Research ArticleMethyl Esters Selectivity of Transesterification Reaction withHomogenous Alkaline Catalyst to Produce Biodiesel in BatchPlug Flow and Continuous Stirred Tank Reactors

N F Nasir12 W R W Daud1 S K Kamarudin1 and Z Yaakob1

1 Department of Chemical and Process Engineering Faculty of Engineering and Built EnvironmentUniversiti Kebangsaan Malaysia (UKM) 43600 Bangi Selangor Malaysia

2 Department of Plant and Automotive Engineering Faculty of Mechanical and Manufacturing EngineeringUniversiti Tun Hussein Onn Malaysia Batu Pahat 86400 Parit Raja Johor Malaysia

Correspondence should be addressed to N F Nasir fitriahnasirgmailcom

Received 28 March 2014 Revised 24 July 2014 Accepted 7 August 2014 Published 25 August 2014

Academic Editor Janez Levec

Copyright copy 2014 N F Nasir et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Selectivity concept is essential in establishing the best operating conditions for attaining maximum production of the desiredproduct For complex reaction such as biodiesel fuel synthesis kinetic studies of transesterification reaction have revealed themechanismof the reaction and rate constantsThe objectives of this research are to develop the kinetic parameters for determinationof methyl esters and glycerol selectivity evaluate the significance of the reverse reaction in transesterification reaction and examinethe influence of reaction characteristics (reaction temperaturemethanol to oilmolar ratio and the amount of catalyst) on selectivityFor this study published reaction rate constants of transesterification reaction were used to develop mathematical expressions forselectivities In order to examine the base case and reversible transesterification two calculation schemes (Case 1 and Case 2) wereestablished An enhanced selectivity was found in the base case of transesterification reactionThe selectivity was greatly improvedat optimum reaction temperature (60∘C) molar ratio (9 1) catalyst concentration (15 wt) and low free fatty acid feedstockFurther research might explore the application of selectivity for specifying reactor configurations

1 Introduction

Biodiesel a major renewable fuel to replace fossil fuelis clean environmental friendly and derived from readilyavailable sources such as vegetable oils and animal fats In thebiodiesel production transesterification reaction is used toconvert triglycerides to esters It can be defined as alcoholysisof oil and fat with an alcohol to form esters and glycerol [1]Various types of catalysts such as acidic and basic catalystswhich are either homogeneous or heterogeneous as well asenzymes can catalyse the reaction

Transesterification of the oil often represented by triglyc-erides T with methanol A in the presence of a catalystusually alkaline yields esters of fatty acids E and glycerol G

Monoglyceride M and diglyceride D are the intermediatesThe overall reaction is written typically as

T + 3AcatalystlArr997904997904997904rArr 3E + G (1)

However (1) is misleading because the rates of the for-ward reactions are not equal The transesterification reactionis known to occur in three stages where D produced frommethanolysis in the first stage reaction becomes the reactantfor the second stage methanolysis and the M produced fromthe second stage reaction becomes the reactant for the thirdstage reaction The third stage reaction produces G as abyproduct All three reactions produce different types of

Hindawi Publishing CorporationInternational Journal of Chemical EngineeringVolume 2014 Article ID 931264 13 pageshttpdxdoiorg1011552014931264

2 International Journal of Chemical Engineering

methyl esters collectively designated by E The reactions areshown in (2) to (4) where 119896

+1ndash119896minus3

are rate constants

T + A119896+1

lArrrArr

119896minus1

E1 + D (2)

D + A119896+2

lArrrArr

119896minus2

E2 +M (3)

M + A119896+3

lArrrArr

119896minus3

E3 + G (4)

A stoichiometric balance of the above three reversiblereactions yield the correct form of the overall reaction whichis given below

T + (1 +

(119903+2

minus 119903minus2)

(119903+1

minus 119903minus1)

+

(119903+3

minus 119903minus3)

(119903+1

minus 119903minus1)

)A

catalyst997888997888997888997888997888rarr E

1+

(119903+2

minus 119903minus2)

(119903+1

minus 119903minus1)

E2+

(119903+3

minus 119903minus3)

(119903+1

minus 119903minus1)

E3

+ (

(119903+3

minus 119903minus3)

(119903+1

minus 119903minus1)

)G

(5)

where 119903+1

is the rate of the forward reaction in reaction 1119903minus1

is the rate of the backward reaction in reaction 1 119903+2

is the rate of the forward reaction in reaction 2 119903minus2

is therate of the backward reaction in reaction 2 119903

+3is the rate

of the forward reaction in reaction 3 and 119903minus3

is the rate ofthe backward reaction in reaction 3 Equation (5) reduces to(1) if and only if all the net rates of reactions are equal or(119903+1

minus 119903minus1) = (119903+2

minus 119903minus2) = (119903+3

minus 119903minus3)

Kinetic studies of the chemical reactions in biodieselproduction provide parameters that are used to predict theextent of the reactions at any time under any conditionPublished kinetic data of biodiesel production are mostlydependent on the type of oil feed stock and the type ofcatalyst used as well as on the reaction conditions suchas reaction temperature and catalyst concentration [2ndash4]Previous evidence suggests that an important factor in thetransesterification process is the degree of mixing betweenthe alcohol A and the triglyceride T phases As T andA phases are not miscible and they form two liquid layersupon their initial introduction into the reactor mechanicalmixing is typically applied to increase the contact between thereactants resulting in an increase in mass transfer rate [5]

Many works have studied the kinetics of the transester-ification reaction mechanism and determined its reactionrate constants [2ndash11] Leevijit et al [3] who conducted batchtransesterification reaction and evaluated the reaction rateconstants 119896

+1ndash119896minus3

found that the forward reactions are fasterthan the reverse reactions The rate constants are presentedas dataset 10 in Table 1 Similar kinetic study of palm oilmethanolysis was conducted by Narvaez et al [9] in orderto investigate the effects of temperatures and concentrationof NaOH catalyst His results also suggest that the reactionkinetics for the forward reactions dominate over the reverseFrom the result of their study on overall reaction of transes-terification the energy of activation for the forward reaction

(164 kcal gmolminus1) is greater than the energy of activation forthe reverse reaction (136 kcal gmolminus1)

A kinetic study on the transesterification of Jatrophacurcas oil by Jain and Sharma [4] using a two-step acid-basecatalyst process in a batch system found that the esterificationreaction was slower than the transesterification reactionbecause the process was assisted by the esterification reactionApart from that recent studies reported the kinetics oftransesterification reaction in the absence of a catalyst usingsoybean oil palm oil and rapeseeds oil [6ndash8 10] The rateconstants conversion and yield of E showed an increasingtrend with the reaction temperature but the E content in thereaction product decreased as the reaction temperature wasincreased

Reactor design uses information knowledge and expe-rience from a variety of areas such as thermodynamicschemical kinetics fluid mechanics heat transfer mass trans-fer and economics [12] A considerable research has beendevoted into the determination of the reaction rate constantsof transesterification reactions of various types of edible andinedible vegetable oils The published reaction rate constantsat various conditions can be further used to determine theselectivity of E and G providing opportunities for specifyingreactor configurations using process system engineering toolssuch as the attainable region method Selectivity can bedescribed in a number of different ways such as the pro-duction of the desirable component divided by the amountof limiting reactant converted or the production of desiredcomponent divided by the production of the undesiredcomponent [13] The objectives of this present work are todevelop the kinetic models of transesterification reactionand determine the selectivity of E and G using publishedreaction kinetic constants of the transesterification reactionsand to investigate the effect of reaction conditions on them Inaddition this paper evaluates the significance of the reversereactions in transesterification reaction on the E and Gselectivities

2 Methodology

21 Selectivity of Methyl Esters and Glycerol in Plug FlowReactor Theamount of free fatty acids (FFAs) in oil feedstockcould vary from 3 to 40 depending on types of oil used [14]The saponification may occur in alkali-catalyzed transesteri-fication reaction due to the reaction of acids with catalyst toproduce soaps [15] The transesterification reaction with theresulting soap formation tends to become viscous or forms agel and it is difficult to separate the glycerol from themixture[16] The saponification reaction is undesirable because itbinds the catalyst into a form that does not contribute toaccelerating the reaction [14] For feedstock having a high freefatty acid content pretreatment to the oil can be performedwith methanol [17] or glycerol [18 19] to decrease its acidityand thus reducing the potential for saponification to occurduring the reaction The presence of water in catalyzedtransesterification reaction is also undesirable because watercan consume the catalyst and reduce catalyst efficiency [20]The saponification reaction can be taken into account while

International Journal of Chemical Engineering 3

Table1Re

actio

nrateconstantsd

atafor

transeste

rificatio

nreactio

nin

biod

ieselprodu

ction

Srnum

ber

12

34

56

78

910

119896+1

(Lm

olsdots)

00500

00920

01650

000

60000

6300021

00031

01672

02251

0634

119896minus1

(Lm

olsdots)

0110

001750

02710

00016

000

0700035

000

0009373

04711

0119896+2

(Lm

ols)

02150

05440

13050

004

42000

9200072

00123

03553

01317

7104

0119896minus2

(Lm

ols)

12280

24350

464

1000127

00023

00102

01224

02674

03917

49120

119896+3

(Lm

ols)

02420

03270

04340

00050

00070

00231

000

9219

608

0119

078

600

119896minus3

(Lm

ols)

00070

00110

00170

000

0300027

00035

000

0000077

00181

01210

Temperature

(∘ C)

5060

7065

6530

3060

6060

Molar

ratio

119872R

61

61

61

91

31

91

91

61

61

61

Catalystconcentration(w

t)

02

02

02

1515

1505

1010

10Oilfeed

stock

Soybean

Soybean

Soybean

Casto

rCa

stor

Casto

rCa

stor

Rapeseed

WasteSunfl

ower

Palm

Reference

[5]

[5]

[5]

[28]

[28]

[28]

[28]

[27]

[27]

[3]

4 International Journal of Chemical Engineering

developing the kinetic model of alkali-catalyzed transes-terification reaction [21] However the kinetics parameterfor alkali-catalyzed transesterification in the present workis developed by assuming that triglycerides were pretreatedearlier Also this work represents a preliminary design ofreactors for a biodiesel plant Therefore some importantissues such as the existence of competing reaction alongwith the transesterification such as saponification reactionand the presence of water in the oil the transport processheterogeneity of the reaction and loss of polarity of analkaline catalyst were not considered

The kinetic model was developed by first performingstoichiometric mole balance of each species in a plug flowreactor (PFR) using the reaction kinetics in (2) to (4)However since a simpler mole balance of each species in abatch reactor produces the same solution as in Section 3 thebatch reactor balance is used instead

Mole balance of T is as follows

minus

119889119862T119889119905

= 119896+1119862T119862A minus 119896

minus1119862D119862E1 (6)

Mole balance of D is as follows

minus

119889119862D119889119905

= minus (119896+1119862T119862A minus 119896

minus1119862D119862E1 minus 119896

+2119862D119862A + 119896

minus2119862M119862E2)

(7)

