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Reaction kinetics of the catalytic esterification of acrylic acidwith propylene glycol

Mehmet R. Altıokka *, Elif Odes 

Department of Chemical Engineering, Anadolu University, 26470, Eskisehir, Turkey

1. Introduction

Various acrylic esters are useful chemicals. Their excellentclarity, toughness, color retention, UV stability and chemicalinertness make acrylic ester emulsion polymers prime paint

binders. Acrylics are widely used in all types of paint formulations.Large volumes of acrylic emulsion polymers are used as binders forfiberfill and nonwoven fabrics, textile bonding or laminating,flocking, back coating and pigment printing binders. These are alsoused for leather finishing, textile and fiberfill bonding and as

adhesives [1].Among the other many acrylates, hydroxypropyl acrylates are

used in production of acrylate polymers   [2–4]   and as a co-

monomer in adhesives, elastomers [5], inks, radiation curable [6],automotive top coating, nanocomposites materials [7], photo cureresins and oil additives and as a viscosity reducer  [8].

Hydroxypropyl acrylate contains both vinyl and hydroxyl

functionality. Vinyl allows copolymerization with a variety of other vinyl monomers in aqueous and nonaqueous systems. Wideco-monomer selection provides easy control of physical andchemical properties such as glass transition temperature and

solution viscosity. On the other hand hydroxyl functionality of hydroxypropyl acrylate provides the reaction readily witholigomeric di- or polyisocyanates, anhydrides, or epoxides. The

resulting adducts carry pendant vinyl unsaturation making theseresinsradiation curable by ultraviolet light or an electron beam [9].

Esterification of acrylic acid with alcohol has been performedcommercially by using homogeneous catalysts such as sulfuricacid, hydrofluoric acid and para-toluenesulfonic acid; but these aretoxic, corrosive and often hard to remove from the products. Thus

it is keenly desirable to develop new types of solid acid catalysts toreplace them, because the solid acid is less toxic and facilitates therecovery and recycling of catalysts [10,11].

No study has been reported in the literature for the esterifica-

tion of acrylic acid with propylene glycol. However, a number of studies related to the catalytic esterification reactions of acrylicacid with some other alcohols have been reported. Although the

catalytic activities of the various types of catalysts were comparedwith each other, kinetic information has not been given in thesestudies [1,12–18].

Esterification reaction between acrylic acid and 2-ethylhexanol

was investigated in an isothermal semi-batch reactor by usingsulfuric acid as a homogeneous catalyst. The reaction kinetics wasfound to be second order  [14].

Esterification of acrylic acid with 1-butanol has been studied in

the presence of Cs2.5H0.5PW12O40, solid oxides and organic resinsas heterogeneous catalysts. In this solid–liquid reaction system itwas found that Cs2.5H0.5PW12O40   exhibited the highest catalyticactivity, in the unit of catalyst weight, among the solid oxide

catalysts, while the activity Cs2.5H0.5PW12O40 was less than thoseof organic resins such as Nafion and Amberlyst-15 [16].

In the study of transesterification of cyclohexyl acrylate withn-butanol and 2-ethylhexanol, it was found that while the acid

Applied Catalysis A: General 362 (2009) 115–120

A R T I C L E I N F O

 Article history:

Received 8 January 2009

Received in revised form 12 March 2009Accepted 15 April 2009

Available online 23 April 2009

Keywords:

Esterification

Hydroxypropyl acrylate

Heterogeneous catalysis

Kinetic modeling

A B S T R A C T

The kinetics of esterification of acrylic acid with propylene glycol has been studied in the presence of 

Amberlyst-15 as a heterogeneous catalyst. The reaction was realized in a batch reactor at different

temperatures and initial reactant mol ratios. The simultaneous dimerization/polymerization of acrylic

acid and products, in addition to the reversible esterification reaction, was proposed as the reaction

mechanism. Kinetic equations corresponding to the reaction mechanism have also been developed.

Temperature dependence of the reaction rates and activation energies was determined.

 2009 Elsevier B.V. All rights reserved.

* Corresponding author. Tel.: +90 222 321 35 50/6505; fax: +90 222 323 95 01.

