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3198 S.H. Ali et al. / Chemical Engineering Science 62 (2007) 3197 3217

side reactions than sulfuric acid. A somewhat higher molarconcentration of the sulfonic acid may be required in orderto achieve the same reaction rate that can be obtained with agiven quantity of sulfuric acid (McKetta, 1983 ). In industrialapplications, the use of mineral acids as catalysts is limitedbecause it suffers from several drawbacks. The acid catalyst

recovery is uneconomical ( Sharma et al., 1973 ) and high acidconcentration will increase the corrosion rate, which increasesthe cost of the operation ( Liu and Tan, 2001 ). Furthermore,dealing with homogeneous catalysts waste is very hard becausethey have to be neutralized for product separation (Bhatia et al.,1973), which is considered to be a costly process (Sharma et al.,1973). The use of solid catalyst such as ion-exchange resinshas received great attention. Application of these catalysts hasseveral advantages; recovery of the catalyst is easily achievedby ltration ( Dakshinamurty et al., 1984 ); continuous operationin columns is possible ( Nagaraju and Mehboob, 1996 ); thepurity of the products is higher compared with homogeneouscatalyst since solid acid catalysts are selective and the formationof by-products is less signicant ( Bhatia et al., 1973 ); wasteor disposal problems are eliminated ( Nagaraju and Mehboob,1996); isolation of reaction intermediates is possible (Roy andBhatia, 1987 ).

El Ewady et al. (1984) studied the effect of acid structure onthe reaction rate. This study was carried out by the esterica-tion reaction of methanol with a homologous series of aliphaticorganic acids in the presence of Amberlite IR-120 as the cat-alyst. Also, Awad et al. (1997) studied the effect of alcoholstructure and molecular weight on the reaction rate constantfor the esterication reaction of propionic acid with differentalcohols over styrenebutadienephenol formaldehyde (SBPF)

as a catalyst. Esterication of acetic, propionic and pentanoicacids with different alcohols using a polymer ber-supportedsulfonic acid, Smopex-101, as a catalyst was studied by Liljaet al. (2002) . Since there is a lack of information on the inu-ence of acid and/or alcohol structure on esterication reactionscatalyzed by Dowex 50Wx8-400 it was decided to be one of the aims of this investigation.

Dakshinamurty et al. (1984) studied the esterication of 1-propanol with propionic acid using Dowex-50W. The exper-iments were carried out in a batch reactor. The inuence of different variables on the conversion of the reactants was stud-ied. An empirical model correlating the specic reaction rate

constant in terms of the studied variables wasestablished. It wasproposed that the surface reaction is the rate controlling stepbetween adsorbed propionic acid and non-adsorbed 1-propanol.However, Dakshinamurty et al. (1984) did not account for thesystem non-ideality or for differences in the adsorption of thereactants and products. Therefore, the lack of systematic kineticstudies for the esterication of propionic acid with 1-propanolwith the aim of establishing the inuences of reaction parame-ters on the reaction kinetics along with elucidation of the mostprobable reaction mechanism by systematic testing of estab-lished mathematical models is the main impetus for the currentstudy.

Several kinetic models have been adopted to describe the ki-netics of heterogeneous catalytic esterication reactions. The

pseudo-homogeneous (P-H) model is similar to the power-law model for homogeneous reactions ( Xu and Chuang, 1996;Ppken et al., 2000; Lee et al., 2002; Gangadwala et al., 2003 ).The P-H model assumes that surface reaction is the controllingstep and adsorption is negligible for all components. Wheneverthe adsorption of the molecules taking part in the reaction oc-

curs, the LH model is applicable for correlating the kineticdata ( Bhatia et al., 1973; Lee et al., 2000; Ppken et al., 2000;Chiplunkar et al., 2005 ). On the other hand, the EleyRideal(ER) model can be applied when the reaction between oneadsorbed species and one non-adsorbed reactant from the bulk liquid phase is assumed to occur ( Bart et al., 1996; Liu andTan, 2001; Gangadwala et al., 2003 ).

Our research group ( Ali and Merchant, 2006 ) studied theesterication reaction of acetic acid with 2-propanol usingdifferent ion-exchange resins (Dowex 50Wx8-400, Amber-lite IR-120 and Amberlyst 15). Under the studied conditions,the highest conversion was obtained for the system catalyzedby Dowex 50Wx8-400 at 4 h and 343 K, 1:1 acid to alcoholmolar ratio and 40 g drycat/L catalyst loading. It was alsofound that the systems catalyzed by gel-type resins (Dowex50Wx8-400 and Amberlite IR-120) exhibited some similari-ties in their reaction kinetics. The data were tted to differentmodels such as the P-H, the ER, the LH and the M-LHmodels.

The purpose of our investigation is to study the reaction of 1-propanol with propionic acid catalyzed by the cation-exchangeresin Dowex 50Wx8-400. The impact of different variablessuch as catalyst loading, temperature and acid to alcohol ra-tio was investigated. Other factors investigated include the im-pact of catalyst moisture content on the esterication reaction,

the effect of using sulfuric acid rather than Dowex 50Wx8-400, and the effect of ion-exchange resin catalyst type andthe impact of the presence of water on the reaction. The reac-tion of acetic or butyric versus propionic acid with 1-propanolwas compared using Dowex 50 Wx8-400. Also, a comparisonwas made between ve different alcohols, methanol, ethanol,1-propanol, 2-propanol and 1-butanol, reacting with propionicacid in the esterication reaction using Dowex 50 Wx8-400.On the other hand, the signicance of both external and inter-nal diffusion limitations on the esterication system was stud-ied. Several kinetic models were tested to correlate the kineticdata, namely the P-H model, the ER model, the LH model,

the modied EleyRideal (M-ER) model and the modiedLangmuirHinshelwood (M-LH) model. The non-ideality of the system behavior was accounted for by universal functionalactivity coefcient (UNIFAC).

2. Theory

2.1. Reaction and reaction mechanism

Esters can be formed by the reaction of a carboxylic acidwith an alcohol forming the ester and water molecules. This es-terication (reversible) reaction, also called the intermoleculardehydration reaction, is a very important and a common typeof reaction in the chemical industry. The general esterication
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S.H. Ali et al. / Chemical Engineering Science 62 (2007) 31973217 3199

reaction is shown below:

acid + alcohol ester + water. (1)

The catalytic esterication reaction of a propionic acid and 1-propanol to form 1-propyl propionate and water is given by

CH3CH2COOH + CH3CH2CH2OHkf

kb

CH3CH2COOCH 2CH2CH3 + H2O. (2)

The reaction mechanism for the formation of esters from car-boxylic acids and alcohols in the presence of acidic catalystwas presented by Lilja et al. (2002) . The reaction is initiatedby the transfer of a proton from the catalyst to the carboxylicacid. The proton becomes attached to one of the lone pairs onthe oxygen which is double-bonded to the carbon. The trans-fer of the proton to the oxygen gives it a positive charge. Thisresults in a fair amount of positive charge on the carbon atom.Then, the positive charge on the carbon atom is attacked by the

hydroxyl group of the alcohol molecule. After that, a moleculeof water is lost from the ion. Finally, the catalyst is recoveredby the transfer of proton from the ion to the catalyst surface.This mechanism is represented by the following scheme:

R

O

OH

H- CAT+R

OH

OH

+ CAT

ROH

OH

+HO-R' R

OH

O

+H

O

H

+ CAT

R'

ROH

OR'

RO

OR'

H- CAT+

The donation of a proton is commonly assumed to be a faststep, while the nucleophilic substitution is usually assumed tobe slow followed by fast steps resulting in the formation of ester and water and the recovery of the catalyst.

