fraction of vacant sitesandK4is the adsorption coefficient for step 4.

The total activity composed of vacant and the adsorbed specieson the catalyst surface can be expressed as:

a0 aSaASaBSaCSaDSaI1 SaI2 S

aSKs;AaAaSKs;BaBaSKs;CaCaSKs;DaDaS

Ks;AKs;BK3aAaBaSKs;CaCaSKs;AK5aA

aS 1 Ks;AaAKs;BaBKs;CaCKs;DaDKs;AKs;BK3aAaB Ks;CaCKs;AK5aAh i

B9

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Takinghjas the fraction of catalyst sites occupied by a particularspecies, can be expressed as:

hj ajSa0

B10

From the Eq.(B8)using the corresponding values ofhjwe have,

Rk4aI1 Sa0

aSa0

1

K4

aI2 Sa0

aDSa0

k4K3aASaBS

a0aS

aS

a0

1

K4 aCSaS

K5a0aAS

aDS

a0

k4K3Ks;AKs;BaAaBa

2S

a20

1

K4

Ks;CKs;DaCaDKs;AK5aA

a2Sa20

k4 Ks;AKs;BK3aAaB 1

K4


aSa0

2

k4

Ks;AKs;BK3aAaB 1

K4


1 Ks;AaAKs;BaBKs;CaCKs;DaDKs;AKs;BK3aAaB Ks;CaCKs;AK5aA

2

k4Ks;AKs;BK3

aAaB Ks;CKs;D

K2s;AKs;B

1

K3K4K5

!aCaDaA

1 Ks;AaAKs;BaBKs;CaCKs;DaDKs;AKs;BK3aAaB Ks;CaCKs;AK5aA

2B11

Now the overall reaction can be expressed by:

2AB keqCD B12

where the overall equilibrium constant Keqis,

KeqaCaD

a2AaB

aCSaSKs;C

aDSaSKs;D

a2AS

a2SK02s;A

aBSaSKs;B

K2s;AKs;B

Ks;CKs;D

aCSaDS

a2ASaBSaS

K2s;AKs;B

Ks;CKs;DK3K4K5 B13

Adding Eqs.(B1)(B3), we get:

2AB 2Sk

0

I1I1SAS B14

whereK0I1 aI1 SaASa2AaBa

2S

a2AS

a2Aa2S

aBSaBaS

aI1SaS

aASaBS

K2s;AKs;BK3

Taking KI1 K0I1Ks;A

Ks;AKs;BK3 B15

Similarly, adding Eqs.(B1), (B5) and (B6), we have:

I2S 2A k0I2ASC B16

whereK0I2 aASaC

aI2 Sa2

A

aCSaSaI2 S

aAS

a2AS

a2A

a2S

aCSaCaS

K5K

2s;A

Ks;C

Taking KI2 Ks;A

K0I2 Ks;CK5Ks;A

B17

Using the values ofKI1 ,KI2 andKeq, Eq.(B12)can be rearrangedas:

R kcaAaB

aCaDKeqaA

1 Ks;AaAKs;BaBKs;CaC Ks;DaDKI1aAaBKI2aCaAh i

2

B18

wherekc k4Ks;AKs;BK3

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Table A.1

Relative molecular volume and surface parameters of the pure species.

Molecule (i) Group identification

No. of main group No. of secondary group v

ik

Rk Qk

Ethanol CH3 1 1 1 0.9011 0.848CH2 1 2 1 0.6744 0.540OH 5 15 1 1.0000 1.200

Butyraldehyde CH3 1 1 1 0.9011 0.848CH2 1 2 2 0.6744 0.540CHO 10 21 1 0.9980 0.948

DEB CH3 1 1 3 0.9011 0.848CH2 1 2 2 0.6744 0.540CH 1 3 1 0.4469 0.228CH2O 13 26 2 0.9183 0.780

Water H2O 7 17 1 0.9200 1.400

Table A.2

Interaction parameters for UNIFAC method.

am,n am,n

1 5 7 10 13

1 0 986.5 1318 677 251.55 156.4 0 353.5 203.6 28.067 300 229.1 0 116 540.510 505.7 529 480.8 0 304.113 83.36 237.7 -314.7 7.838 0

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thermodynamic and kinetic studies for synthesis of the acetal (1,1-diethoxybutane) catalyzed by...

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