Mole balance of M is as follows

minus

119889119862M119889119905

= minus (119896+2119862D119862A minus 119896

minus2119862M119862E2 minus 119896

+3119862M119862A + 119896

minus3119862G119862E3)

(8)

Mole balance of E1 is as follows

minus

119889119862E1119889119905

= minus (119896+1119862T119862A minus 119896

minus1119862D119862E1) (9)

Mole balance of E2 is as follows

minus

119889119862E2119889119905

= minus (119896+2119862D119862A minus 119896

minus2119862M119862E2) (10)

Mole balance of E3 is as follows

minus

119889119862E3119889119905

= minus (119896+3119862M119862A minus 119896

minus3119862G119862E3) (11)

Mole balance of A (methanol) is as follows

minus

119889119862A119889119905

= 119896+1119862T119862A minus 119896

minus1119862D119862E1 + 119896

+2119862D119862A

minus 119896minus2119862M119862E2 + 119896

+3119862M119862A minus 119896

minus3119862G119862E3

(12)

Mole balance of G is as follows

minus

119889119862G119889119905

= minus (119896+3119862M119862A minus 119896

minus3119862G119862E3) (13)

Published reaction rate constants (119896+1ndash119896119909minus3

) are listed inTable 1 In this work methanol is assumed in excess whiletriglyceride is the limiting reactant

Closed form simultaneous solution of ordinary differen-tial equations (6) to (13) by analysis is possible if only theforward reactions are considered significant but the backwardreactions are neglected On the other hand if both forwardand reverse reactions are equally significant closed formsolution for (6) to (13) cannot be found and they have to besolved numerically using a 4th order Runge-Kutta algorithmwhich is available in MATLAB The solution generates themolar concentrations of all species 119862

119894 as functions of the

design variables that is the conversion of the limitingreactant 119883T and the molar ratio of the excess variable 119872

119877

Conversion is defined as

conversion =

loss of reactantfeed of reactant

(14)

For reactant T the conversion is

119883T =

119873T0 minus 119873T119873T0

= 1 minus

119873T0119881

119873T0119881= 1 minus

119862T119862T0

(15)

Selectivity is defined as the ratio of the desired product tothe amount of limiting reactant that has undergone chemicalchange [22] That is

Selectivity

=

amount of desired productamount of limiting reactant that has undergone chemical change

(16)

In this study the total methyl ester is defined as

Total methyl ester = methyl ester 1 +methyl ester 2

+methyl ester 3

(17)

The selectivity of the totalmethyl ester 119878E and of glycerol119878G defined as the moles of total methyl ester or glycerolproduced respectively per moles of the limiting reactantT that have reacted is then formulated as functions of theconversion of triglyceride119883T as shown in

119878E =

119862E1 + 119862E2 + 119862E3119862T119900119883T

119878G =

119862G119862T119900119883T

(18)

22 Selectivity of Methyl Esters and Glycerol in ContinuousStirred Tank Reactor The kinetic model for continuousstirred tank reactor (CSTR) is much simpler The stoichio-metric mole balance of each species in a CSTR using thereaction kinetics in (2) to (4) yields a set of nonlinearequations in (19) to (26)

Mole balance of T is as follows

119862T119900 minus 119862T =

119881

119865T(119896+1119862T119862A minus 119896

minus1119862D119862E1)

= 120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1)

(19)

International Journal of Chemical Engineering 5

Mole balance of D is as follows

119862D119900 minus 119862D

= minus120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1 minus 119896

+2119862D119862A + 119896

minus2119862M119862E2)

(20)

Mole balance of M is as follows

119862M119900 minus 119862M

= minus120591 (119896+2119862D119862A minus 119896

minus2119862M119862E2 minus 119896

+3119862M119862A + 119896

minus3119862G119862E3)

(21)

Mole balance of E1 is as follows

119862E1119900 minus 119862E1 = minus120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1) (22)

Mole balance of E2 is as follows

119862E2119900 minus 119862E2 = minus120591 (119896+2119862D119862A minus 119896

minus2119862M119862E2) (23)

Mole balance of E3 is as follows

119862E3119900 minus 119862E3 = minus120591 (119896+3119862M119862A minus 119896

minus3119862G119862E3) (24)

Mole balance of A (methanol) is as follows

119862A119900 minus 119862A

= 120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1 + 119896

+2119862D119862A minus 119896

minus2119862M119862E2

+119896+3119862M119862A minus 119896

minus3119862G119862E3)

(25)

Mole balance of G is as follows

119862G119900 minus 119862G = minus120591 (119896+3119862M119862A minus 119896

minus3119862G119862E3) (26)

Closed form simultaneous solution of nonlinear equa-tions (19) to (26) by analysis is not possible They have to besolved numerically using amatrix inversion algorithmwhichis available in MATLAB The solution generates the molarconcentrations of all species 119862

119894 as functions of the design

variables that is the conversion of the limiting reactant andthe molar ratio of the excess variable 119860

3 Solution of the PFR and CSTR

31 Removal of Temporal Dependence Equations (6) to (13)cannot be solved in their time dependent forms because of thesingle degree of freedom of the problem In order to solve theequations simultaneously the degree of freedom is reduced tozero by changing the independent variable from time to theconversion or concentration of the limiting reactant using thechain rule and the mole balance equation for T (6) Considerthe following

119889119862119894

119889119862T= (

119889119862119894

119889119905

)(

119889119905

119889119862T) (27)

Hence (7) to (13) can be rewritten with concentration ofT as their independent variable as follows

119889119862D119889119862T

= minus(1 minus

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119889119862M119889119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2 minus 120572

4119862M119862A + 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119889119862E1119889119862T

= minus1

119889119862E2119889119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119889119862E3119889119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119889119862A119889119862T

= 1 +

1205722119862D119862A minus 120572

3119862M119862E2 + 120572

4119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

119889119862G119889119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

(28)

where

1205721=

119896minus1

119896+1

1205722=

119896+2

119896+1

1205723=

119896minus2

119896+1

1205724=

119896+3

119896+1

1205725=

119896minus3

119896+1

(29)

Similarly (28) cannot be solved in their time dependentforms because of the single degree of freedom of the problemIn order to solve the equations simultaneously the degreeof freedom is reduced to zero by changing the independentvariable from time to the conversion or concentration of thelimiting reactant using algebraic manipulation and the molebalance equation for T (19) Consider the following

119862119894119900minus 119862119894

119862T119900 minus 119862T= minus(

119862119894119900minus 119862119894

120591

)(

120591

119862T119900 minus 119862T) (30)

Hence (28) can be rewritten with concentration of T astheir independent variable as follows

119862D119900 minus 119862D119862T119900 minus 119862T

= minus(1 minus

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119862M119900 minus 119862M119862T119900 minus 119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2 minus 120572

4119862M119862A + 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119862E1119900 minus 119862E1119862T119900 minus 119862T

= minus1

6 International Journal of Chemical Engineering

119862E2119900 minus 119862E2119862T119900 minus 119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119862E3119900 minus 119862E3119862T119900 minus 119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119862A119900 minus 119862A119862T119900 minus 119862T

= 1 +

1205722119862D119862A minus 120572

3119862M119862E2 + 120572

4119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

119862G119900 minus 119862G119862T119900 minus 119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

) (31)

Two main cases are considered the base case where thereactions (2) to (4) are irreversible and the alternative casewhere the reactions are reversible

32 Case 1 Base Case Irreversible Reactions In Case 1 thebase case is considered by assuming (2) to (4) to be irre-versible reactions In other words the forward reactions areso dominant that the reverse reaction can be neglected andthe overall effect is that the reactions are irreversible Theresults of the base case can then be compared with that of thealternative Case 2 where the reactions are all reversible inorder to verify the importance of the reverse reaction and itsimplication to the maximum attainable molar concentrationof methyl ester Since the reverse reactions are omitted thevalue of 120572

1 1205723 and 120572

5is zero Hence (28) for PFR can be

rewritten as follows

119889119862D119889119862T

= minus(1 minus

1205722119862D

119862T) (32)

119889119862M119889119862T

= minus(

1205722119862D minus 120572

4119862M

119862T) (33)

119889119862E1119889119862T

= minus1 (34)

119889119862E2119889119862T

= minus

1205722119862D

119862T (35)

119889119862E3119889119862T

= minus

1205724119862M119862T

(36)

119889119862A119889119862T

= 1 +

1205722119862D + 120572

4119862M

119862T (37)

119889119862G119889119862T

= minus

1205724119862M119862T

(38)

The solution of the set of ordinary differential equations(32) can be found analytically by using the integrating factormethod [23] The concentrations of all the species generated

by the solution are then expressed in terms of the triglyceridesconversion119883T as shown in

119862T = 119862T119900 (1 minus 119883T)

119862D =

119862T1199001205722minus 1

[(

119862T119862T119900

) minus (

119862T119862T119900

)

1205722

]

=

119862T1199001205722minus 1

[(1 minus 119883T) minus (1 minus 119883T)1205722

]

119862M = 119862T119900 [1205722

1 minus 1205722

[

(1 minus 119883T)

1 minus 1205724

minus

(1 minus 119883T)1205722

1205722minus 1205724

]

+

1205722(1 minus 119883T)

1205724

(1 minus 1205724) (1205722minus 1205724)

]

119862E1 = 119862T119900 (1 minus (

119862T119862T119900

)) = 119862T119900 (1 minus (1 minus 119883T)) = 119862T119900119883T

119862E2 = 119862T119900 1 minus

1205722

1205722minus 1

[(1 minus 119883T) minus(1 minus 119883T)

1205722

1205722

]

119862E3 = 1205724119862T119900 [

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

119862A = 119862T119900 119872119877+

1205722

(1 minus 1205722)

times [(

(1 minus 1205722)

1205722

+

21205724minus 1

(1 minus 1205724)

)119883T

minus (

21205724minus 1205722

1205722(1205722minus 1205724)

) [1 minus (1 minus 119883T)1205722

]

minus

(1 minus 1205722)

(1 minus 1205724) (1205722minus 1205724)

times [1 minus (1 minus 119883T)1205724

] ]

119862G = 1205724119862T119900 [

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(39)

For the CSTR (31) can be manipulated algebraically andrewritten with conversion of T as their independent variableas follows

119862D =

119862T119900119883T (1 minus 119883T)

(1 minus (1 minus 1205722)119883T)

(40)

International Journal of Chemical Engineering 7

119862M =

1205722119862T119900119883

2

T (1 minus 119883T)

(1 minus (1 minus 1205724)119883T) (1 minus (1 minus 120572

2)119883T)

(41)

119862E1 = 119862T119900119883T (42)

119862E2 =1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

(43)

119862E3 =12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(44)

119862A = 119862T119900 (119872119877minus 1 +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

)

(45)

119862G =

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(46)

33 Case 2 Alternative Case Reversible Reactions In Case 2an alternative case was considered by assuming that thereactions in (2) to (4) are reversible Together with the basecase where the reactions are irreversible it can be used todiscover the significance of the reverse and forward reactions