2.2. Diffusion

To have a purely kinetic study, it is necessary to eliminateboth external and internal diffusion limitations. For our casestudy, where the reaction of propionic acid with 1-propanol oversolid catalyst was carried out in a batch reactor, the externalmass transfer resistance to the esterication reaction is directlyrelated to the stirrer speed. The effect of external diffusion lim-itation on the esterication reaction rate was studied by earlierworkers (Krishnaiah and Rao, 1984; Yadav and Kulkarni, 2000;Yadav and Thathagar, 2002; Ali and Merchant, 2006 ). To studythe external diffusion effect on the reaction rate, different stirrer

speeds should be applied to the reaction system. If the produc-tion of the ester is independent of stirrer speed, this indicatesthat external diffusion is not the rate controlling step. Thus, toensure that the reaction rate is not inuenced by external dif-fusion, the experiments should be run at a high enough stirrerspeed. In general, external diffusion controls the overall rate

in catalytic processes if the viscosity of the reactant mixture isvery high or the stirrer speed is very low (Othmer, 1994 ).The effect of internal diffusion on the rate of the reaction cat-

alyzed by a solid catalyst (ion-exchange resin) is dependent onmany parameters such as catalyst composition, particle size, re-action medium and temperature. The effect of internal diffusionon the catalytic reaction can be studied by screening catalystinto different particle sizes or by calculating certain dimension-less parameters such as the well-known WeiszPrater criterion.Earlier workers studied the signicance of internal diffusion onthe esterication reactions (Bhatia et al., 1973; Krishnaiah andRao, 1984; Bart et al., 1996; Gangadwala et al., 2003;Pkknenand Krause, 2003; Ali and Merchant, 2006 ). Some of thesestudies tested the reaction for internal diffusion limitation byusing different particle sizes ( Bhatia et al., 1973; Gangadwala

et al., 2003; Pkknen and Krause, 2003 ), while other studiesused certain criterion for such a purpose ( Krishnaiah and Rao,1984; Bart et al., 1996; Ali and Merchant, 2006 ). The mea-

sured values of the rate of the reaction ( rA( obs) ) are used tocalculate the WeiszPrater criterion in order to determine thepossibility of internal diffusion limiting the reaction. The di-mensionless WeiszPrater parameter (C W P ) can be dened asfollows ( Fogler, 1992 ):

CW P = rA( obs) c R

2c

D e C li, (3)

where rA( obs) is the rate of the reaction at a given time inmol/g of catalyst/s, c is the catalyst density in g / cm3, Rc isthe effective radius of the catalyst is the ratio of catalyst pelletvolume to catalyst pellet external surface area in cm, D e is the
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Table 1Rate expressions for different rate controlling mechanisms

Adsorption status of reactants Limiting step Rate expression a

Non Surface reaction ri = M catkf (a acid a alc 1K a a ester awater )

Adsorbed propionic acid reactingwith 1-propanol in the uid

Surface reaction ri =M catkf K acid (a acid a alc (a ester awater /K a ))

(1 + K acid a acid + K water a water )

Adsorption of acid ri =M cat kacid (a acid (a ester awater /(K a a alc )))

(1 + KacidK a (a ester awater /a alc ) + K water awater )

Desorption of ester ri =M cat K a kester (a alca acid /a water (a ester /K a ))(1 + K acid a acid + K a K ester (a alc a acid /a water ))

Desorption of water ri =M cat K a kwater (a alca acid /a ester (a water /K a ))(1 + K acid a acid + K a K water (a alca acid /a ester ))

Adsorbed 1-propanol reacting withpropionic acid in the uid

Surface reaction ri =M catkf K alc (a acid a alc (a ester awater /K a ))

(1 + K alca alc + K water awater )

Adsorption of alcohol ri =M catkalc (a alc (a ester awater /(K a a acid )))

(1 + KalcKa

(a ester awater /a acid ) + K water awater )

Desorption of ester ri =M catK a kester (a alca acid /a water (a ester /K a ))(1 + K alca alc + K a K ester (a alca acid /a water ))

Desorption of water ri =M catK a kwater (a alca acid /a ester (a water /K a ))(1 + K alca alc + K a K water (a alca acid /a ester ))

Adsorbed propionic acid reactingwith adsorbed 1-propanol

Surface reaction ri =M cat kf K acid K alc (a acid a alc (a ester awater /K a ))

(1 + K acid a acid + K alca alc + K ester a ester + K water awater )2

Adsorption of acid ri =M catkacid (a acid (a ester awater /(K a a alc )))

(1 + KacidK a (a ester awater /a alc ) + K alc a alc + K ester a ester + K water awater )

Adsorption of alcohol ri =M cat kalc (a alc (a ester awater /(K a a acid )))

(1 + KalcK a (a ester awater /a acid ) + K acid a acid + K ester a ester + K water awater )

Desorption of ester ri = M catK a kester (a alca acid /a water (a ester /K a ))(1 + K acid a acid + K alca alc + K a K ester (a alca acid /a water ) + K water a water )

Desorption of water ri =M catK a kwater (a alca acid /a ester (a water /K a ))

(1 + K acid a acid + K alca alc + K ester a ester + K a K water (a alca acid /a ester ))

aawater = (x water water ) .

Surface area fraction and volume fraction are as follows:

i =qi xi

j qj xj , (10)

i =r i xi

j r j xj . (11)

Parameters r i and q i are calculated as the sum of the individ-ual group volume and surface area parameters Rk and Q k asfollows:

r i =k

v (i)k Rk , (12)

qi =k

v (i)k Q k , (13)

where v (i)k is the number of k groups in molecule i.

The residual part of the activity coefcient (Hansen et al.,1992) is given by

ln Ri =k

v (i)k (ln k ln(i)k ), (14)

where k is the group residual activity coefcient in the mixtureand (i)k is the residual activity coefcient of group k in areference solution containing only molecules of types i (purecomponent). The k or

(i)k is calculated by

ln k (or (i)k )

= Q k 1 lnm

m mk m

m km

n n nm. (15)

Here m is the area fraction of group m and it is calculatedaccording to the following equation:

m =

Q m X m

n Q n X n , (16)

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where Q m is a group parameter and X m is the mole fraction of group m in the mixture:

X m =i v

(i)m xi

i n vin xi

. (17)

The group interaction coefcient mn (Hansen et al., 1992 ) isgiven by

mn = exp a mn + bmn T

T . (18)

3. Experimental

3.1. Catalysts

Three ion-exchange catalysts were used; Dowex 50Wx8-400(Aldrich catalog # 217514), Amberlyst 15 (Aldrich catalog #216380) and Amberlite IR-120 (Aldrich catalog # 216534).These catalysts were used after they have been vacuum-driedat a temperature of 343K for 48 h. Drying at much highertemperatures (temperature > 373 K) could lead to the loss of active sulfonic acid sites of the catalysts. The properties of theion-exchange resins are shown in Table 2 . The homogeneouscatalyst used, sulfuric acid (product # UN1830), was suppliedby BDH and had a purity of greater than 99% and a specicgravity of 1.835.

3.2. Chemicals

1-Propanol with a purity of 99.5% was supplied by Schar-

lau (catalog # AI0437). 2-Propanol with a purity of 99.5%was supplied by Fluka (catalog # 59300). Methanol analyticalgrade (99.8% pure) was supplied by AJAX chemicals (UN #1230). Ethanol reagent grade with 99.8% purity was suppliedby Scharlau (catalog # ET0016). 1-Butanol reagent grade of 99.5% purity was supplied by Fluka (catalog # 19420). Propi-onic acid having a product # 81912 and Butyric acid with a cat-alog # 19215 both have a purity of 99% and were supplied byFluka, while acetic acid with a purity of 99.8% was supplied byRiedel-de Haen (product # 27225). The purity of all alcohols

Table 2

Propertiesa

of the cation exchange resins usedCatalyst Dowex 50Wx8-400 Amberlite IR-120 Amberlyst 15

Manufacturer Dow Chemical Co. Rohm & Haas Rohm & HaasSupplier Aldrich Aldrich AldrichCatalog # 217514 216534 216380Polymer type Gel-type Gel-type Macro reticularMatrix type Styrenedivinyl benzene (DVB) Styrenedivinyl benzene (DVB) Styrenedivinyl benzene (DVB)Functional group Sulfonic acid Sulfonic acid Sulfonic acidStandard ionic form H + H+ H+Total exchange capacity (meq/mL) 1.7 1.9 1.8Cross-linking (% DVB) 8 8 20Moisture content (% mass) 54 45 < 1.6Particle size range (mm) 0.040.07 0.301.20 0.301.20

aAs reported by the manufacturer.

and acids was checked by gas chromatographic analysis andfound to be comparable to the listed values mentioned above.