E-mail address:  mraltiokka@anadolu.edu.tr (M.R. Altıokka).

Contents lists available at ScienceDirect

Applied Catalysis A: General

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a p c a t a

0926-860X/$ – see front matter    2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.apcata.2009.04.028

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treated clay, Engelhard F-24, was an effective catalyst for thetransesterification reaction at moderate temperatures, tetrabutyltitanates as catalyst increase cyclohexanol selectivity at highertemperatures. It was also shown that transesterification reaction

follows LHHW mechanism in the presence of Engelhard F-24 [1].In another study it has been reported that heteropoly acids,

such as phosphorous tungstic acid, show higher activities than theconventional acids in the esterification of methacrylic acid with

tripropylene glycol [17].The role of Mn andFe as promoters of sulfated zirconiahas been

studied in the reaction of acrylic acid esterification by 1-butene tosec-butyl acrylate at 343 K. It was reported that Mn and Fe did not

improve the catalytic activity and selectivity to sec-butyl acrylatecompared with Amberlite resins or sulfuric acid but they stronglyresist deactivation [18].

In the present work, Amberlyst-15 and Amberlyst-36 andcesium salt of phosphorous tungstic acid were used as theheterogeneous catalysts for the esterification of acrylic acid with

propylene glycol. The best catalyst among them was to bedetermined in point of activity and selectivity towards hydro-xypropyl acrylate. Thereafter, the kinetic study of esterificationwasto be studied at the present of theselectedcatalysts among thecatalysts tested.

2. Experimental

 2.1. Materials

Acrylic acid (>99.5%) and propylene glycol (>99%) wereobtained from Acros. Toluene, as a solvent, was supplied bySigma–Aldrich. Properties of catalysts used in this study are givenin Table 1. The catalysts were dried at 80   8C for overnight prior to

the experiment. Phenothiazine used as polymerization inhibitorwas obtained from Fluka.

 2.2. Equipments

The reactor consisted of a two-necked spherical Pyrex flask of 250 ml capacity fitted with a spiral coil condenser and a sampledevice. The temperature was controlled within 0.1 K by circulat-

ing water from a thermostat into the water jacket of the reactor. The

reaction mixture was magnetically stirred at about 600 rpm.

 2.3. Experimental procedure

In a typical run, toluene as a solvent and one reactant were

placed in the reactor. A known amount of catalyst and inhibitor

was added and the reactor contents were mixed well. After asteady value of desired temperature was attained, the second

reactant was added and this was taken as zero time for a run. Onemilliliters of the liquid sample was withdrawn from the reactor atregular intervals for analysis and immediately transferred to acrucible in an ice bath in order to ensure that no further reaction

took place.

 2.4. Analysis

Thesamples were analyzedwith a gaschromatograph(HP 5890Series II) equipped with a flame ionization detector (FID) and acapillary column (TRB-FFAP). The column oven was held at 313 Kfor 3 min, ramped at 10 K/min to 333 K held for 3 min, followed by

10 K/min ramp-up to 433 K, held for 4 min and then ramped at10 K/min to 453 K, held for 2 min. The concentration of water inthe reaction mixture was measured by Karl Fischer titration(Metrohm KF-784). After verifying that the measured water

content corresponds to the calculated values based on stoichio-metric equation, the amount of water was determined fromstoichiometric mass balance equation.

3. Results and discussion

The effects of parameters, such as catalyst type and loading,

temperature and reactant mol ratio, on the reaction rate werestudied.

Swelling effect of the catalyst was neglected since preliminaryexperiment showed that the swelling process reaches the

equilibrium in a few minutes that the reactions were realized inthe presence of the reasonably stable catalyst. Therefore, theproposed model in this work comprises the effect of catalystswelling.