Since the values of all 120572119894rsquos in (28) for the PFR and

(31) for the CSTR are not zero no closed form solutionto them can be found because they are too complex foranalytical solution The solution of both sets of equationscan be achieved by numerical methods using a computersimulation software Equations (28) for the PFR are solvedby using the ordinary differential equation 45 (ODE 45) inMATLAB Concentration of each species is obtained usingRungge-Kutta numerical integration algorithm On the otherhand (31) for the CSTR are solved by using the simultaneousnonlinear equations solver in MATLAB Concentration ofeach species is obtained using the multivariable Newton-Raphson algorithm

34 Selectivity of Methyl Esters and Glycerol for Case 1 andCase 2 The net concentration of methyl esters is the sum ofconcentration of ester 1 ester 2 and ester 3 In Case 1 the netconcentration of methyl esters in the PFR is given by

119862E1 + 119862E2 + 119862E3

= 119862T119900 1 + 119883T minus

1205722

1205722minus 1

[(1 minus 119883T) minus(1 minus 119883T)

1205722

1205722

]

+1205724[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(47)

Similarly the net concentration of methyl esters in theCSTR for Case 1 is given by

119862E1 + 119862E2 + 119862E3

= 119862E1119900 + 119862E2119900 + 119862E3119900

+ [119862T119900119883T +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(48)

The selectivity of methyl esters in Case 1 for PFR is givenby

119878E =

119883T + 1

119883Tminus

1205722

1205722minus 1

[

(1 minus 119883T)

119883Tminus

(1 minus 119883T)1205722

1205722119883T

]

+1205724[

1205722

1 minus 1205722

[

1

1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722119883T

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724119883T

]

(49)

The selectivity of glycerol in Case 1 for PFR is given by

119878G =

1205724

119883T[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(50)

On the other hand the selectivity of methyl esters inCase 1 for CSTR is given by

119878E = [1 +

1205722119883T

(1 minus (1 minus 1205722)119883T)

+

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(51)

The selectivity of glycerol in Case 1 for CSTR is given by

119878G =

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(52)

For Case 2 there is no closed form expression for selec-tivity of methyl esters and glycerolThe selectivities of methylesters and glycerol have to be calculated using (18) fromthe concentration of the species generated by the numericalsolution

4 Results and Discussion

41 Comparison of Selectivities for Cases 1 and 2 This studyhas shown the development of kinetic parameters for deter-mining methyl esters and glycerol selectivity in a biodiesel

8 International Journal of Chemical Engineering

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

ity

Conversion of triglyceride XT

Case 1-T = 60∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 60∘C MR = 6 1 catalyst = 02 wt

Figure 1 Selectivity plots of Cases 1 and 2 at reaction temperature60∘C molar ratio 6 1 and catalyst concentration 02 wt

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

ity

Conversion of triglyceride XT

Case 1-T = 70∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 70∘C MR = 6 1 catalyst = 02 wt

Figure 2 Selectivity plots of Cases 1 and 2 at reaction temperature70∘C molar ratio 6 1 and catalyst concentration 02 wt

transesterification reaction it has also established severalmathematical equations for the same Furthermore a par-ticularly important parameter for designing a reactor thatis product selectivity was determined for each case andcondition For comparing the base case and an alternativecase datasets 2 and 3 were evaluated using each calculationschemesThe difference in the selectivity between Case 1 andCase 2 which were investigated under the same conditionsis very significant and is attributed to the reversibility factorof the reaction as illustrated in Figures 1 and 2The results ofthe base case show that when all the reactions are irreversibleit implies that the maximum attainable molar concentrationand selectivity ofmethyl ester have been reachedThis verifiesthe significant role of the forward reactions in (2)ndash(4)

For a simple reversible reaction we can see the effectsof thermodynamic parameter like temperature on thereversibility of the reaction whereas the reversibility ofa reaction is controlled by reaction equilibrium constant

Table 2 Selectivity at 07ndash09 triglycerides conversion for datasets(1ndash3) and (6-7)

Conversion119883T Dataset Methyl esters selectivityCase 1 Case 2

07

1 2610 25262 2643 25113 2630 24706 2610 26137 2493 2313

08

1 2766 26752 2784 26663 2769 26296 2764 27667 2682 2480

09

1 2895 28322 2903 28163 2892 27886 2893 28797 2852 2655

The reaction equilibrium constant 119870 is defined as theforward rate constant divided by the reverse rate constant andaffected by temperature [12] This transesterification reactionis a complex reaction which consists of three reversibleand consecutive reactions Therefore for simplification andpreliminary design purpose selectivity is effectively used todetermine the effect of temperature and role of catalyst onthe reversibility Figures 1 and 2 show significant changes ofthe selectivity plots for conversion of triglycerides from 07to 09 and the plots finally reach the equilibrium at the endof the reaction In order to access the role of temperature andamount of catalyst on the reversibility of transesterificationreaction Table 2 was constructed by observing the methylesters selectivity for conversion of triglycerides from 07 to09 It presents the difference in selectivity for Case 1 andCase 2 Datasets (1ndash3) are used to determine the effects ofdifferent temperatures on the reversibility of the transesterifi-cation reaction which represent a temperature of 50 60 and70 respectively Conversion of triglyceride at 09 is selectedfor analysis From this data we can see that the forwardreaction alone is able to provide better selectivity than reversereaction at any temperature Datasets (6-7) are used to ana-lyze the role catalyst on the reversibility of transesterificationreaction whereas datasets 6 and 7 represent the amount ofcatalyst of 15 and 05 respectively A significant role ofthe forward reaction once again was determined at a highercatalyst concentrationThe results obtained also indicate thata higher catalyst concentration controls the forward reactionsand gives preferably product selectivity

According to Narvaez et al [9] and Noureddini and Zhu[5] the forward reactions in a transesterification reaction arethe most important reactions However Diasakou et al [7]claimed that the reverse reactions during a transesterificationreaction do not influence the forward reactions In this studya lower concentration of methyl ester was found for Case 2

International Journal of Chemical Engineering 9

Table 3 Activation energy

Reaction Activation energy (calmol)T rarr D 13145D rarr T 9932D rarr M 19860M rarr D 14639M rarr G 6421G rarr M 9588

which affects the selectivity and methyl ester conversionwhich is likely due to the reverse nature of the reaction [4]This result suggests that for establishing the optimal chemicalprocess for biodiesel fuel production it can be assumed thatwhen irreversible reactions are employed better selectivitycan be obtained because of the absence of reverse reactions

42 Effects of Reaction Characteristics on Selectivity Thereactor design stage for a biodiesel plant utilizes methyl esterselectivity for the material balances and stream costs Attain-ing the appropriate operating conditions through productselectivity can eliminate material and energy recycling thusreducing costsThe effects of the reaction temperature molarratio of methanol to oil and the catalyst concentration on theselectivity of methyl esters and glycerol are analyzed for bothCase 1 and Case 2 in the following subsections

421 Effect of ReactionTemperature on Selectivity An investi-gation on the effect of temperature onmethyl ester selectivitywas conducted using datasets (1ndash3) where the molar ratio ofalcohol to oil and the catalyst concentration are fixed TheArrhenius equation was used for this investigation

119896 = 119896∘exp(minus

119864

119877119879

) (53)

According to (53) the reaction rate 119896 is an integralpart of the selectivity expressions It depends on the energyof activation (119864) obtained from the Arrhenius equation[22] For reactions at different temperatures fixed molarratios and catalyst concentrations the activation energy isconstant In this study the kinetic data used to analyzethe temperature effect were adapted from Noureddini andZhu [5] Because the data published in their research utilizethe average reaction rate constants at 50∘C and constantactivation energy (53) can bemanipulated to obtain the otherreaction rate constants (at 60∘C and 70∘C) listed in Table 1The results of the activation energy investigated in their studyare shown in Table 3

Figures 3 and 4 show the effects of the reaction tempera-ture on the selectivity ofmethyl esters and glycerol for Cases 1and 2 respectively The reaction temperature had a small butsubstantial effect on the selectivity The figures show thatthe selectivity of methyl esters is high at a high temperaturein the early conversion of T However in both figures theselectivities of E for both Cases 1 and 2 at 70∘C were foundto decrease toward the completion of the reaction As theboiling point of methanol is 647∘C an additional 5∘C has

0

02

04

06

08

1

12

00

05

10

15

20

25

30

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 3 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 1

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 4 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 2

the effect of lowering the product concentration and affectingthe selectivity of E at the equilibriumThis temperature effectchanges the slope of selectivity from a concave to a convexshape which is also related with the reaction rate constant atdifferent temperatures

According to Darnoko and Cheryan [2] the transester-ification reaction rates were increased at 65∘C as comparedwith those at 50∘C The results of their research also showedan enhanced methyl ester yield at 65∘C compared withthat at 50∘C which was because of the higher viscosity ofoil at 50∘C In addition 55∘C is a stable temperature thatcan maintain the oil liquidity This result indicates that anoptimum temperature promotes the formation of methylesters and thus contributes to a higher selectivity of biodieselproducts It can also be suggested that the reaction rateconstant 119896 which is greatly dependent on the temperatureand selectivity of E is greatly improved at the optimumtemperature

10 International Journal of Chemical Engineering

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 5 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 1

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 6 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 2

The findings confirm that methyl ester selectivity effectscan be realistically obtained at the optimum temperaturewhich is 60∘C in this study As the reactor optimizationrequires the relationship between the conversion and selec-tivity in both cases (Case 1 and Case 2) the selectivity withinthe studied temperature indicates that the biodiesel reactormay work more efficiently in converting T to E at 60∘C

422 Effect of Molar Ratio of Methanol to Oil on SelectivityAn investigation into the effects of the methanol-to-oil molarratio involves datasets 4 and 5 Selectivity plots of methylesters and glycerol are shown in Figures 5 and 6 For Cases 1and 2 the selectivity of methyl esters and glycerol was rela-tively affected by the molar ratio of methanol to oil It can beseen from the figures that the higher molar ratio of methanolto oil encourages the formation of transesterification reactionproducts thus contributing to a higher selectivity

The most striking result to emerge from the figures isthe change in the shape of the selectivity plot from concave

0

02

04

06

08

1

12

0 02 04 06 08 1

Sele

ctiv

ity

(a)(b)

(c)

Triglyceride conversion XT

Figure 7 Selectivity plots (a) methyl ester 1 (b) methyl ester 2 and(c) methyl ester 3 for dataset 4

to convex for a molar ratio of 9 1 An increasing selectivityof methyl ester can be found in an early conversion oftriglyceride but toward equilibrium the selectivity is foundto slightly decrease A possible explanation for this mightbe that the methyl ester concentration has both quadratic aswell as cubic effects that can be explained by (42)ndash(44) andFigure 7

According to (42) the selectivity of methyl ester 1 isconstant at 1 Equation (43) is a quadratic equation whichgives a parabolic shape to the plot of methyl ester 2 Equation(44) clearly illustrates the selectivity of methyl ester 3 whenthe equation is a cubic one In more detail the power of twois more dominant at an 119883T of less than 03 which meansthat the formation of E2 is more active under this conditionHowever we can see an active formation of E3 at an 119883Tof 05ndash1 when the power of three is dominant At the sametime E1 is formed linearly with a triglyceride conversionThe stepwise transesterification reaction in (2)ndash(4) shows thateach E is formed consecutivelyThismeans that to achieve themaximum yield the maximum selectivity at the maximum Tconversion is necessary and each E must be formed duringthe process Therefore it can be assumed that the selectivityof methyl ester is more greatly affected by the quadratic andcubic functions at a highermolar ratio ofmethanol to oil thanat a lower one