For titration purposes, the alkali used was a standard solutionof sodium hydroxide (NaOH) with 0.1024 N in water. This so-lution was supplied by Aldrich (product # 31,948-1). The con-centration of the alkali solution was conrmed by back titrating

with a freshly prepared solution of potassium hydrogen phtha-late of known concentration. Potassium hydrogen phthalate wassupplied by Aldrich (catalog # 17992-2) and had purity greaterthan 99.9%.

3.3. Kinetic runs

All the kinetic runs were carried out in a Lab-Max reactorsystem. The equipment used in this experiment ( Fig. 1 ) con-sisted mainly of a 1 L glass batch reactor system. The reac-tor was continuously stirred using a four blade glass impellerdriven by an electrical motor. The shell of the reactor vesselwas lled with oil to either heat or cool the reaction mixture. Atemperature probe was inserted into the reactor to measure themixtures temperature with an accuracy of 0.1 K. The reactortemperature was automatically controlled. The Lab-Max had astirrer speed ranging from 0 to 1500 rpm. A measured amountof acid and catalyst (liquid or vacuum-dried solid catalyst) wasadded to the reactor, and the temperature of the reactor wasraised to the required reaction temperature. A certain amountof alcohol was separately preheated to the reaction temperaturein a heating bath. The preheated alcohol was added to the re-actor and the time of initiation of the reaction was noted (zerotime). A sample of the reaction mixture was immediately with-drawn, ltered and quenched to stop the reaction. The sample

was titrated with a standard NaOH solution. The reproducibil-ity of the titration results was found to be within 1.5%. Thiswas done by repeating the titration procedure three times. Othersamples were withdrawn and titrated at different time intervalsand the reaction was followed for 240 min.

3.4. Equilibrium runs

The equilibrium runs were carried out in 80cm 3 glass cellshaving outer glass jackets facilitating water ow to control the

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Fig. 1. Experimental setup of the Lab-Max apparatus.

temperature from a circulating water bath. The glass stoppersfor the cells were tted with smaller diameter stoppers at thetop to facilitate the removal of the reaction sample by meansof a thin graduated pipette. This involved removing only thesmall upper stopper. Equimolar amounts of propionic acid and1-propanol (around 0.2 mol of each) along with 2% by volumeof concentrated sulfuric acid were allowed to react in the cellsuntil equilibrium was reached (as evidenced by the absence of any change in the amount of alkali required to neutralize the

acid present in 0.1 ml of the withdrawn sample). The reactionvolume was not allowed to exceed half the volume of the cells.The reaction temperatures studied were 303.15, 313.15 and323.15K.

4. Results and discussion

The reaction conditions were systematically altered to studythe effect of rpm, nature of catalyst, catalyst loading, temper-ature, acid to alcohol molar ratio, presence of water, changingacid and alcohol types on the reaction kinetics. In addition,three runs were carried out using sulfuric acid as the catalyst to

determine the reaction equilibrium. The details of the reactionconditions of these runs are given in Table 3 .

4.1. External and internal diffusion signicance

The esterication reaction in this investigation is aliquidsolid catalytic reaction where different processes aretaking place: external and internal diffusions, adsorption of atleast one of the reactants, surface reaction and desorption of products followed by back diffusion of the products into the liq-uid bulk. To study the kinetics of the esterication reaction, theeffect of external and internal diffusion limitations should beeliminated. The external mass transfer resistance is affected bythe speed of agitation in our case as has been stated previously.

Therefore, ve experiments were carried out at different stirrerspeeds (100 , 200 , 600, 900 and 1000 rpm). It was found thatthe conversion of acid was independent of stirrer speed exceptat 100 rpm as shown in Fig. 2 , because at 100rpm the catalystwas not well distributed inside the reactor. This means that forthe setup used in this study (stirrer of 5 cm diameter 1 cmbore diameter and reactor of 10 cm internal diameter), theexternal diffusion limitation is negligible at stirrer speeds of 200 rpm and above. Therefore, a stirrer speed of 900 rpm was

maintained during all experiments to ensure that the measuredreaction rate was free from external diffusion effects. Xu andChuang (1996) studied the methyl acetate synthesis using Am-berlyst 15 and they found that there was no external diffusioneffect for stirrer speed ranging from 160 to 760 rpm. In thestudy undertaken by Xu and Chuang (1996) , low rpm valueswere found to have a negligible effect on reaction rate becauseof the low viscosity of the studied system (reaction of methanolwith dilute acetic acid solution). Furthermore, Ppken et al.(2000) studied the effect of stirrer speed (ranged from 100to 560 rpm) for methyl acetate synthesis using Amberlyst 15,and found that at stirrer speeds of 170 rpm and above, externaldiffusion did not control the overall rate in the ion-exchangeresin catalyzed process. This result is in line with the work of Xu and Chuang (1996) . Roy and Bhatia (1987) found thata stirrer speed of 500 rpm was sufcient to eliminate externaldiffusion limitations for the esterication reaction of benzylalcohol with acetic acid with Amberlyst 15 catalyst. Ali andMerchant (2006) found that in the reaction of 2-propanol withacetic acid, external mass transfer limitation was negligibleat a stirrer speed above or equal to 500 rpm (the stirrer speedstudied range was from 50 to 900rpm). A higher range of stirrer speeds (7001200) rpm was studied by Krishnaiah andRao (1984) for the esterication of 1-propanol with acetic acidover Dowex-50W. The absence of a stirrer speed effect wasobserved at 1100 and 1200rpm, which is much higher than

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Table 3Summary of experimental conditions

Run # Temperature (K) Acid to alcoholrounded molarratio

Catalystloading(gdry cat/L)

Stirrer speed(rpm)

Acid Alcohol Water Catalyst

1 323.15 1:1 40 100 Propionic 1-Propanol Dowex 50Wx8-4002 323.15 1:1 40 200 Propionic 1-Propanol Dowex 50Wx8-4003 323.15 1:1 40 600 Propionic 1-Propanol Dowex 50Wx8-4004 323.15 1:1 40 900 Propionic 1-Propanol Dowex 50Wx8-4005 323.15 1:1 40 1000 Propionic 1-Propanol Dowex 50Wx8-4006 323.15 1:1 60 900 Propionic 1-Propanol Amberlyst 157 323.15 1:1 60 900 Propionic 1-Propanol Amberlite IR-1208 323.15 1:1 60 900 Propionic 1-Propanol Dowex 50Wx8-4009 323.15 1:1 10 900 Propionic 1-Propanol Dowex 50Wx8-400