 3.1. Catalyst selection

In the experiments, two types of ion exchange resins

(Amberlyst-15 and Amberlyst-36) as well as cesium salt of phosphorous tungstic acid exhibiting self-inhibiting effect forpolymerization   [16], have been tested as the heterogeneouscatalysts. Experiments were carried out at 353 K and reactant mol

ratio of 1/1 with the same amount of catalyst andinhibitor. Resultsare given in   Table 2. As seen from   Table 2   that Amberlyst-36accelerates the reaction rate most. But its product selectivity isconsiderably lower than that of Amberlyst-15 at the same

conversion level of 0.45. On the other hand, althoughits selectivityis very high (100%), the activity of cesium salt of phosphoroustungstic acid is very low compared to that of the others and itshould also be noticed that its selectivity is given at very low

conversion of 0.04. It is believed that this high selectivity cannot besustained in entire range of conversion. Therefore Amberlyst-15

was chosen as a heterogeneous catalyst in this study.Effect of inhibitor, phenothizine,loading was also studied in the

presence of 0.1, 0.3 and 0.5 (wt%) in the reaction mixture. The bestratio was found to be 0.3 (wt%). This ratio was also proposed inliterature [12–14].

 3.2. Effect of catalyst loading 

Experiments were carried out in the presence of 3.11, 5.06 and8.46 wt% of Amberlyst-15 on dry basis keeping the otherparameters constant. At the conversion levels less than 10% the

initial reaction rate can be safely calculated by using Eq.  (1):

r A0 ¼C A0 X A

t 

  (1)

Nomenclature

C    concentration (mol/L)

 X    conversion

t    time (min)

r    reaction rate (mol/L min)

CsHPA cesium salt of phosphorous tungstic acid

T    absolute temperature (K)k   reaction rate constant (L/mol min)

K    equilibrium constant

E    activation energy (kJ/mol)

Subscripts

A, P, T and W acrylic acid, propylene glycol, hydroxypropyl

acrylate and water, respectively

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A plot of the reaction rate, calculated from Eq.  (1), vs. catalystloading is given in   Fig. 1. As seen in   Fig. 1, the reaction rateincreases linearly, as expected, with catalyst loading since theactive surface area is proportional to the amount of catalyst.

Intersection of the line with ordinate will give the uncatalyzedreaction rate at given parameters. The mathematical expressionrelating the initial reaction rate to the catalyst loading can be

derived from Fig. 1 as follows:

r A0 ¼ 0:0002þ 0:0004ð%wtÞmol=L :min (2)

where(wt%)is theweight percent of the catalyst on drybasis in thereaction mixture. It should also be kept in mind that Eq. (2) is valid

only at the given parameters of 0.3 (wt%) inhibitor, 1/1 reactantmol ratio and 353 K at which the experiments were performed.However, it does not alter the conclusion that the general reactionrate increases linearly with the catalyst loading.

 3.3. Effect of initial concentration

Initial reaction rate was determined by altering the concentra-tion of the component under investigation while keeping those of 

the others constant. The results are shown in   Figs. 2–5. Theordinate valuesof thesefigures were obtained from Eq.(1) by usingthe experimental data. It is evident from these figures that all

reactants and products are adsorbed on the catalyst since theinitial reaction rate is becoming nearly independent of theconcentrations as their corresponding values increase   [19].However, the initial reaction rate, as seen in Figs. 2 and 4, is not

completely independent of the concentrations of acrylic acid andproduct. This is attributed to their dimerization/polymerizationreaction.

 3.4. Kinetic modeling 

As seen in   Figs. 2–5, reaction rate is highly temperaturesensitive. It is almost doubling in every temperature rising of 10 K.Therefore, it is reasonable to accept that the overall reaction iscontrolled by the surface reaction since internal and external

 Table 1

Properties of catalysts reported by manufacturer.

Amberlyst-15 Amberlyst-36 Cs2.5H0.5PW12O40

Manufacturer Rohm & Haas Co. Rohm & Haas Co. Nippon Organic Colour

& Chemical Company

Matrix Styrene-divinylbenzene

(macroreticular)

Styrene-divinylbenzene

(macroreticular)

–

Standard ionic form H+ H+ –

Surface area (m2/g) 50a 33 116a

% Moisture   48   55 –Particle size (mm) 0.23–0.6 0.6–0.85 –

Cation exchange capacity (mmol/g) 4.7 5.4 0.15a

Maximum operating temperature (K) 393 423 –

a Ref. [16].