In addition Freedman et al [11] reported that the bestmethyl ester conversion is achieved at a molar ratio of 6 1with alkaline catalyst and that higher molar ratios do notincrease the productivity but do increase the cost of alcoholrecovery At a high molar excess of methanol a pseudo-first-order reaction appeared more likely than a second-order reaction However high molar ratio of methanol isused for noncatalytic and supercritical methanol reaction[6 11 20 24] Narvaez et al [9] stated that when an excessamount of methanol is used it can positively affect thereversible characteristic of the reaction and the displacementof the reaction toward the product As a consequence excessmethanol does not necessarily contribute to an increase in theconcentration of methyl ester and glycerol

International Journal of Chemical Engineering 11

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 8 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 9 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 2

423 Effect of Catalyst Concentration on Selectivity Apartfrom the temperature and molar ratio the parameters thataffect the selectivity are the same as those influencing thereaction rates namely the catalyst The effects of the catalystconcentration are studied through datasets 6 and 7 andthe selectivity plots can be seen in Figures 8 and 9 Whenanalyzing the figures it can be seen that the selectivity of bothproducts is higher at a higher catalyst concentration

Toward the equilibrium of the reaction the selectivitywas observed to increase at a higher catalyst concentra-tion thus contributing to an increased amount of methylester formation Vicente et al [25] stated that the largestmethyl ester conversions are obtained when a large catalystconcentration is employed (13) at a mild temperature(20ndash50∘C) This agrees with the resulting selectivity curvesplotted which indicates that the catalyst concentration hasa positive effect on the selectivity of methyl esters andglycerol However a greater application of an alkali catalystcan lead to the production of large amounts of soap andextra cost is required to remove the catalyst from the reactionsystem Srivastava and Prasad [26] have stated that a catalyst

0

02

04

06

08

1

12

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity

(a)

(c)(b)

Triglyceride conversion XT

Figure 10 Selectivity plots (a)methyl ester 1 (b)methyl ester 2 and(c) methyl ester 3 for dataset 6

concentration of 05ndash1 can yield up to a 99 methyl esterconversion

In Figures 8 and 9 there is a clear increasing trend of theselectivity ofmethyl ester for a 15 wt catalyst concentrationduring the early conversion of the reactant which decreasesat the end of the reactionThe same transition trend has beenfound when analyzing the influence of the molar ratio onmethyl ester selectivity A further detailed analysis showedthat the quadratic and cubic effects are more significantat a higher catalyst concentration than at a lower catalystconcentration As shown in Figure 10 the selectivity of E2 hasa quadratic plot whereas the selectivity of E3 has a parabolicshape Referring to (42)ndash(44) we can see that E1 is linearlyformed with a T conversion E2 is produced more at a Tconversion of lower than 035 where we can see that thepower of two in (43) is more dominant at this stage At aT conversion of over 05 the effect of the power of three in(44) is dominant causing a higher formation of E3 Becausethe transesterification reaction is a reversible and consecutiveequation the formation of three Es is important to achievea better selectivity With an optimum amount of catalyst thereactor becomesmore efficient in converting the reactant intothe products

43 Comparison ofMethyl Ester Selectivities fromDifferent OilFeedstocks To compare the selectivities of methyl esters andglycerol from different feedstocks datasets (8ndash10) were usedFigure 11 presents the selectivity ofmethyl esters derived fromrapeseed oil waste sunflower oil and palm oil for Case 1 andCase 2 As can be seen from the graph the methyl estersand glycerol were more likely to form if palm oil is used asthe feedstock compared to the other two oil feedstocks Thepresent finding also suggests that the selectivity of methylester was much lower when using low cost feedstock such aswaste sunflower oil Waste oil contains large amounts of freefatty acids (FFAs) (about 20) which affect the yield of fuelfrom that process The amount of FFAs in palm oil is 064[3] but for rapeseed oil the author used fresh oil [27] whichis estimated less than 1

12 International Journal of Chemical Engineering

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

PO-case 1 RO-case 1

WSO-case 1 WSO-case 2RO-case 2PO-case 2

Conversion of triglyceride XT

Sele

ctiv

ity o

f met

hyl e

sters

Figure 11 Selectivity plots of methyl ester from various feedstockfor Cases 1 and 2

As discussed before these free fatty acids will reactwith alkali catalysts to produce soaps that will inhibit thetransesterification reaction Soaps will allow emulsificationthat causes the phase separation of methyl ester and glycerolto be less sharp It produces water that can hydrolyze thetriglycerides and contribute to the formation of more soap[14] The effect of reversibility of transesterification can beseen significantly when analysing the selectivity of methylester derived from palm oil In Figure 11 methyl ester derivedfrom palm oil shows a higher selectivity plot for base caseThis finding suggests that forward reaction dominates thereaction and contributes to a better selectivity when lowFFAs feedstock is used in biodiesel production As there aremany low cost feedstocks available for biodiesel productiona pretreatment to these feedstocks can be carried out in orderto ensure the value of FFAs is within the allowable range

5 Conclusions

This paper has presented a comprehensive kinetic modelingof a transesterification reaction for biodiesel with homoge-neous alkaline catalyst The purpose of the study was todevelop the kinetic models of transesterification reactiondetermine the selectivity of methyl ester and glycerol andevaluate the significance of the reverse reactions in the trans-esterification reaction This study has shown that a processmodel solution was found for two types of common biodieselreactors The concentration of each species during transes-terification was found leading to a selectivity determinationduring the biodiesel production In addition the reversibleand irreversible effects of a transesterification reaction werediscovered The forward reaction is more dominant than thereverse reaction and the maximum selectivity can be foundif a base case of transesterification reaction is assumed tohave occurred in the biodiesel reactor system For the variousreaction characteristics under investigation the selectivities

are influenced by the temperature molar ratio of methanolto oil catalyst concentration and type of oil used as thefeedstock Furthermore an analysis of the selectivity plotsindicates an enhanced effect of the reaction characteristicson the selectivity This research has shown that the selectivityof methyl ester is maximized at 60∘C a 9 1 molar ratio ofmethanol to oil and a catalyst concentration of 15 Thisinvestigation into the effects of the molar ratio of methanolto oil and the catalyst concentration on the selectivity canbe made more interesting if several more curves are plottedat a molar ratio of methanol to oil between 3 1 to 9 1 anda catalyst concentration between 05 and 15 Howevera limitation of this research remains in the availability ofthe reaction rate constants under various reaction condi-tions In addition a comparison should be made throughmutual reaction conditionsThe findings from this study willenhance the concept of selectivity and its applications inthe evaluation of complex transesterification reactions whenthe goal is to attain the maximum production of methylesters and glycerol It is recommended that further researchis undertaken in exploring the selectivity data for specifyingthe reactor configurations and may be used in the synthesisof reactor network for biodiesel production

Nomenclature

119896+1 119896minus1 119896+2

119896minus2 119896+3 119896minus3

Reaction constant

119862T 119862D 119862M 119862G119862E1 119862E2 119862E3119862A 119862E

Molar concentration of triglyceridediglyceride monoglyceride glycerolester 1 ester 2 ester 3 methanol andmethyl ester

119883T Conversion of triglyceride119872119877 Molar ratio

119862T0 Initial molar concentration oftriglyceride

119878E 119878G Selectivity of methyl ester glycerol120572 Reaction rate constant factorwt Weight percentT TriglycerideD DiglycerideM MonoglycerideA MethanolG GlycerolE Methyl esterE1 Methyl ester 1E2 Methyl ester 2E3 Methyl ester 3PFR Plug flow reactorCSTR Continuous stirred tank reactor119873T0 Initial amount of triglyceride at 119905 = 0

119873T The amount of triglyceride present attime 119905

119881 VolumePO Palm oilRO Rapeseed oilWSO Waste sunflower oilNaOH Sodium hydroxide

International Journal of Chemical Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgment

Thework was carried out with the financial support from theMinistry of Education Malaysia

References

[1] A Demirbas ldquoBiodiesel from triglycerides via transesterifica-tionrdquo in Biodiesel pp 121ndash140 Springer London UK 2008

[2] D Darnoko and M Cheryan ldquoKinetics of palm oil transesteri-fication in a batch reactorrdquo JAOCS Journal of the American OilChemistsrsquo Society vol 77 no 12 pp 1263ndash1267 2000

[3] T Leevijit WWisutmethangoon G Prateepehaikul C Tongu-rai and M Allen ldquoA second order kinetics of palm oil transes-terification in a batch reactorrdquo in Proceedings of the Joint Inter-national Conference on Sustainable Energy and Environment pp277ndash281 2004

[4] S Jain andM P Sharma ldquoKinetics of acid base catalyzed trans-esterification of Jatropha curcas oilrdquo Bioresource Technology vol101 no 20 pp 7701ndash7706 2010

[5] H Noureddini and D Zhu ldquoKinetics of transesterification ofsoybean oilrdquo Journal of the American Oil Chemistsrsquo Society vol74 no 11 pp 1457ndash1463 1997

[6] D Kusdiana and S Saka ldquoKinetics of transesterification in rape-seed oil to biodiesel fuel as treated in supercritical methanolrdquoFuel vol 80 no 5 pp 693ndash698 2001

[7] M Diasakou A Louloudi and N Papayannakos ldquoKinetics ofthe non-catalytic transesterification of soybean oilrdquo Fuel vol 77no 12 pp 1297ndash1302 1998

[8] H Maeda S Hagiwara H Nabetani et al ldquoBiodiesel fuelsfrom palm oil via the non-catalytic transesterification in abubble column reactor at atmospheric pressure a kinetic studyrdquoRenewable Energy vol 33 no 7 pp 1629ndash1636 2008

[9] P C Narvaez S M Rincon and F J Sanchez ldquoKinetics of palmoil methanolysisrdquo Journal of the American Oil Chemistsrsquo Societyvol 84 pp 971ndash977 2007

[10] E Minami and S Saka ldquoKinetics of hydrolysis and methylesterification for biodiesel production in two-step supercriticalmethanol processrdquo Fuel vol 85 no 17-18 pp 2479ndash2483 2006

[11] B Freedman R O Butterfield and E H Pryde ldquoTransesteri-fication kinetics of soybean oil 1rdquo Journal of the American OilChemistsrsquo Society vol 63 no 10 pp 1375ndash1380 1986

[12] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

[13] J M Douglas Conceptual Design of Chemical ProcessesMcGraw Hill 1988

[14] J van Gerpen B Shanks R Pruszko D Clements and GKnothe Biodiesel Production Technology Subcontractor ReportNational Reanewable Energy Laboratory 2004

[15] H J Wright J B Segur H V Clark S K Coburn E ELangdon and R N DuPuis ldquoA report on ester interchangerdquoOilamp Soap vol 21 no 5 pp 145ndash148 1944