10 323.15 1:1 20 900 Propionic 1-Propanol Dowex 50Wx8-40011 323.15 1:1 60 900 Propionic 1-Propanol Dowex 50Wx8-40012 323.15 1:1 40 900 Propionic 1-Propanol Wet Dowex 50Wx8-40013 323.15 1:1 2% Volume 900 Propionic 1-Propanol H 2SO414 303.15 1:1 2% Volume 900 Propionic 1-Propanol H 2SO415 303.15 1:1 40 900 Propionic 1-Propanol Dowex 50Wx8-40016 313.15 1:1 40 900 Propionic 1-Propanol Dowex 50Wx8-40017 333.15 1:1 40 900 Propionic 1-Propanol Dowex 50Wx8-40018 323.15 2:1 40 900 Propionic 1-Propanol Dowex 50Wx8-40019 323.15 1:2 40 900 Propionic 1-Propanol Dowex 50Wx8-40020 323.15 1:4 40 900 Propionic 1-Propanol Dowex 50Wx8-40021 323.15 4:1 40 900 Propionic 1-Propanol Dowex 50Wx8-40022 323.15 1:1 40 900 Propionic 1-Propanol Water added Dowex 50Wx8-40023 323.15 1:1 40 900 Acetic 1-Propanol Dowex 50Wx8-40024 323.15 1:1 40 900 Butyric 1-Propanol Dowex 50Wx8-40025 323.15 1:1 40 900 Propionic Methanol Dowex 50Wx8-40026 323.15 1:1 40 900 Propionic Ethanol Dowex 50Wx8-40027 323.15 1:1 40 900 Propionic 1-Butanol Dowex 50Wx8-40028 323.15 1:1 40 900 Propionic 2-Propanol Dowex 50Wx8-40029 303.15 1:1 2% Volume Equilibrium runs Propionic 1-Propanol H 2SO430 313.15 1:1 2% Volume Propionic 1-Propanol H 2SO4

31 323.15 1:1 2% Volume Propionic 1-Propanol H 2SO4

0

0.1

0.2

0.3

0.4

0.5

0 3600 7200 10800 14400 18000Time (sec)

C o n v e r s i o n o f p r o p

i o n i c a c

i d

100 rpm200 rpm600 rpm900 rpm1000 rpm

Fig. 2. Effect of stirrer speed (rpm) on the conversion of propionic acid at323K, 1:1 propionic acid to 1-propanol molar ratio and 40 g dry cat/L catalyst

loading of Dowex 50Wx8-400.

that found by Xu and Chuang (1996) and Ppken et al. (2000) .Therefore, the signicance of external mass transfer limitationwhich is directly related to stirrer speed in batch systems de-pends on several factors such as the viscosity of the system,reactions conditions, type of species used and the presence of diluents, in addition to the type and properties of catalyst used.

To investigate the internal diffusion effect on the reactionrate, analysis based on the WeiszPrater criterion was under-taken. Data from 10 experiments (4, 10, 11 and 1521) weretted to the WeiszPrater equation where Dowex 50Wx8-400was the catalyst. The WeiszPrater criterion was determinedfor the initial stages (1800 s) of runs 4, 10, 11 and 1521 (theseruns were used for modeling purpose). The results are shownin Table 4 . It was found that values of the internal diffusionparameter are signicantly less than one (C WP > 1). Theseresults indicate that internal diffusion does not limit the reac-tion of propionic acid with 1-propanol over Dowex 50Wx8-400 for the reaction conditions implemented in this study. TheCW P parameter values ranges between 3 .63E 4 to 1 .22E 3.These values are of the same order as those obtained by Bartet al. (1996) and Krishnaiah and Rao (1984) , which variedfrom 1 .3E 4 to 1 .0E 2 and from 6 .0E 4 to 1 .7E 3, re-

spectively. Both studies were undertaken for the esterication

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Table 4Signicance of internal diffusion for different runs

Run # Experimental parameters a C li at 30 min (mol/cm 3) rA (obs) at 30 min (mol/g cat /s) D e (cm2 /s) CW P

4 40/323.15/1 0.0055 8.78E 06 1.22E 06 8.73E 0410 20/323.15/1 0.0058 1.02E 05 1.16E 06 1.02E 03

11 60/323.15/1 0.0052 7.84E

06 1.31E

06 7.73E

0415 40/303.15/1 0.0060 2.35E 06 7.23E 07 3.63E 0416 40/313.15/1 0.0059 3.80E 06 9.21E 07 4.70E 0417 40/333.15/1 0.0048 1.48E 05 1.69E 06 1.22E 0318 40/323.15/2 0.0077 7.51E 06 9.00E 07 7.29E 0419 40/323.15/0.5 0.0036 6.22E 06 1.44E 06 8.03E 0420 40/323.15/0.25 0.0021 4.01E 06 1.58E 06 7.97E 0421 40/323.15/4 0.0096 6.39E 06 5.83E 07 7.71E 04

aFirst number: catalyst loading in g dry cat/L; second number: temperature in K; third number: acid to alcohol molar ratio.

Table 5Equilibrium mole fractions, conversions, activity coefcients and constants

T (K) Acetic acid 1-Propanol Propyl propionate Water Equilibrium

constant K sEquilibrium Equilibrium Activity Equilibrium Equilibrium Activity Equilibrium Activity Equilibrium Activitymole conversion c oefcient mole conversion c oefcient mole coefcient mole coefcientfraction fraction fraction fraction

303.15 0.1638 0.6724 0.6842 0.1638 0.6724 1.0698 0.3362 1.9273 0.3362 2.9911 33.1789313.15 0.1654 0.6692 0.7101 0.1654 0.6692 1.0505 0.3346 1.9083 0.3346 2.9248 30.6202323.15 0.1678 0.6644 0.7239 0.1678 0.6644 1.0376 0.3322 1.8815 0.3322 2.8897 28.3703

of 1-propanol with acetic acid; Bart et al. (1996) used Dowexmonospheres, while Krishnaiah and Rao (1984) used Dowex-50W as the catalyst. In addition, in a previous work, our groupfound C

W P to range from 9 .3E 5 to 5 .0E 4 for the esteri-

cation of 2-propanol with acetic acid over Dowex 50Wx8-400(Ali and Merchant, 2006 ).

4.2. Effect of temperature on reaction equilibrium

Three experimental runs were carried out at 303.15, 313.15and 323.15K to obtain the equilibrium constant values. Thealcohol to acid molar ratio of 1:1 and sulfuric acid with aconcentration of 2% by volume were used. The experimentswere undertaken to determine the equilibrium mole fractions of propionic acid, 1-propanol, propyl propionate and water. Theresults for the equilibrium runs are shown in Table 5 .

The following equation was used to determine the equilib-rium constant K s :

K s =(x ester )eq (x water )eq

(x acid )eq (x alc )eqester water

acid alc, (19)

where (x i )eq is the equilibrium mole fraction of component iand i is the activity coefcient of component i determinedby the UNIFAC model. The values of the activity coefcientsare reported in Table 5 . From Table 5 it is obvious that theactivity coefcients of 1-propanol, 1-propyl propionate andwater decreased and the activity coefcient of propionic acidincreased as the reaction temperature increased. Increasing the

3.32

3.34

3.36

3.38

3.4

3.42

3.44

3.46

3.48

3.5

3.52

0.00305 0.0031 0.00315 0.0032 0.00325 0.0033 0.003351/T (1/K)

l n K s

Experimental Run

Linear fit

Fig. 3. The natural logarithm of equilibrium constant versus the reciprocalof the absolute temperature.

temperature from 303.15 to 323.15 K, the equilibrium conver-sion of the reactants decreased from 0.6724 to 0.6644.