 Table 2

Effect of catalyst type on the reaction rate and product selectivity at 353 K and in the presence of 0.3 (wt%) inhibitor.

Catalyst Catalyst

loading (wt%)

Conversion

time (min)

Initial

concentration (M)

Conversion   r AðavÞ  ¼C A0 X A

t 

(mol/L min 103)

Selectivity

C A0   C P0

CsHPAa 4.73 180 3.3 2.9 0.04 0.736 1.00

Amb–36 5.57 240 2.7 2.2 0.45 5.047 0.494

Amb–15 5.54 420 2.8 2.3 0.45 3.003 0.736

a Inhibitor is not used since it has self-inhibiting effect  [16].

Fig. 1. Effectof catalystloading onthe reactionrate at353 K,0.3 (wt%)inhibitor,and

1/1 reactant mol ratio.

Fig. 2. Effectof acrylic acidconcentrationon theinitial reaction rate (C P0 = 0.83 mol/

L, 5 (wt%) catalyst on dry basis, and 0.3 (wt%) inhibitor).

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diffusions, as the physical steps, are not strongly temperaturedependent. This conclusion was further confirmed by Eq.   (2),

verifying the Madon Boudart test stating that reaction rate isproportional to the catalyst loading [20].

It is also reported that the influence of external and internaldiffusions can be neglected for most of the reactions catalyzed by

the Amberlyst series resins [21–29].

As concluded, from Figs. 2–5, that both reactants and productsare adsorbed on the catalyst surface. Under these assumptions the

general reaction stoichiometry and corresponding reaction rateexpression, in the form of Langmuir–Hinshelwood–Hougen–Watson model, can be written as:

CH2¼CHCOOHðAÞ

þCH3CHOHCH2OHðPÞ

, CH2¼CHCOOC3H6OHðTÞ

þH2OðWÞ

(3)

r 00A ¼  kðC AC P ðC TC W=K ÞÞ

ð1 þ K AC A þ K PC P þ K TC T þ K WC W þ K UC UÞ2

  (4)

respectively, where U is solvent.Eq.   (4)   involves seven arbitrary constants that must be

evaluated. This makes it rather impractical. For this reason, some

simplified rate expressions, fitting experimental data, wereproposed in literature   [30]. Furthermore, Eq.   (3)   will never beheld due to simultaneous polymerization of acrylic acid and

products.Taking intoaccount the general esterificationreactionas well as

polymerization of acrylic acid and products, the overall reaction

mechanism is proposed to be:

Aþ P,k1

k2

Tþ W;   ðesterificationreactionÞ   (5a)

2A)k3

dimer (5b)

2T)k4

dimer (5c)

Some of the dimer molecules formed here may transform intopolymer.

Assuming that each reaction step is elementary, the corre-

sponding rate expression can be written as follows:

dC Adt   ¼ k1C AC P þ k2C TC W k3C 2A   (6a)

dC Pdt   ¼ k1C AC P þ k2C TC W   (6b)

dC Tdt   ¼ k1C AC P k2C TC W k4C 2T   (6c)

dC Wdt   ¼ k1C AC P k2C TC W   (6d)

In Eqs.  (6s), concentrations were used instead of activities sinceactivity can be defined as:

ai  ¼ g ic i   (7)

The coefficientg i canreadilybe combined with thereaction rateconstants in Eqs. (6s). Furthermore, to use concentrations insteadof activities is more practical.

The reaction rate constants,  k1, k2, k3  and  k4, in Eqs. (6s) weredetermined by applying nonlinear regression analysis in MATLAB7.0 program to the experimental data for each temperature.Results together with their confidence limits are given in  Table 3.

 3.5. Effect of temperature

Applying the Arrhenius equation to the values in Table 3, the

temperature dependency of the constants as well as theircorresponding activation energies was found to be:

k1 ¼ expð22:17 9667=T Þ L =mol min;   DE ¼ 80:37kJ=mol (8a)

Fig. 3.   Effect of propylene glycol concentration on the initial reaction rate

(C A0 = 0.96 mol/L, 5 (wt%) catalyst on dry basis, and 0.3 (wt%) inhibitor).