[16] H Fukuda A Kondo and H Noda ldquoBiodiesel fuel productionby transesterification of oilsrdquo Journal of Bioscience and Bioengi-neering vol 92 no 5 pp 405ndash416 2001

[17] L Friesenhagen and H Lepper ldquoProcess for the productionof fatty acid esters of short-chain aliphatic alcohols from fatsandor oils containing free fatty acidsrdquoUS Patent 4608202 1986

[18] P Felizardo J MacHado D Vergueiro M J N Correia J PGomes and J M Bordado ldquoStudy on the glycerolysis reactionof high free fatty acid oils for use as biodiesel feedstockrdquo FuelProcessing Technology vol 92 no 6 pp 1225ndash1229 2011

[19] A Tafesh and S Basheer ldquoPretreatment methods in biodieselproduction processesrdquo in Pretreatment Techniques for Biofuelsand Biorefineries Z Fang Ed Green Energy and Technologypp 417ndash434 Springer Berlin Germany 2013

[20] D Kusdiana and S Saka ldquoEffects of water on biodiesel fuelproduction by supercritical methanol treatmentrdquo BioresourceTechnology vol 91 no 3 pp 289ndash295 2004

[21] K Komers F Skopal R Stloukal and J Machek ldquoKinetics andmechanism of the KOHmdashcatalyzed methanolysis of rapeseedoil for biodiesel productionrdquo European Journal of Lipid Scienceand Technology vol 104 pp 728ndash737 2002

[22] A K CokerModeling of Chemical Kinetics and Reactor DesignGulf Publishing Houston Tex USA 2001

[23] C D Holland and R G Anthony Fundamentals of ChemicalReaction Engineering Prentice-Hall 1979

[24] J K Rodrıguez-Guerrero M F Rubens and P T V RosaldquoProduction of biodiesel from castor oil using sub and super-critical ethanol effect of sodium hydroxide on the ethyl esterproductionrdquoThe Journal of Supercritical Fluids vol 83 pp 124ndash132 2013

[25] G Vicente M Martınez and J Aracil ldquoOptimisation ofintegrated biodiesel production Part I A study of the biodieselpurity and yieldrdquoBioresource Technology vol 98 no 9 pp 1724ndash1733 2007

[26] A Srivastava and R Prasad ldquoTriglycerides-based diesel fuelsrdquoRenewable and Sustainable Energy Reviews vol 4 no 2 pp 111ndash133 2000

[27] B Klofutar J Golob B Likozar C Klofutar E Zagar andI Poljansek ldquoThe transesterification of rapeseed and wastesunflower oils mass-transfer and kinetics in a laboratory batchreactor and in an industrial-scale reactorseparator setuprdquoBioresource Technology vol 101 no 10 pp 3333ndash3344 2010

[28] S D Crymble ldquoOptimization and Reaction Kinetics of the Pro-duction of Biodiesel from Castor Oil via Sodium Methoxide-Catalyzed Methanolysisrdquo Dave C Swalm School of ChemicalEngineering Mississippi State University Miss USA 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

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2 International Journal of Chemical Engineering

methyl esters collectively designated by E The reactions areshown in (2) to (4) where 119896

+1ndash119896minus3

are rate constants

T + A119896+1

lArrrArr

119896minus1

E1 + D (2)

D + A119896+2

lArrrArr

119896minus2

E2 +M (3)

M + A119896+3

lArrrArr

119896minus3

E3 + G (4)

A stoichiometric balance of the above three reversiblereactions yield the correct form of the overall reaction whichis given below

T + (1 +

(119903+2

minus 119903minus2)

(119903+1

minus 119903minus1)

+

(119903+3

minus 119903minus3)

(119903+1

minus 119903minus1)

)A

catalyst997888997888997888997888997888rarr E

1+

(119903+2

minus 119903minus2)

(119903+1

minus 119903minus1)

E2+

(119903+3

minus 119903minus3)

(119903+1

minus 119903minus1)

E3

+ (

(119903+3

minus 119903minus3)

(119903+1

minus 119903minus1)

)G

(5)

where 119903+1

is the rate of the forward reaction in reaction 1119903minus1

is the rate of the backward reaction in reaction 1 119903+2

is the rate of the forward reaction in reaction 2 119903minus2

is therate of the backward reaction in reaction 2 119903

+3is the rate

of the forward reaction in reaction 3 and 119903minus3

is the rate ofthe backward reaction in reaction 3 Equation (5) reduces to(1) if and only if all the net rates of reactions are equal or(119903+1

minus 119903minus1) = (119903+2

minus 119903minus2) = (119903+3

minus 119903minus3)

Kinetic studies of the chemical reactions in biodieselproduction provide parameters that are used to predict theextent of the reactions at any time under any conditionPublished kinetic data of biodiesel production are mostlydependent on the type of oil feed stock and the type ofcatalyst used as well as on the reaction conditions suchas reaction temperature and catalyst concentration [2ndash4]Previous evidence suggests that an important factor in thetransesterification process is the degree of mixing betweenthe alcohol A and the triglyceride T phases As T andA phases are not miscible and they form two liquid layersupon their initial introduction into the reactor mechanicalmixing is typically applied to increase the contact between thereactants resulting in an increase in mass transfer rate [5]

Many works have studied the kinetics of the transester-ification reaction mechanism and determined its reactionrate constants [2ndash11] Leevijit et al [3] who conducted batchtransesterification reaction and evaluated the reaction rateconstants 119896

+1ndash119896minus3

found that the forward reactions are fasterthan the reverse reactions The rate constants are presentedas dataset 10 in Table 1 Similar kinetic study of palm oilmethanolysis was conducted by Narvaez et al [9] in orderto investigate the effects of temperatures and concentrationof NaOH catalyst His results also suggest that the reactionkinetics for the forward reactions dominate over the reverseFrom the result of their study on overall reaction of transes-terification the energy of activation for the forward reaction

(164 kcal gmolminus1) is greater than the energy of activation forthe reverse reaction (136 kcal gmolminus1)

A kinetic study on the transesterification of Jatrophacurcas oil by Jain and Sharma [4] using a two-step acid-basecatalyst process in a batch system found that the esterificationreaction was slower than the transesterification reactionbecause the process was assisted by the esterification reactionApart from that recent studies reported the kinetics oftransesterification reaction in the absence of a catalyst usingsoybean oil palm oil and rapeseeds oil [6ndash8 10] The rateconstants conversion and yield of E showed an increasingtrend with the reaction temperature but the E content in thereaction product decreased as the reaction temperature wasincreased

Reactor design uses information knowledge and expe-rience from a variety of areas such as thermodynamicschemical kinetics fluid mechanics heat transfer mass trans-fer and economics [12] A considerable research has beendevoted into the determination of the reaction rate constantsof transesterification reactions of various types of edible andinedible vegetable oils The published reaction rate constantsat various conditions can be further used to determine theselectivity of E and G providing opportunities for specifyingreactor configurations using process system engineering toolssuch as the attainable region method Selectivity can bedescribed in a number of different ways such as the pro-duction of the desirable component divided by the amountof limiting reactant converted or the production of desiredcomponent divided by the production of the undesiredcomponent [13] The objectives of this present work are todevelop the kinetic models of transesterification reactionand determine the selectivity of E and G using publishedreaction kinetic constants of the transesterification reactionsand to investigate the effect of reaction conditions on them Inaddition this paper evaluates the significance of the reversereactions in transesterification reaction on the E and Gselectivities

2 Methodology

21 Selectivity of Methyl Esters and Glycerol in Plug FlowReactor Theamount of free fatty acids (FFAs) in oil feedstockcould vary from 3 to 40 depending on types of oil used [14]The saponification may occur in alkali-catalyzed transesteri-fication reaction due to the reaction of acids with catalyst toproduce soaps [15] The transesterification reaction with theresulting soap formation tends to become viscous or forms agel and it is difficult to separate the glycerol from themixture[16] The saponification reaction is undesirable because itbinds the catalyst into a form that does not contribute toaccelerating the reaction [14] For feedstock having a high freefatty acid content pretreatment to the oil can be performedwith methanol [17] or glycerol [18 19] to decrease its acidityand thus reducing the potential for saponification to occurduring the reaction The presence of water in catalyzedtransesterification reaction is also undesirable because watercan consume the catalyst and reduce catalyst efficiency [20]The saponification reaction can be taken into account while

International Journal of Chemical Engineering 3

Table1Re

actio

nrateconstantsd

atafor

transeste

rificatio

nreactio

nin

biod

ieselprodu

ction

Srnum

ber

12

34

56

78

910

119896+1

(Lm

olsdots)

00500

00920

01650

000

60000

6300021

00031

01672

02251

0634

119896minus1

(Lm

olsdots)

0110

001750

02710

00016

000

0700035

000

0009373

04711

0119896+2

(Lm

ols)

02150

05440

13050

004

42000

9200072

00123

03553

01317

7104

0119896minus2

(Lm

ols)

12280

24350

464

1000127

00023

00102

01224

02674

03917

49120

119896+3

(Lm

ols)

02420

03270

04340

00050

00070

00231

000

9219

608

0119

078

600

119896minus3

(Lm

ols)

00070

00110

00170

000

0300027

00035

000

0000077

00181

01210

Temperature

(∘ C)

5060

7065

6530

3060

6060

Molar

ratio

119872R

61

61

61

91

31

91

91

61

61

61

Catalystconcentration(w

t)

02

02

02

1515

1505

1010

10Oilfeed

stock

Soybean

Soybean

Soybean

Casto

rCa

stor

Casto

rCa

stor

Rapeseed

WasteSunfl

ower

Palm

Reference

[5]

[5]

[5]

[28]

[28]

[28]

[28]

[27]

[27]

[3]

4 International Journal of Chemical Engineering

developing the kinetic model of alkali-catalyzed transes-terification reaction [21] However the kinetics parameterfor alkali-catalyzed transesterification in the present workis developed by assuming that triglycerides were pretreatedearlier Also this work represents a preliminary design ofreactors for a biodiesel plant Therefore some importantissues such as the existence of competing reaction alongwith the transesterification such as saponification reactionand the presence of water in the oil the transport processheterogeneity of the reaction and loss of polarity of analkaline catalyst were not considered

The kinetic model was developed by first performingstoichiometric mole balance of each species in a plug flowreactor (PFR) using the reaction kinetics in (2) to (4)However since a simpler mole balance of each species in abatch reactor produces the same solution as in Section 3 thebatch reactor balance is used instead

Mole balance of T is as follows

minus

119889119862T119889119905

= 119896+1119862T119862A minus 119896

minus1119862D119862E1 (6)

Mole balance of D is as follows

minus

119889119862D119889119905

= minus (119896+1119862T119862A minus 119896

minus1119862D119862E1 minus 119896

+2119862D119862A + 119896

minus2119862M119862E2)

(7)

Mole balance of M is as follows

minus

119889119862M119889119905

= minus (119896+2119862D119862A minus 119896

minus2119862M119862E2 minus 119896

+3119862M119862A + 119896

minus3119862G119862E3)

(8)