The plot of ( ln K s ) versus (1/T ) with a linear regression of R 2t = 0.99 (Fig. 3 ) gives the following equation:

K s = 2.6445 Exp (6376 /RT) . (20)

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This equation is consistent with the Vant Hoff equation forthe effect of temperature on the chemical reaction equilibriumconstant:

ln KS K SR

= H 0RR

1T

1

T R. (21)

Accordingly, the standard enthalpy change of reaction H 0Ris 6.4 kJ/ mol. Therefore, the reaction of propionic acid with1-propanol is exothermic, and the equilibrium constant has aweak dependence on temperature. The same trend was ob-tained by Song et al. (1998) for the methyl acetate synthe-sis with H 0R equal to 6.5 kJ / mol. The equilibrium constantwas found to have values of 30.2, 27.4 and 24.0 at 313.15,318.15 and 323.15 K, respectively. Also, in a previous work (Ali and Merchant, 2006 ) we have found that H 0R was equalto 5.4 kJ / mol for the esterication reaction between aceticacid and 2-propanol, and the equilibrium constant to be 29.4,26.0 and 23.0 at 303, 323 and 343K, respectively. These re-sults indicate that the reaction is mildly exothermic. Differentresults were obtained by Bart et al. (1996) for the estericationof acetic acid with 1-propanol and Liu and Tan (2001) for theesterication of propionic acid with 1-butanol. They found thatthe equilibrium constant increased with increasing temperature,which indicates that these esterication reactions are endother-mic. Bart et al. (1996) found that the equilibrium constants at303.15, 323.15 and 343.15K were 10.3, 21.7 and 32.3, respec-tively, while Liu and Tan (2001) found that the correspondingvalues at 363, 373 and 383 K are 29.1, 29.4 and 30.1, respec-tively. It has to be mentioned that the equilibrium constant isfound to be independent of temperature for many esterication

reactions, because the heat of reaction for these reactions werealmost equal to zero or quite small in value (McKetta, 1983 ).In this study the performance of several models (in which

different components are assumed to be adsorbed to differentextents on the catalyst surface) were compared. The P-H model,which is the simplest model used, assumes reaction homogene-ity and its rate equation calls for a homogeneous reaction equi-librium constant (K s ) as given by Eq. (20). In all other modelsthe reaction is heterogeneously catalyzed by Dowex 50Wx8-400. Therefore, the equilibrium constant (K a ) is a combinationof adsorption equilibrium constants (K i ) for different speciesi in addition to the surface reaction equilibrium constant (K s )as expressed in Eq. (6). Since the functional group in the solidcatalyst (Dowex 50Wx8-400) used is sulfonic acid, it wasconsidered useful to obtain values of the surface reactionequilibrium constant (K s ) from a reaction system catalyzedhomogeneously by sulfuric acid at the same catalyst load-ing. The homogeneous reaction equilibrium constant (K s )was maintained for all other models in order to be able tohave a clear direct comparison of different species adsorptionequilibrium constants (K i ) calculated by these models.

4.3. Effect of reaction parameters

By eliminating both external and internal diffusion limita-tions, the esterication reaction is purely kinetically controlled.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 3600 7200 10800 14400 18000Time (sec)

C o n v e s i o n o f p r o p

i o n i c a c i

d

Amberlyst 15

Amberlite IR-120

Dowex 50Wx8-400

Fig. 4. Effect of catalyst type on the conversion of propionic acid at 323 K,900rpm, 1:1 propionic acid to 1-propanol molar ratio and 60 g drycat/Lcatalyst loading.

4.3.1. Effect of type of ion-exchange resin catalyst Ion-exchange resins have been found to be suitable catalysts

for esterication reactions ( Sharma et al., 1973; Dakshina-murty et al., 1984; Xu and Chuang, 1996; Yadav and Thathagar,2002). In recent studies, sulfuric acid is being replaced

by ion-exchange resins due to environmental regulations.Moreover, using ion-exchange resins has several advantages asdiscussed previously. In this investigation, three types of ion-exchange resins (Dowex 50Wx8-400, Amberlite IR-120 andAmberlyst 15) were chosen for this purpose. Among thesecatalysts, Dowex 50Wx8-400 was found to be the best, yield-ing the highest conversion of propionic acid as shown in Fig.4. The performance of different ion-exchange resin catalystsfor this kind of reactions is actually attributed to the type of reactants and products involved, in addition to the structureand characterization of the ion-exchange resins.

4.3.2. Effect of using sulfuric acid (H 2SO 4) compared with Dowex 50Wx8-400 as a catalyst A comparison of the effect of using sulfuric acid rather than

Dowex 50Wx8-400 on the conversion of propionic acid as afunction of time was made at two different temperatures (303.15and 323.15 K) with identical experimental conditions (Fig. 5 ).In these experiments, equivalent catalyst loadings were usedfor both Dowex (40g drycat/L) and sulfuric acid (almost 2%of total liquid volume so as to equal 40 g drycat/L). Higherconversion of propionic acid over a period of time of 4 h wasobtained with sulfuric acid rather than Dowex 50Wx8-400 atthe two temperatures studied. Since sulfuric acid is in the samephase as the reactants (homogeneous liquid phase), the avail-ability of free protons in this liquidliquid catalytic reaction
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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 3600 7200 10800 14400 18000Time (sec)

C o n v e r s

i o n o

f p r o p

i o n i c a c

i d

H2SO4 at 323.15 KDowex 50Wx8-400 at323.15 KH2SO4 at 303.15 KDowex 50Wx8-400 at303.15 K

Fig. 5. Effect of H 2SO4 compared with Dowex 50Wx8-400 on the conversionof propionic acid at different temperatures, 900rpm, 1:1 acid to alcohol molarratio and 40g drycat/L catalyst loading.

mixture results in having faster rates of reaction compared tothe case where ion-exchange resins are used (liquidsolid re-action mixture). However, taking into consideration the advan-tages of ion-exchange resin, Dowex 50Wx8-400 is the preferredcatalyst. Roy and Bhatia (1987) compared the behavior of the

ion-exchange resin Amberlyst 15 with the behavior of sulfuricacid as catalyst for the conversion of acetic acid as a functionof time. The concentration of catalyst and the reaction condi-tions were maintained the same. They ( Roy and Bhatia, 1987 )found that sulfuric acid resulted in a higher conversion thanAmberlyst 15. However, by taking into consideration that us-ing sulfuric acid as a catalyst suffers from several drawbacksin industrial application, Amberlyst 15 was found to be moreeffective as a catalyst for the synthesis of benzyl alcohol withacetic acid. The effect of using a homogeneous catalyst versusheterogeneous catalyst for the esterication of propionic acidwith 1-butanol was investigated by Liu and Tan (2001) . Sulfuricacid was compared with Amberlyst 35 among other solid cat-alysts at the same catalyst concentration of 1wt% in solution.They found that using a concentration of 1wt% Amberlyst 35in solution gave less conversion than a concentration of 1 wt%of sulfuric acid in solution. However, Amberlyst 35 was se-lected as the best choice for this synthesis because it withstandshigher temperatures than the other tested solid catalysts.

4.3.3. Effect of catalyst loadingThe effect of catalyst loading of Dowex 50Wx8-400 on the

conversion of propionic acid was investigated by setting thecatalyst loadings at 10, 20, 40 and 60 g drycat/L. It is observedthat the conversion of propionic acid increases proportionallywith catalyst loading (see Fig. 6 ). As expected, increasing the

0

0.1

0.2

0.3

0.4

0.5

0.6

0 3600 7200 10800 14400 18000Time (sec)

C o n v e r s

i o n o f p r o p

i o n i c a c i

d

10 g dry cat/L20 g dry cat/L40 g dry cat/L60 g dry cat/L

Fig. 6. Effect of Dowex 50Wx8-400 loading on the conversion of propionicacid at 323K, 900rpm and 1:1 propionic acid to 1-propanol molar ratio.

catalyst loading means more available active sites for this reac-tion, which results in higher reaction rate. A similar trend wasobtained by earlier workers (Rao et al., 1979; Xu and Chuang,

1996; Bart et al., 1996; Yadav and Kulkarni, 2000 ). This re-sult agrees with the model rate expression where the term M catis explicitly added. This clearly indicates that M cat is directlyproportional to the reaction rate.