Fig. 4.   Effect of hydroxypropyl acrylate concentration on the initial reaction rate

(C A0 = 1.06 mol/L,   C P0 = 0.84 mol/L, 5 (wt%) catalyst on dry basis, and 0.3 (wt%)

inhibitor).

Fig. 5. Effect of water concentration on the initial reaction rate ( C A0 = 0.96 mol/L,

C P0 = 0.71 mol/L, 5 (wt%) catalyst on dry basis, and 0.3 (wt%) inhibitor).

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k2  ¼ expð13:83 7797=T Þ L =molmin;   DE ¼ 64:82kJ=mol (8b)

k3  ¼ expð62:63 24; 710=T Þ L =mol min;   DE 

¼ 205:44kJ=mol (8c)

k4  ¼ expð30:56 12;340=T Þ L =mol min;   DE 

¼ 102:59kJ=mol (8d)

where  T  is absolute temperature in K.The equilibrium constant, depending on temperature, for

reaction  (5a), can also be calculated from the values of  k1  and  k2

given in Eqs. (8a) and (8b) respectively, as follows:

K  ¼k1

k2¼ expð1870=T þ 8:33Þ   (9)

The heat of reaction, assuming independent of temperatureranging from 333 to 358 K, calculated to be

DH ¼ 1:870 8:314 ¼ 15:55kJ=mol (10)

This value is in good agreement with the literature value of 15.5 kJ/mol calculated by the method described in DIPPR 801 [31].

 3.6. Comparison of model and experimental data

Using the numerical values of the reaction rate constants givenin Eqs.   (8s),   Eqs.   (6s)   was solved simultaneously by applyingRunge–Kutta method for the chosen temperature. Thus concen-

tration–time curves based on the model were obtained undergiven reaction conditions. These curves, together with theexperimental data, are shown in  Figs. 6–8.

As seen in   Figs. 6–8, there is a reasonably good agreementbetween calculated curves and experimental points.

4. Conclusions

The kinetics of esterification of acrylic acid with propylene

glycol has been studied batchwise in the presence of Amberlyst-15as heterogeneous catalyst. Phenothiazine (0.3 (wt%)) was also usedas inhibitor to reduce the polymerization of acrylic acid andproduct. Taking into account the general esterification reaction as

well as polymerization of acrylic acid and products, the overallreaction mechanism can be given by Eqs. (5s). Four rate constantsin Eqs.   (6s)   were also determined from the experimental dataapplying MATLAB 7.0 program. Variations of these constants with

temperature are presented in Eqs. (8s). It was also concluded thatthe selectivity of hydroxypropyl acrylate is significantly low at

high conversion levels of acrylic acid. Therefore, to work at low

 Table 3

The average values of rate constant with 95% confidence interval at different temperatures (5 (wt%) catalyst on dry basis, and 0.3 (wt%) inhibitor).

T  (K)   k1  (104 L/mol min)   k2  (104 L/mol min)   k3 (104 L/mol min)   k4 (104 L/mol min)

333 11.21 0.81   0.74 0.56   0.09 0.015   14.95 3.09

348 30.46 3.13   1.60 1.08   2.60 0.92   78.99 5.33

358 88.84 8.13   3.94 1.42   15.48 3.08   196.48 26.16

Fig. 7. Experimental points and calculated curve from Eqs.  (6s) and (8s) (T  = 348 K,

reactant mol ratio; 1/1, 5 (wt%) catalyst on dry basis, and 0.3 (wt%) inhibitor).

Fig. 6. Experimental points and calculated curve from Eqs.  (6s) and (8s) (T  = 333 K,

reactant mol ratio; 1/1, 5 (wt%) catalyst on dry basis, and 0.3 (wt%) inhibitor).Fig. 8. Experimental points and calculated curve from Eqs.  (6s) and (8s) (T  = 358 K,

reactant mol ratio; 1/1, 5 (wt%) catalyst on dry basis, and 0.3 (wt%) inhibitor).