Mole balance of E1 is as follows

minus

119889119862E1119889119905

= minus (119896+1119862T119862A minus 119896

minus1119862D119862E1) (9)

Mole balance of E2 is as follows

minus

119889119862E2119889119905

= minus (119896+2119862D119862A minus 119896

minus2119862M119862E2) (10)

Mole balance of E3 is as follows

minus

119889119862E3119889119905

= minus (119896+3119862M119862A minus 119896

minus3119862G119862E3) (11)

Mole balance of A (methanol) is as follows

minus

119889119862A119889119905

= 119896+1119862T119862A minus 119896

minus1119862D119862E1 + 119896

+2119862D119862A

minus 119896minus2119862M119862E2 + 119896

+3119862M119862A minus 119896

minus3119862G119862E3

(12)

Mole balance of G is as follows

minus

119889119862G119889119905

= minus (119896+3119862M119862A minus 119896

minus3119862G119862E3) (13)

Published reaction rate constants (119896+1ndash119896119909minus3

) are listed inTable 1 In this work methanol is assumed in excess whiletriglyceride is the limiting reactant

Closed form simultaneous solution of ordinary differen-tial equations (6) to (13) by analysis is possible if only theforward reactions are considered significant but the backwardreactions are neglected On the other hand if both forwardand reverse reactions are equally significant closed formsolution for (6) to (13) cannot be found and they have to besolved numerically using a 4th order Runge-Kutta algorithmwhich is available in MATLAB The solution generates themolar concentrations of all species 119862

119894 as functions of the

design variables that is the conversion of the limitingreactant 119883T and the molar ratio of the excess variable 119872

119877

Conversion is defined as

conversion =

loss of reactantfeed of reactant

(14)

For reactant T the conversion is

119883T =

119873T0 minus 119873T119873T0

= 1 minus

119873T0119881

119873T0119881= 1 minus

119862T119862T0

(15)

Selectivity is defined as the ratio of the desired product tothe amount of limiting reactant that has undergone chemicalchange [22] That is

Selectivity

=

amount of desired productamount of limiting reactant that has undergone chemical change

(16)

In this study the total methyl ester is defined as

Total methyl ester = methyl ester 1 +methyl ester 2

+methyl ester 3

(17)

The selectivity of the totalmethyl ester 119878E and of glycerol119878G defined as the moles of total methyl ester or glycerolproduced respectively per moles of the limiting reactantT that have reacted is then formulated as functions of theconversion of triglyceride119883T as shown in

119878E =

119862E1 + 119862E2 + 119862E3119862T119900119883T

119878G =

119862G119862T119900119883T

(18)

22 Selectivity of Methyl Esters and Glycerol in ContinuousStirred Tank Reactor The kinetic model for continuousstirred tank reactor (CSTR) is much simpler The stoichio-metric mole balance of each species in a CSTR using thereaction kinetics in (2) to (4) yields a set of nonlinearequations in (19) to (26)

Mole balance of T is as follows

119862T119900 minus 119862T =

119881

119865T(119896+1119862T119862A minus 119896

minus1119862D119862E1)

= 120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1)

(19)

International Journal of Chemical Engineering 5

Mole balance of D is as follows

119862D119900 minus 119862D

= minus120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1 minus 119896

+2119862D119862A + 119896

minus2119862M119862E2)

(20)

Mole balance of M is as follows

119862M119900 minus 119862M

= minus120591 (119896+2119862D119862A minus 119896

minus2119862M119862E2 minus 119896

+3119862M119862A + 119896

minus3119862G119862E3)

(21)

Mole balance of E1 is as follows

119862E1119900 minus 119862E1 = minus120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1) (22)

Mole balance of E2 is as follows

119862E2119900 minus 119862E2 = minus120591 (119896+2119862D119862A minus 119896

minus2119862M119862E2) (23)

Mole balance of E3 is as follows

119862E3119900 minus 119862E3 = minus120591 (119896+3119862M119862A minus 119896

minus3119862G119862E3) (24)

Mole balance of A (methanol) is as follows

119862A119900 minus 119862A

= 120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1 + 119896

+2119862D119862A minus 119896

minus2119862M119862E2

+119896+3119862M119862A minus 119896

minus3119862G119862E3)

(25)

Mole balance of G is as follows

119862G119900 minus 119862G = minus120591 (119896+3119862M119862A minus 119896

minus3119862G119862E3) (26)

Closed form simultaneous solution of nonlinear equa-tions (19) to (26) by analysis is not possible They have to besolved numerically using amatrix inversion algorithmwhichis available in MATLAB The solution generates the molarconcentrations of all species 119862

119894 as functions of the design

variables that is the conversion of the limiting reactant andthe molar ratio of the excess variable 119860

3 Solution of the PFR and CSTR

31 Removal of Temporal Dependence Equations (6) to (13)cannot be solved in their time dependent forms because of thesingle degree of freedom of the problem In order to solve theequations simultaneously the degree of freedom is reduced tozero by changing the independent variable from time to theconversion or concentration of the limiting reactant using thechain rule and the mole balance equation for T (6) Considerthe following

119889119862119894

119889119862T= (

119889119862119894

119889119905

)(

119889119905

119889119862T) (27)

Hence (7) to (13) can be rewritten with concentration ofT as their independent variable as follows

119889119862D119889119862T

= minus(1 minus

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119889119862M119889119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2 minus 120572

4119862M119862A + 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119889119862E1119889119862T

= minus1

119889119862E2119889119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119889119862E3119889119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119889119862A119889119862T

= 1 +

1205722119862D119862A minus 120572

3119862M119862E2 + 120572

4119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

119889119862G119889119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

(28)

where

1205721=

119896minus1

119896+1

1205722=

119896+2

119896+1

1205723=

119896minus2

119896+1

1205724=

119896+3

119896+1

1205725=

119896minus3

119896+1

(29)

Similarly (28) cannot be solved in their time dependentforms because of the single degree of freedom of the problemIn order to solve the equations simultaneously the degreeof freedom is reduced to zero by changing the independentvariable from time to the conversion or concentration of thelimiting reactant using algebraic manipulation and the molebalance equation for T (19) Consider the following

119862119894119900minus 119862119894

119862T119900 minus 119862T= minus(

119862119894119900minus 119862119894

120591

)(

120591

119862T119900 minus 119862T) (30)

Hence (28) can be rewritten with concentration of T astheir independent variable as follows

119862D119900 minus 119862D119862T119900 minus 119862T

= minus(1 minus

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119862M119900 minus 119862M119862T119900 minus 119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2 minus 120572

4119862M119862A + 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119862E1119900 minus 119862E1119862T119900 minus 119862T

= minus1

6 International Journal of Chemical Engineering

119862E2119900 minus 119862E2119862T119900 minus 119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119862E3119900 minus 119862E3119862T119900 minus 119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119862A119900 minus 119862A119862T119900 minus 119862T

= 1 +

1205722119862D119862A minus 120572

3119862M119862E2 + 120572

4119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

119862G119900 minus 119862G119862T119900 minus 119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

) (31)

Two main cases are considered the base case where thereactions (2) to (4) are irreversible and the alternative casewhere the reactions are reversible

32 Case 1 Base Case Irreversible Reactions In Case 1 thebase case is considered by assuming (2) to (4) to be irre-versible reactions In other words the forward reactions areso dominant that the reverse reaction can be neglected andthe overall effect is that the reactions are irreversible Theresults of the base case can then be compared with that of thealternative Case 2 where the reactions are all reversible inorder to verify the importance of the reverse reaction and itsimplication to the maximum attainable molar concentrationof methyl ester Since the reverse reactions are omitted thevalue of 120572

1 1205723 and 120572

5is zero Hence (28) for PFR can be

rewritten as follows

119889119862D119889119862T

= minus(1 minus

1205722119862D

119862T) (32)

119889119862M119889119862T

= minus(

1205722119862D minus 120572

4119862M

119862T) (33)

119889119862E1119889119862T

= minus1 (34)

119889119862E2119889119862T

= minus

1205722119862D

119862T (35)

119889119862E3119889119862T

= minus

1205724119862M119862T

(36)

119889119862A119889119862T

= 1 +

1205722119862D + 120572

4119862M

119862T (37)

119889119862G119889119862T

= minus

1205724119862M119862T

(38)

The solution of the set of ordinary differential equations(32) can be found analytically by using the integrating factormethod [23] The concentrations of all the species generated

by the solution are then expressed in terms of the triglyceridesconversion119883T as shown in

119862T = 119862T119900 (1 minus 119883T)

119862D =

119862T1199001205722minus 1

[(

119862T119862T119900

) minus (

119862T119862T119900

)

1205722

]

=

119862T1199001205722minus 1

[(1 minus 119883T) minus (1 minus 119883T)1205722

]

119862M = 119862T119900 [1205722

1 minus 1205722

[

(1 minus 119883T)

1 minus 1205724

minus

(1 minus 119883T)1205722

1205722minus 1205724

]

+

1205722(1 minus 119883T)

1205724

(1 minus 1205724) (1205722minus 1205724)

]

119862E1 = 119862T119900 (1 minus (

119862T119862T119900

)) = 119862T119900 (1 minus (1 minus 119883T)) = 119862T119900119883T

119862E2 = 119862T119900 1 minus

1205722

1205722minus 1

[(1 minus 119883T) minus(1 minus 119883T)

1205722

1205722

]

119862E3 = 1205724119862T119900 [

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

119862A = 119862T119900 119872119877+

1205722

(1 minus 1205722)

times [(

(1 minus 1205722)

1205722

+

21205724minus 1

(1 minus 1205724)

)119883T

minus (

21205724minus 1205722

1205722(1205722minus 1205724)

) [1 minus (1 minus 119883T)1205722

]

minus

(1 minus 1205722)

(1 minus 1205724) (1205722minus 1205724)

times [1 minus (1 minus 119883T)1205724

] ]

119862G = 1205724119862T119900 [

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(39)

For the CSTR (31) can be manipulated algebraically andrewritten with conversion of T as their independent variableas follows

119862D =

119862T119900119883T (1 minus 119883T)

(1 minus (1 minus 1205722)119883T)

(40)

International Journal of Chemical Engineering 7

119862M =

1205722119862T119900119883

2

T (1 minus 119883T)

(1 minus (1 minus 1205724)119883T) (1 minus (1 minus 120572

2)119883T)

(41)

119862E1 = 119862T119900119883T (42)

119862E2 =1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

(43)

119862E3 =12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(44)

119862A = 119862T119900 (119872119877minus 1 +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

)

(45)

119862G =

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(46)

33 Case 2 Alternative Case Reversible Reactions In Case 2an alternative case was considered by assuming that thereactions in (2) to (4) are reversible Together with the basecase where the reactions are irreversible it can be used todiscover the significance of the reverse and forward reactions

Since the values of all 120572119894rsquos in (28) for the PFR and

(31) for the CSTR are not zero no closed form solutionto them can be found because they are too complex foranalytical solution The solution of both sets of equationscan be achieved by numerical methods using a computersimulation software Equations (28) for the PFR are solvedby using the ordinary differential equation 45 (ODE 45) inMATLAB Concentration of each species is obtained usingRungge-Kutta numerical integration algorithm On the otherhand (31) for the CSTR are solved by using the simultaneousnonlinear equations solver in MATLAB Concentration ofeach species is obtained using the multivariable Newton-Raphson algorithm