4.3.4. Effect of the catalyst moisture content (wet versus dry Dowex 50Wx8-400)

To study the effect of moisture content of the ion-exchangeresin on the reaction, two experiments were conducted at thesame reaction conditions for a time period of 4 h as shownin Fig. 7 . The rst experiment was undertaken using a wetcatalyst (stock sample) where the weight of water was taken

into account, while for the second experiment the catalyst wasvacuum-dried at a temperature of 343 K for 48 h. The two ex-periments were carried out using the same dry mass of cata-lyst. As shown in Fig. 7 , the conversion of acid was higherwith dry catalyst compared with wet catalyst. Earlier work-ers used different dried ion-exchange resins (Dowex 50W-x8and x2, Amberlyst 15 and 35, Amberlite IR-120) for studyingthe kinetics of the esterication synthesis ( Sharma et al., 1973;Krishnaiah and Rao, 1984; Ppken et al., 2000; Gangadwalaet al., 2003; Ali and Merchant, 2006 ). Sharma et al. (1973)oven-dried Dowex 50w-x8 at 353.15358.15K for the ester-ication of ethanol with propionic acid. Amberlyst 15 wasvacuum-dried at 363.15 K for 48 h by Ppken et al. (2000)for the methyl acetate synthesis. Furthermore, Krishnaiah and
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0

0.1

0.2

0.3

0.4

0.5

0 3600 7200 10800 14400 18000Time (sec)

C o n v e r s

i o n o f p r o p

i o n i c a c i

d

Wet Dowex 50Wx8-400

Dry Dowex 50Wx8-400

Fig. 7. Effect of moisture content (wet versus dry Dowex) on the conversionof propionic acid at 323K, 900rpm, 1:1 propionic acid to 1-propanol molarratio and 40g drycat/L catalyst loading.

Rao (1984) , who studied the esterication of 1-propanol withacetic acid, preheated Dowex 50W-x2 and x8 in an air oven at338.15 K for 20 min before use. They found that the moisture

content of the solid ion-exchange resins had a retarding effecton the conversion of acid. Moreover, a recent study on homo-geneously catalyzed esterication ( Liu et al., 2006 ) has estab-lished that besides promoting ester hydrolysis, the presence of water signicantly decreases the activity of the catalytic pro-tons. The presence of water can be expected to have a simi-lar effect for the studied heterogeneous systems also, since thecatalyst used is acidic in nature. Therefore, it is important todry the catalyst before running an experiment since the pres-ence of water can promote ester hydrolysis and adversely effectcatalytic activity. Both these factors can cause considerable de-crease in the acid conversions. The role of water in heteroge-neous esterication is further discussed in the section Effectof adding water to the reaction mixture.

4.3.5. Effect of temperatureThe effect of temperature was studied by varying the reaction

temperature from 303.15 to 333.15K at constant conditions of acid to alcohol molar ratio, catalyst concentration and stirrerspeed. Fig. 8 shows that increasing the temperature brings morecollisions and therefore more successful collisions. These suc-cessful collisions have sufcient energy (activation energy) tobreak the bonds and form products and thus result in highervalues of conversion of propionic acid, which agrees with pre-vious esterication studies ( Venkateswarlu et al., 1976; Raoet al., 1976; Sai, 1988; Lee et al., 1999; Awad et al., 1997;

0

0.1

0.2

0.3

0.4

0.5

0.6

0 3600 7200 10800 14400 18000

Time (sec)

C o n v e r s

i o n o f p r o p

i o n i c a c

i d

303.15 K313.15 K323.15 K333.15 K

Fig. 8. Effect of temperature on the conversion of propionic acid at 900 rpm,1:1 propionic acid to 1-propanol molar ratio and 40g dry cat/L catalyst loadingof Dowex 50Wx8-400.

Ali and Merchant, 2006 ). The temperature 323.15K was se-lected as the standard temperature for subsequent runs becauseit is high enough to yield a high conversion, while gas-bubble

formation is insignicant.

4.3.6. Effect of acid to alcohol molar ratioThe effect of acid to alcohol molar ratio was investigated

by varying the acid to alcohol molar ratio (ranging from 1:4to 4:1). From Fig. 9 it is obvious that increasing the amountof alcohol initially increases the conversion of propionic acid.After 4 h of reaction time the conversion of propionic acid forthe run with acid to alcohol molar ratio of 1:4 is approximately17% more than that for the run with a ratio of 1:2 and 32%more than that for the run with a ratio of 1:1. Dakshinamurtyet al. (1984) , who studied the esterication reaction of 1-propa-

nol with propionic acid over Dowex-50W, found that the con-version of acid increased with increasing initial alcohol to acidmolar ratio. Also, some other workers ( Yadav and Kulkarni,2000; Yadav and Thathagar, 2002 ) found that the conversionof acid increases with decreasing the acid to alcohol molar ra-tio. Fig. 10 is a re-plot of Fig. 9 but in terms of conversionof the limiting reactant rather than propionic acid. As shownin Fig. 10 , changing the molar ratio from 1:1 to 1:2 increasesthe conversion of the limiting reactant. A further increase inthe amount of alcohol initially leads to a higher conversionof the limiting reactant. Also, increasing the molar ratio from1:1 to 2:1 increases the conversion of the limiting reactantand a further increase in the acid to alcohol initial molar ra-tio leads to a more signicant increase in the conversion of the
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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 3600 7200 10800 14400 18000Time (sec)

C o n v e r s

i o n o f a c

i d

Propionic acid

Acetic acid

Butyric acid

Fig. 12. Effect of using different acids on the conversion of the acid at 323 K,900rpm, 1:1 acid to 1-propanol molar ratio and 40g dry cat/L catalyst loadingof Dowex 50Wx8-400.

This implies that the conversion and hence the reaction rate in-creases as the chain length decreases. A similar conclusion wasmade by Lilja et al. (2002) .

4.3.9. Effect of using different alcoholsThe effect of different alcohols on the conversion of pro-

pionic acid was investigated by running multiple experimentsusing different alcohols (methanol, ethanol, 1-propanol and 1-butanol) and holding other parameters constant. Increasing thechain length of the alcohol decreased the conversion of propi-onic acid, as indicated in Fig. 13 . The propionic acid conversionat 4 h of reaction was 67%, 55%, 48%, 46% when reacting withmethanol, ethanol, 1-propanol and 1-butanol, respectively. Thehindrance effect is the main reason for the decrease in the con-version of propionic acid as the alcohol chain length increases.Awad et al. (1997) and Lilja et al. (2002) results agree with our

results. These authors concluded that alcohol chain length hada retarding effect on the overall reaction rate. The estericationof propionic acid with 1-propanol and 2-propanol over Dowex50Wx8-400 was investigated and the results are shown inFig. 14 . As shown in Fig. 14 , the reaction of propionic acid with1-propanol had a higher conversion than the reaction of thepropionic acid with 2-propanol. At 4h of reaction, it was foundthat the conversion of propionic acid reacting with 1-propanolis 48% while the conversion of propionic acid reacting with2-propanol is 10%. This indicates that branching of the alcoholhad a retarding effect on the conversion and hence the reactionrate due to steric hindrance. Awad et al. (1997) found thatthe rate of esterication reaction of propionic acid with linearalcohols was higher than that of branched ones. Lilja et al.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 3600 7200 10800 14400 18000

Time (sec)

C o n v e r s

i o n o f p r o p

i o n i c a c

i d

methanol

ethanol1-propanol1-butanol

Fig. 13. Effect of using different alcohols on the conversion of propionic acidat 323K, 900 rpm, 1:1 propionic acid to alcohol molar ratio and 40g drycat/Lcatalyst loading of Dowex 50Wx8-400.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 3600 7200 10800 14400 18000Time (sec)

C o n v e r s

i o n o f p r o p

i o n i c a c

i d

2-propanol1-propanol

Fig. 14. Effect of using 2-propanol versus 1-propanol on the conversion of propionic acid at 323 K, 900 rpm, 1:1 propionic acid to alcohol ratio and40g drycat/L catalyst loading of Dowex 50Wx8-400.