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conversion with a proper recycle of unreacted stream, afterproduct separation, is recommended in industrial usage.

References

[1] B. Saha, M. Streat, React. Funct. Polym. 40 (1999) 13.[2] D. Chistova,R. Velichova, W. Loos, E.J.Goethals, F.D.Prez, Polymer 44 (2003) 2255.[3] E. Ruckenstein, Y. Yuan, Polymer 38 (1997) 3855.[4] G. Moad, E. Rizzardo, S.H. Thang, Polymer 49 (2008) 1079.

[5] J. Mueller, U.S. Patent 6,512,059 (2003).[6] G.W. Borden, U.S. Patent 3,943,103 (1976).[7] M.J.Percy,J.I. Amalvy, D.P.Randall,S.P. Armes, S.J.Greaves,J.F. Watts,Langmuir 20

(2004) 2184.[8] C.D. Vo, J. Rosselgong, S.P. Armes, N.C. Billingham, Macromolecules 40 (2007)

7119.[9] The Dow Chemical Company, Product Information, Hydroxypropyl Acrylate.

[10] M.R. Altıokka, A. Cıtak, Appl. Catal. A 239 (2003) 141.[11] M.R. Altıokka, H.L. Hosgun, Ind. Eng. Chem. Res. 46 (2007) 1058.[12] V.C. Malshe, S.B. Chandalia, Chem. Eng. Sci. 32 (1977) 1530.[13] G.A. Chubarov, S.M. Danov, V.I. Logutov, T.N. Obmelyukhina, J. Appl. Chem. USSR 

57 (1984) 192.[14] V.A. Fomin, I.V. Etlis, V.I. Kulemin, J. Appl. Chem. USSR 64 (1991) 1811.

[15] P. Dupont, J.C. Vedrine, E. Paumard, G. Hecquet, F. Lefebvre, Appl. Catal. A 129(1995) 217.

[16] X. Chen, Z. Xu, T. Okuhara, Appl. Catal. A 180 (1999) 261.[17] S. Shanmugam, B. Vieswanathan, T.K. Varadarajan, J. Mol. Catal. A. 223 (2004)

143.[18] N. Essayem, V. Martin, A. Riondel, J.C. Vedrine, Appl. Catal. A 326 (2007) 74.[19] H.S. Fogler, Elementsof Chemical Reaction Engineering, Prentice Hall, NewJersey,

1999.[20] R.J. Madon, M. Boudart, Ind. Eng. Chem. Fundam. 21 (1982) 438.[21] P. Delgado, M.T. Sanz, S. Beltran, Chem. Eng. J. 126 (2007) 111.[22] W.T. Liu, Ch.S. Tan, Ind. Eng. Chem. Res. 40 (2001) 3281.

[23] V.J. Cruz, J.F. Izquierdo, F. Cunill, J. Tejero, M. Iborra, C. Fite, R. Bringue, React.Funct. Polym. 67 (2007) 210.[24] M.P. Titus, M. Bausach, J. Tejero, M. Iborra, C. Fite, F. Cunill, J.F. Izquierdo, Appl.

Catal. A 323 (2007) 38.[25] S.H. Ali, A. Tarakmah, S.Q. Merchant, T.Al-Sahhaf, Chem. Eng. Sci. 62 (2007) 3197.[26] W. Mao, X. Wang, H. Wang, H. Chang, X.Zhang, J. Han, Chem. Eng. Proc. 47 (2008)

761.[27] G.D. Yadav, H.B. Kulkarni, React. Funct. Polym. 44 (2000) 153.[28] O. Darge, F.C. Thyrion, J. Chem. Technol. Biotechnol. 58 (1993) 351.[29] S. Dassy, H. Wiame, F.C. Thyrion, J. Chem. Technol. Biotechnol. 59 (1994) 149.[30] O. Levenspiel, Chemical Reaction Engineering, Wiley, Canada, 1972.[31] Design Institute for Physical Properties Research (DIPPR), American Institute of 

Chemical Engineers, Project 801, 2006.

M.R. Altıokka, E. O des / Applied Catalysis A: General 362 (2009) 115–120120