34 Selectivity of Methyl Esters and Glycerol for Case 1 andCase 2 The net concentration of methyl esters is the sum ofconcentration of ester 1 ester 2 and ester 3 In Case 1 the netconcentration of methyl esters in the PFR is given by

119862E1 + 119862E2 + 119862E3

= 119862T119900 1 + 119883T minus

1205722

1205722minus 1

[(1 minus 119883T) minus(1 minus 119883T)

1205722

1205722

]

+1205724[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(47)

Similarly the net concentration of methyl esters in theCSTR for Case 1 is given by

119862E1 + 119862E2 + 119862E3

= 119862E1119900 + 119862E2119900 + 119862E3119900

+ [119862T119900119883T +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(48)

The selectivity of methyl esters in Case 1 for PFR is givenby

119878E =

119883T + 1

119883Tminus

1205722

1205722minus 1

[

(1 minus 119883T)

119883Tminus

(1 minus 119883T)1205722

1205722119883T

]

+1205724[

1205722

1 minus 1205722

[

1

1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722119883T

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724119883T

]

(49)

The selectivity of glycerol in Case 1 for PFR is given by

119878G =

1205724

119883T[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(50)

On the other hand the selectivity of methyl esters inCase 1 for CSTR is given by

119878E = [1 +

1205722119883T

(1 minus (1 minus 1205722)119883T)

+

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(51)

The selectivity of glycerol in Case 1 for CSTR is given by

119878G =

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(52)

For Case 2 there is no closed form expression for selec-tivity of methyl esters and glycerolThe selectivities of methylesters and glycerol have to be calculated using (18) fromthe concentration of the species generated by the numericalsolution

4 Results and Discussion

41 Comparison of Selectivities for Cases 1 and 2 This studyhas shown the development of kinetic parameters for deter-mining methyl esters and glycerol selectivity in a biodiesel

8 International Journal of Chemical Engineering

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

ity

Conversion of triglyceride XT

Case 1-T = 60∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 60∘C MR = 6 1 catalyst = 02 wt

Figure 1 Selectivity plots of Cases 1 and 2 at reaction temperature60∘C molar ratio 6 1 and catalyst concentration 02 wt

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

ity

Conversion of triglyceride XT

Case 1-T = 70∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 70∘C MR = 6 1 catalyst = 02 wt

Figure 2 Selectivity plots of Cases 1 and 2 at reaction temperature70∘C molar ratio 6 1 and catalyst concentration 02 wt

transesterification reaction it has also established severalmathematical equations for the same Furthermore a par-ticularly important parameter for designing a reactor thatis product selectivity was determined for each case andcondition For comparing the base case and an alternativecase datasets 2 and 3 were evaluated using each calculationschemesThe difference in the selectivity between Case 1 andCase 2 which were investigated under the same conditionsis very significant and is attributed to the reversibility factorof the reaction as illustrated in Figures 1 and 2The results ofthe base case show that when all the reactions are irreversibleit implies that the maximum attainable molar concentrationand selectivity ofmethyl ester have been reachedThis verifiesthe significant role of the forward reactions in (2)ndash(4)

For a simple reversible reaction we can see the effectsof thermodynamic parameter like temperature on thereversibility of the reaction whereas the reversibility ofa reaction is controlled by reaction equilibrium constant

Table 2 Selectivity at 07ndash09 triglycerides conversion for datasets(1ndash3) and (6-7)

Conversion119883T Dataset Methyl esters selectivityCase 1 Case 2

07

1 2610 25262 2643 25113 2630 24706 2610 26137 2493 2313

08

1 2766 26752 2784 26663 2769 26296 2764 27667 2682 2480

09

1 2895 28322 2903 28163 2892 27886 2893 28797 2852 2655

The reaction equilibrium constant 119870 is defined as theforward rate constant divided by the reverse rate constant andaffected by temperature [12] This transesterification reactionis a complex reaction which consists of three reversibleand consecutive reactions Therefore for simplification andpreliminary design purpose selectivity is effectively used todetermine the effect of temperature and role of catalyst onthe reversibility Figures 1 and 2 show significant changes ofthe selectivity plots for conversion of triglycerides from 07to 09 and the plots finally reach the equilibrium at the endof the reaction In order to access the role of temperature andamount of catalyst on the reversibility of transesterificationreaction Table 2 was constructed by observing the methylesters selectivity for conversion of triglycerides from 07 to09 It presents the difference in selectivity for Case 1 andCase 2 Datasets (1ndash3) are used to determine the effects ofdifferent temperatures on the reversibility of the transesterifi-cation reaction which represent a temperature of 50 60 and70 respectively Conversion of triglyceride at 09 is selectedfor analysis From this data we can see that the forwardreaction alone is able to provide better selectivity than reversereaction at any temperature Datasets (6-7) are used to ana-lyze the role catalyst on the reversibility of transesterificationreaction whereas datasets 6 and 7 represent the amount ofcatalyst of 15 and 05 respectively A significant role ofthe forward reaction once again was determined at a highercatalyst concentrationThe results obtained also indicate thata higher catalyst concentration controls the forward reactionsand gives preferably product selectivity

According to Narvaez et al [9] and Noureddini and Zhu[5] the forward reactions in a transesterification reaction arethe most important reactions However Diasakou et al [7]claimed that the reverse reactions during a transesterificationreaction do not influence the forward reactions In this studya lower concentration of methyl ester was found for Case 2

International Journal of Chemical Engineering 9

Table 3 Activation energy

Reaction Activation energy (calmol)T rarr D 13145D rarr T 9932D rarr M 19860M rarr D 14639M rarr G 6421G rarr M 9588

which affects the selectivity and methyl ester conversionwhich is likely due to the reverse nature of the reaction [4]This result suggests that for establishing the optimal chemicalprocess for biodiesel fuel production it can be assumed thatwhen irreversible reactions are employed better selectivitycan be obtained because of the absence of reverse reactions

42 Effects of Reaction Characteristics on Selectivity Thereactor design stage for a biodiesel plant utilizes methyl esterselectivity for the material balances and stream costs Attain-ing the appropriate operating conditions through productselectivity can eliminate material and energy recycling thusreducing costsThe effects of the reaction temperature molarratio of methanol to oil and the catalyst concentration on theselectivity of methyl esters and glycerol are analyzed for bothCase 1 and Case 2 in the following subsections

421 Effect of ReactionTemperature on Selectivity An investi-gation on the effect of temperature onmethyl ester selectivitywas conducted using datasets (1ndash3) where the molar ratio ofalcohol to oil and the catalyst concentration are fixed TheArrhenius equation was used for this investigation

119896 = 119896∘exp(minus

119864

119877119879

) (53)

According to (53) the reaction rate 119896 is an integralpart of the selectivity expressions It depends on the energyof activation (119864) obtained from the Arrhenius equation[22] For reactions at different temperatures fixed molarratios and catalyst concentrations the activation energy isconstant In this study the kinetic data used to analyzethe temperature effect were adapted from Noureddini andZhu [5] Because the data published in their research utilizethe average reaction rate constants at 50∘C and constantactivation energy (53) can bemanipulated to obtain the otherreaction rate constants (at 60∘C and 70∘C) listed in Table 1The results of the activation energy investigated in their studyare shown in Table 3

Figures 3 and 4 show the effects of the reaction tempera-ture on the selectivity ofmethyl esters and glycerol for Cases 1and 2 respectively The reaction temperature had a small butsubstantial effect on the selectivity The figures show thatthe selectivity of methyl esters is high at a high temperaturein the early conversion of T However in both figures theselectivities of E for both Cases 1 and 2 at 70∘C were foundto decrease toward the completion of the reaction As theboiling point of methanol is 647∘C an additional 5∘C has

0

02

04

06

08

1

12

00

05

10

15

20

25

30

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 3 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 1

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 4 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 2

the effect of lowering the product concentration and affectingthe selectivity of E at the equilibriumThis temperature effectchanges the slope of selectivity from a concave to a convexshape which is also related with the reaction rate constant atdifferent temperatures

According to Darnoko and Cheryan [2] the transester-ification reaction rates were increased at 65∘C as comparedwith those at 50∘C The results of their research also showedan enhanced methyl ester yield at 65∘C compared withthat at 50∘C which was because of the higher viscosity ofoil at 50∘C In addition 55∘C is a stable temperature thatcan maintain the oil liquidity This result indicates that anoptimum temperature promotes the formation of methylesters and thus contributes to a higher selectivity of biodieselproducts It can also be suggested that the reaction rateconstant 119896 which is greatly dependent on the temperatureand selectivity of E is greatly improved at the optimumtemperature

10 International Journal of Chemical Engineering

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 5 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 1

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 6 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 2

The findings confirm that methyl ester selectivity effectscan be realistically obtained at the optimum temperaturewhich is 60∘C in this study As the reactor optimizationrequires the relationship between the conversion and selec-tivity in both cases (Case 1 and Case 2) the selectivity withinthe studied temperature indicates that the biodiesel reactormay work more efficiently in converting T to E at 60∘C

422 Effect of Molar Ratio of Methanol to Oil on SelectivityAn investigation into the effects of the methanol-to-oil molarratio involves datasets 4 and 5 Selectivity plots of methylesters and glycerol are shown in Figures 5 and 6 For Cases 1and 2 the selectivity of methyl esters and glycerol was rela-tively affected by the molar ratio of methanol to oil It can beseen from the figures that the higher molar ratio of methanolto oil encourages the formation of transesterification reactionproducts thus contributing to a higher selectivity

The most striking result to emerge from the figures isthe change in the shape of the selectivity plot from concave

0

02

04

06

08

1

12

0 02 04 06 08 1

Sele

ctiv

ity

(a)(b)

(c)

Triglyceride conversion XT

Figure 7 Selectivity plots (a) methyl ester 1 (b) methyl ester 2 and(c) methyl ester 3 for dataset 4

to convex for a molar ratio of 9 1 An increasing selectivityof methyl ester can be found in an early conversion oftriglyceride but toward equilibrium the selectivity is foundto slightly decrease A possible explanation for this mightbe that the methyl ester concentration has both quadratic aswell as cubic effects that can be explained by (42)ndash(44) andFigure 7

According to (42) the selectivity of methyl ester 1 isconstant at 1 Equation (43) is a quadratic equation whichgives a parabolic shape to the plot of methyl ester 2 Equation(44) clearly illustrates the selectivity of methyl ester 3 whenthe equation is a cubic one In more detail the power of twois more dominant at an 119883T of less than 03 which meansthat the formation of E2 is more active under this conditionHowever we can see an active formation of E3 at an 119883Tof 05ndash1 when the power of three is dominant At the sametime E1 is formed linearly with a triglyceride conversionThe stepwise transesterification reaction in (2)ndash(4) shows thateach E is formed consecutivelyThismeans that to achieve themaximum yield the maximum selectivity at the maximum Tconversion is necessary and each E must be formed duringthe process Therefore it can be assumed that the selectivityof methyl ester is more greatly affected by the quadratic andcubic functions at a highermolar ratio ofmethanol to oil thanat a lower one