(2002) , who studied the esterication of acetic and propionicacids with different alcohols over Smopex-101, as a catalyst,demonstrated that branching of the alcohol chain decreasedthe reaction rate. In contrast, El-Noamany et al. (1994) foundthat branching in the hydrocarbon chain length of an aliphaticprimary alcohol had insignicant effect on the esterication

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Table 6The UNIFAC groups present in the different components and their R and Qvalues

Group CH 3 CH2 COOH OH H 2O CH2COO

Propionic acid 1 1 1 0 0 01-Propanol 1 2 0 1 0 0

Propyl propionate 2 2 0 0 0 1Water 0 0 0 0 1 0R 0.9011 0.6744 1.3013 1 0.92 1.6764Q 0.848 0.54 1.224 1.2 1.4 1.42

reaction of acetic acid with monohydric alcohols (1-butanol,2-butanol, 1-hexanol, cyclo-hexanol and benzyl alcohol) usingAmberlite IR-120 as a catalyst.

4.4. Modeling

From the different kinetic runs involved in this investiga-tion, 10 runs were selected for modeling. These runs (4, 10,11 and 1521) represented the reaction of propionic acid with1-propanol catalyzed by Dowex 50Wx8-400 at different re-action conditions. Kinetic data from these selected runs aretted to 40 rate expressions as discussed previously. The activ-ity coefcients of the reactants and the products used in theseequations were determined using the UNIFAC model. In thisinvestigation, UNIFAC was incorporated into the used Mathe-matica software. To calculate the UNIFAC activity coefcientsin our system, the four components present in the system weredivided into the following sub-groups as reported in Table 6 :propionic acid (1 CH 3 , 1 CH 2 and 1 COOH); 1-propanol (1

CH3 , 2 CH 2 and 1 OH); 1-propyl propionate (2 CH 3, 2 CH 2and 1 CH 2COO); water (1 H 2O).Experimental data tted to 40 rate expressions were tested

using Mathematica software (Statistics Nonlinear t function).The aim of this tting is to minimize the mean-square differ-ences between calculated values of rate (r calc obtained fromMathematica) with values obtained from experimental data(r exp) as shown below:

min =all data samples

(r calc rexp)2 , (22)

where the experimental data of mole fraction of limiting com-

ponent were tted as a function of time (x exp = f(t)) . Then thisfunction was differentiated in order to obtain the experimentalrate (r exp) as follows:

r exp = ndxexp

dt . (23)

This data-tting wasdone to obtain the model parameters. Someof these models gave negative values for the adsorption equi-librium constants ( K acid , K alc , K ester and/or K water ) and/or thepre-exponential factor (A f ). As a result, out of 40 models only17 models might be suitable for describing the reaction kinet-ics. Tables 79 list the number and ve parts name assignedfor these 40 models. The rst part is for the number of sitesinvolved, either dual (Dl) or single (Sg). The second part is for T a

b l e 7

K i n e t i c p a r a m e t e r s f o r t h e P - H a n d t h e d i f f e r e n t d u a l - s

i t e m o d e l s

M o d e l #

M o d e l

A f

E f

k a ( m o l / g / s )

K a c i d

K a l c

K e s t e r

K w a t e r

T . A v g .

( m o l / g / s )

( J / m o l )

E r r o r

3 0 3 . 1 5 K

3 1 3 . 1 5 K

3 2 3 . 1 5 K

3 3 3 . 1 5 K

1

P H

2 . 6 1 E + 0 6

6 6 , 3

4 2

9 . 7 E

0 6

2 . 2 E

0 5

4 . 9 E

0 5

1 . 0 E

0 4

2 . 2 6

2

D l - A c A l c - A

d s - A c - 1

3 . 1 6 E + 0 8

8 3 , 5

5 7

1 . 3 E

0 6

3 . 6 E

0 6

9 . 8 E

0 6

2 . 5 E

0 5

2 . 0 0

0 . 9 9

0 . 0 0

0 . 4 1

3

D l - A c A l c - A

d s - A c - 2

8 . 6 0 E + 0 8

8 6 , 2

7 9

1 . 2 E

0 6

3 . 5 E

0 6

9 . 7 E

0 6

2 . 5 E

0 5

4 . 0 0

0 . 9 8

0 . 0 1

1 . 0 9

4

D l - A c A l c - A

d s - A c - 3

1 . 0 9 E + 0 9

8 6 , 9

5 5

1 . 1 E

0 6

3 . 4 E

0 6

9 . 6 E

0 6

2 . 5 E

0 5

3 . 0 0

0 . 9 9

0 . 1 0

1 . 9 1

5

D l - A c A l c - A

d s A

l c -

1

4 . 9 3 E + 0 9

9 1 , 4

2 2

8 . 7 E

0 7

2 . 8 E

0 6

8 . 2 E

0 6

2 . 3 E

0 5

1 . 0 5

5 . 3 0

1 4

. 9 3

1 0

6

D l - A c A l c - A

d s - A

l c -

2

8 . 7 1 E + 2 0

1 5 9 , 3 7 3

3 . 0 E

0 7

2 . 3 E

0 6

1 . 5 E

0 5

8 . 9 E

0 5

2

6 . 5 9 E + 2 2

1 . 0 0

1 0 . 0

4

7

D l - A c A l c - A

d s A

l c -

3

8 . 5 0 E + 1 0

9 9 , 3

4 2

6 . 5 E

0 7

2 . 3 E

0 6

7 . 4 E

0 6

2 . 3 E

0 5

1 . 0 9

1 . 6 7

0 . 9 9

9 . 8 0

8

D l - A c A l c - R x n - A c A l c -

1

7 . 1 2 E + 0 6

6 5 , 7

2 0

3 . 4 E

0 5

7 . 8 E

0 5

1 . 7 E

0 4

3 . 5 E

0 4

1 . 0 0

1 . 5 7

0 . 9 0

2 . 0 0

4 . 3 3

9


2

1 . 0 5 E + 0 7

6 8 , 6

1 3

1 . 6 E

0 5

3 . 8 E

0 5

8 . 5 E

0 5

1 . 8 E

0 4

2 . 6 0

3 . 0 0

1 . 5 0

6 . 0 0

2 . 6 3

1 0


3

1 . 1 5 E + 0 7

6 8 5 4 9

1 . 8 E

0 5

4 . 2 E

0 5

9 . 5 E

0 5

2 . 0 E

0 4

1 . 8 0

2 . 4 8

0 . 7 0

6 . 2 8

1 . 8 3

1 1

D l - A c A l c - D e s - W

t - 1

3 . 4 2 E + 0 5

7 4 , 6

7 6

4 . 6 E

0 8

1 . 2 E

0 7

2 . 9 E

0 7

6 . 7 E

0 7

0 . 1 3

0 . 3 7

0 . 7 6

0 . 0 3

1 2


t - 2

5 . 5 7 E + 0 4

5 7 , 3

9 0

7 . 2 E

0 6

1 . 5 E

0 5

2 . 9 E

0 5

5 . 6 E

0 5

2 . 0 0

3 . 0 0

1 . 3 0

6 . 0 0

5 . 7 8

1 3


t - 3

3 . 0 1 E + 0 5

7 0 , 0

6 4

2 . 5 E

0 7

6 . 2 E

0 7

1 . 4 E

0 6

3 . 1 E

0 6

0 . 2 5

0 . 2 5

1 . 3 7 2

0 . 1 3

1 4

D l - A c A l c - D e s - E s - 1

3 . 4 2 E + 0 5

7 0 , 0

0 0

3 . 0 E

0 7

7 . 2 E

0 7

1 . 7 E

0 6

3 . 6 E

0 6

0 . 2 1

0 . 4 6

0 . 1 7

1 . 0 8

1 5

D l - A c A l c - D e s - E s - 2

v e

8 2 , 9

1 5

0 . 0 4

0 . 8 8

5 . 5 8 E

1 2

0 . 3 8

1 6

D l - A c A l c - D e s - E s - 3

2 . 3 2 E

0 1

5 0 , 6

0 6

4 . 4 E

1 0

8 . 4 E

1 0

1 . 5 E

0 9

2 . 7 E

0 9

0 . 3 7

0 . 1 3

0 . 0 0

1 . 3 0

a R e a c t i o n , a d s o r p t i o n o r d e s o r p t i o n .
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0

0.1

0.2

0.3

0.4

0.5

0 3600 7200 10800 14400 18000Time (sec)

M o l e

f r a c

t i o n o f p r o p

i o n i c a c

i d

Exp.; 20 g dry cat/L Sg-Al-Rxn-Al-a2; 20g dry cat/LExp.; 40 g dry cat/L Sg-Al-Rxn-Al-a2; 40g dry cat/LExp.; 60 g dry cat/L Sg-Al-Rxn-Al-a2; 60g dry cat/L

Fig. 15. Experimental versus predicted (by the best model; model # 33) molefraction of propionic acid as a function of time at different catalyst loadingsof Dowex 50Wx8-400 at 323K, 900rpm, 1:1 propionic acid to 1-propanolmolar ratio.

error (STDEV) were performed for models # 32, 33 and 34according to the following equation:

STDEV = (Individ.Error T.Avg.Error )2(N 1) , (25)where Individ.Error is the individual error of each experimental

run, T.Avg.Error is the total average error, and N is the numberof experimental runs considered in the modeling process.

STDEV for models # 32, 33 and 34 were found to be equalto 1.3, 0.8 and 0.8, respectively. This indicates that models #33 and 34 are better than model # 32 in predicting reactionkinetics. Though the standard deviation values of models # 33and 34 are comparable to one another, the total average errorof model # 33 is lower than that of model # 34, 1.65% versus1.77%, respectively. Hence model # 33, a single-site M-ERmodel wherein adsorbed 1-propanol reacts with non-adsorbedpropionic acid resulting in non-adsorbed ester and adsorbedwater (with = 2), is selected as the model best capable of

describing the studied reaction kinetics.Interestingly, earlier workers (Dakshinamurty et al., 1984;Liu and Tan, 2001 ) have also proposed single-site mechanismsfor acidic ion-exchange resin catalyzed esterications involv-ing propionic acid. Dakshinamurty et al. (1984) , who studiedthe propyl propionate esterication reaction over Dowex-50W,proposed that the rate controlling step was the surface reac-tion (involving a single site) between adsorbed propionic acidreacting with 1-propanol in the bulk. However, no such mathe-matical expression was presented; but rather, an empirical rela-tionship correlating the specic reaction rate constant in termsof the studied variables was reported. Furthermore, Liu and Tan(2001) found that their heterogeneously catalyzed estericationreaction over Amberlyst 35 follows the ER theory in which

0

0.1

0.2

0.3

0.4

0.5

0 3600 7200 10800 14400 18000Time (sec)

M o l e

f r a c

t i o n o f p r o p

i o n i c a c

i d

Exp.; 303.15 K Sg-Al-Rxn-Al-a2; 303.15KE xp .; 313 .15 K Sg-Al-Rxn-Al -a2 ; 313 .15KE xp .; 323 .15 K Sg-Al-Rxn-Al -a2 ; 323 .15KE xp .; 333 .15 K Sg-Al-Rxn-Al -a2 ; 333 .15K

Fig. 16. Experimental versus predicted (by the best model; model # 33) molefraction of propionic acid as a function of time at different temperatures, cat-alyst loading 40 g dry cat/L of Dowex 50Wx8-400, 900rpm and 1:1 propionicacid to 1-propanol molar ratio.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 3600 7200 10800 14400 18000Time (sec)

M o l e

f r a c

t i o n o f p r o p i o n

i c a c

i d

Exp. Ratio; 2 : 1 Sg-Al-Rxn-Al-a2; 2 : 1Exp. Ratio; 1 : 2 Sg-Al-Rxn-Al-a2; 1 : 2Exp Ratio; 1 : 1 Sg-Al-Rxn-Al-a2; 1 : 1Exp. Ratio; 1 : 4 Sg-Al-Rxn-Al-a2; 1 : 4Exp. Ratio; 4 :1 Sg-Al-Rxn-Al-a2; 4 : 1

Fig. 17. Experimental versus predicted (by the best model; model # 33) molefraction of propionic acid as a function of time at different propionic acid to1-propanol molar ratios at 323 K, catalyst loading of 40 g drycat/L of Dowex50Wx8-400 and 900 rpm.

adsorbed propionic acid reacts with 1-butanol in the bulk. They(Liu and Tan, 2001 ) assumed that the rate controlling step is theadsorption step involving the acid species. However, there aresome objections regarding the values of the reported adsorptionequilibrium constants for propionic acid and water, which weretted as a function of temperature. One of these objections re-garding the zero values of the adsorption equilibrium constantsfor propionic acid and water at 353K, which are not reasonable.Another one is related to the un-explained and non-systematicvariations and changes in the values of the propionic acid
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the reaction of propionic acid with 1-propanol catalyzed byDowex 50Wx8-400 was best presented by the modied M-ERmodel with a total average error of 1.65%. This model is basedon a controlling step of surface reaction between adsorbed 1-propanol with non-adsorbed propionic acid forming 1-propylpropionate and water (with a correction factor for the resin

afnity for water equal to 2). The activation energy for the for-ward reaction was estimated to be 67.3 kJ/mol. UNIFAC wasused successfully to account for the non-ideal thermodynamicbehavior of the reactants and the products.

Notation

a i activity of component i in the liquid phasea mn a parameter of the interaction coefcient be-

tween groups m and nA f pre-exponential factor for the forward reac-

tion leading to ester formation, mol/g/sbmn a parameter of the interaction coefcient be-

tween groups m and nC li limiting reactant concentration in the mixture

at a given time, mol / cm3

CWP WeiszPrater parameterD e effective diffusivity, cm 2/ sD li diffusivity of limiting reactant in component

i, cm 2/ sD lm diffusivity of limiting reactant in the mixture,

cm2/ sER EleyRideal modelE f activation energy for the forward reaction

leading to ester formation, kJ/molH 0R standard enthalpy change of reaction, kJ/mol

Individ.Error individual error of each experimental runkf forward reaction rate constant for esterica-

tion, mol/g/sk forward reaction rate constant (adsorption,

desorption or surface reaction), mol/g/sK a esterication reaction equilibrium constant

for the overall reactionK i adsorption equilibrium constant for species i

present in the systemK s experimentally measured esterication reac-

tion equilibrium constantK SR surface reaction equilibrium constant at a ref-erence temperature

LH LangmuirHinshelwood modelM-ER modied EleyRideal modelM-LH modied LangmuirHinshelwood modelM cat mass of the catalyst, gM i molar mass of component i , g/moln total number of moles in the system, moln samples number of samplesN total number of runs considered for modelingP-H pseudo-homogeneous modelQ UNIFAC group area parameterr catalyst pellet radius, cm

rA( obs) observed reaction rate at a given time, mol/gof catalyst/s

rcalc calculated reaction rate, mol/srexp reaction rate determined from experimental

data, mol/sR UNIFAC group volume parameter

R c ratio of catalyst pellet volume to catalyst pel-let external surface area, cmR 2t correlation coefcient for a tR g ideal gas law constant, 8.314 J/mol/KSTDEV standard deviationt time, sT temperature, KT.Avg.Error total average errorT R reference temperature, KV i molar volume of component i , cm 3 /molxexp experimental mole fraction(x i )eq equilibrium mole fraction of component ixpred predicted mole fractionz coordination number

Greek letters

exponential term accounting for water afn-ity for the resin

i activity coefcient of component iCi combinatorial part of the activity coefcient

of component iRi residual part of the activity coefcient of

component ii viscosity of component i , cpm viscosity of the mixture, cp

surface area fractionv void fraction of the catalystc catalyst density, g/cm 3

mn energy interaction parameter between com-ponents m and n

k activity coefcient of group k at mixture com-position

ik activity coefcient of group k of pure com-

ponent i volume fraction

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