In addition Freedman et al [11] reported that the bestmethyl ester conversion is achieved at a molar ratio of 6 1with alkaline catalyst and that higher molar ratios do notincrease the productivity but do increase the cost of alcoholrecovery At a high molar excess of methanol a pseudo-first-order reaction appeared more likely than a second-order reaction However high molar ratio of methanol isused for noncatalytic and supercritical methanol reaction[6 11 20 24] Narvaez et al [9] stated that when an excessamount of methanol is used it can positively affect thereversible characteristic of the reaction and the displacementof the reaction toward the product As a consequence excessmethanol does not necessarily contribute to an increase in theconcentration of methyl ester and glycerol

International Journal of Chemical Engineering 11

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 8 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 9 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 2

423 Effect of Catalyst Concentration on Selectivity Apartfrom the temperature and molar ratio the parameters thataffect the selectivity are the same as those influencing thereaction rates namely the catalyst The effects of the catalystconcentration are studied through datasets 6 and 7 andthe selectivity plots can be seen in Figures 8 and 9 Whenanalyzing the figures it can be seen that the selectivity of bothproducts is higher at a higher catalyst concentration

Toward the equilibrium of the reaction the selectivitywas observed to increase at a higher catalyst concentra-tion thus contributing to an increased amount of methylester formation Vicente et al [25] stated that the largestmethyl ester conversions are obtained when a large catalystconcentration is employed (13) at a mild temperature(20ndash50∘C) This agrees with the resulting selectivity curvesplotted which indicates that the catalyst concentration hasa positive effect on the selectivity of methyl esters andglycerol However a greater application of an alkali catalystcan lead to the production of large amounts of soap andextra cost is required to remove the catalyst from the reactionsystem Srivastava and Prasad [26] have stated that a catalyst

0

02

04

06

08

1

12

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity

(a)

(c)(b)

Triglyceride conversion XT

Figure 10 Selectivity plots (a)methyl ester 1 (b)methyl ester 2 and(c) methyl ester 3 for dataset 6

concentration of 05ndash1 can yield up to a 99 methyl esterconversion

In Figures 8 and 9 there is a clear increasing trend of theselectivity ofmethyl ester for a 15 wt catalyst concentrationduring the early conversion of the reactant which decreasesat the end of the reactionThe same transition trend has beenfound when analyzing the influence of the molar ratio onmethyl ester selectivity A further detailed analysis showedthat the quadratic and cubic effects are more significantat a higher catalyst concentration than at a lower catalystconcentration As shown in Figure 10 the selectivity of E2 hasa quadratic plot whereas the selectivity of E3 has a parabolicshape Referring to (42)ndash(44) we can see that E1 is linearlyformed with a T conversion E2 is produced more at a Tconversion of lower than 035 where we can see that thepower of two in (43) is more dominant at this stage At aT conversion of over 05 the effect of the power of three in(44) is dominant causing a higher formation of E3 Becausethe transesterification reaction is a reversible and consecutiveequation the formation of three Es is important to achievea better selectivity With an optimum amount of catalyst thereactor becomesmore efficient in converting the reactant intothe products

43 Comparison ofMethyl Ester Selectivities fromDifferent OilFeedstocks To compare the selectivities of methyl esters andglycerol from different feedstocks datasets (8ndash10) were usedFigure 11 presents the selectivity ofmethyl esters derived fromrapeseed oil waste sunflower oil and palm oil for Case 1 andCase 2 As can be seen from the graph the methyl estersand glycerol were more likely to form if palm oil is used asthe feedstock compared to the other two oil feedstocks Thepresent finding also suggests that the selectivity of methylester was much lower when using low cost feedstock such aswaste sunflower oil Waste oil contains large amounts of freefatty acids (FFAs) (about 20) which affect the yield of fuelfrom that process The amount of FFAs in palm oil is 064[3] but for rapeseed oil the author used fresh oil [27] whichis estimated less than 1

12 International Journal of Chemical Engineering

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

PO-case 1 RO-case 1

WSO-case 1 WSO-case 2RO-case 2PO-case 2

Conversion of triglyceride XT

Sele

ctiv

ity o

f met

hyl e

sters

Figure 11 Selectivity plots of methyl ester from various feedstockfor Cases 1 and 2

As discussed before these free fatty acids will reactwith alkali catalysts to produce soaps that will inhibit thetransesterification reaction Soaps will allow emulsificationthat causes the phase separation of methyl ester and glycerolto be less sharp It produces water that can hydrolyze thetriglycerides and contribute to the formation of more soap[14] The effect of reversibility of transesterification can beseen significantly when analysing the selectivity of methylester derived from palm oil In Figure 11 methyl ester derivedfrom palm oil shows a higher selectivity plot for base caseThis finding suggests that forward reaction dominates thereaction and contributes to a better selectivity when lowFFAs feedstock is used in biodiesel production As there aremany low cost feedstocks available for biodiesel productiona pretreatment to these feedstocks can be carried out in orderto ensure the value of FFAs is within the allowable range

5 Conclusions

This paper has presented a comprehensive kinetic modelingof a transesterification reaction for biodiesel with homoge-neous alkaline catalyst The purpose of the study was todevelop the kinetic models of transesterification reactiondetermine the selectivity of methyl ester and glycerol andevaluate the significance of the reverse reactions in the trans-esterification reaction This study has shown that a processmodel solution was found for two types of common biodieselreactors The concentration of each species during transes-terification was found leading to a selectivity determinationduring the biodiesel production In addition the reversibleand irreversible effects of a transesterification reaction werediscovered The forward reaction is more dominant than thereverse reaction and the maximum selectivity can be foundif a base case of transesterification reaction is assumed tohave occurred in the biodiesel reactor system For the variousreaction characteristics under investigation the selectivities

are influenced by the temperature molar ratio of methanolto oil catalyst concentration and type of oil used as thefeedstock Furthermore an analysis of the selectivity plotsindicates an enhanced effect of the reaction characteristicson the selectivity This research has shown that the selectivityof methyl ester is maximized at 60∘C a 9 1 molar ratio ofmethanol to oil and a catalyst concentration of 15 Thisinvestigation into the effects of the molar ratio of methanolto oil and the catalyst concentration on the selectivity canbe made more interesting if several more curves are plottedat a molar ratio of methanol to oil between 3 1 to 9 1 anda catalyst concentration between 05 and 15 Howevera limitation of this research remains in the availability ofthe reaction rate constants under various reaction condi-tions In addition a comparison should be made throughmutual reaction conditionsThe findings from this study willenhance the concept of selectivity and its applications inthe evaluation of complex transesterification reactions whenthe goal is to attain the maximum production of methylesters and glycerol It is recommended that further researchis undertaken in exploring the selectivity data for specifyingthe reactor configurations and may be used in the synthesisof reactor network for biodiesel production

Nomenclature

119896+1 119896minus1 119896+2

119896minus2 119896+3 119896minus3

Reaction constant

119862T 119862D 119862M 119862G119862E1 119862E2 119862E3119862A 119862E

Molar concentration of triglyceridediglyceride monoglyceride glycerolester 1 ester 2 ester 3 methanol andmethyl ester

119883T Conversion of triglyceride119872119877 Molar ratio

119862T0 Initial molar concentration oftriglyceride

119878E 119878G Selectivity of methyl ester glycerol120572 Reaction rate constant factorwt Weight percentT TriglycerideD DiglycerideM MonoglycerideA MethanolG GlycerolE Methyl esterE1 Methyl ester 1E2 Methyl ester 2E3 Methyl ester 3PFR Plug flow reactorCSTR Continuous stirred tank reactor119873T0 Initial amount of triglyceride at 119905 = 0

119873T The amount of triglyceride present attime 119905

119881 VolumePO Palm oilRO Rapeseed oilWSO Waste sunflower oilNaOH Sodium hydroxide

International Journal of Chemical Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgment

Thework was carried out with the financial support from theMinistry of Education Malaysia

References

[1] A Demirbas ldquoBiodiesel from triglycerides via transesterifica-tionrdquo in Biodiesel pp 121ndash140 Springer London UK 2008

[2] D Darnoko and M Cheryan ldquoKinetics of palm oil transesteri-fication in a batch reactorrdquo JAOCS Journal of the American OilChemistsrsquo Society vol 77 no 12 pp 1263ndash1267 2000

[3] T Leevijit WWisutmethangoon G Prateepehaikul C Tongu-rai and M Allen ldquoA second order kinetics of palm oil transes-terification in a batch reactorrdquo in Proceedings of the Joint Inter-national Conference on Sustainable Energy and Environment pp277ndash281 2004

[4] S Jain andM P Sharma ldquoKinetics of acid base catalyzed trans-esterification of Jatropha curcas oilrdquo Bioresource Technology vol101 no 20 pp 7701ndash7706 2010

[5] H Noureddini and D Zhu ldquoKinetics of transesterification ofsoybean oilrdquo Journal of the American Oil Chemistsrsquo Society vol74 no 11 pp 1457ndash1463 1997

[6] D Kusdiana and S Saka ldquoKinetics of transesterification in rape-seed oil to biodiesel fuel as treated in supercritical methanolrdquoFuel vol 80 no 5 pp 693ndash698 2001

[7] M Diasakou A Louloudi and N Papayannakos ldquoKinetics ofthe non-catalytic transesterification of soybean oilrdquo Fuel vol 77no 12 pp 1297ndash1302 1998

[8] H Maeda S Hagiwara H Nabetani et al ldquoBiodiesel fuelsfrom palm oil via the non-catalytic transesterification in abubble column reactor at atmospheric pressure a kinetic studyrdquoRenewable Energy vol 33 no 7 pp 1629ndash1636 2008

[9] P C Narvaez S M Rincon and F J Sanchez ldquoKinetics of palmoil methanolysisrdquo Journal of the American Oil Chemistsrsquo Societyvol 84 pp 971ndash977 2007

[10] E Minami and S Saka ldquoKinetics of hydrolysis and methylesterification for biodiesel production in two-step supercriticalmethanol processrdquo Fuel vol 85 no 17-18 pp 2479ndash2483 2006

[11] B Freedman R O Butterfield and E H Pryde ldquoTransesteri-fication kinetics of soybean oil 1rdquo Journal of the American OilChemistsrsquo Society vol 63 no 10 pp 1375ndash1380 1986

[12] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

[13] J M Douglas Conceptual Design of Chemical ProcessesMcGraw Hill 1988

[14] J van Gerpen B Shanks R Pruszko D Clements and GKnothe Biodiesel Production Technology Subcontractor ReportNational Reanewable Energy Laboratory 2004

[15] H J Wright J B Segur H V Clark S K Coburn E ELangdon and R N DuPuis ldquoA report on ester interchangerdquoOilamp Soap vol 21 no 5 pp 145ndash148 1944

[16] H Fukuda A Kondo and H Noda ldquoBiodiesel fuel productionby transesterification of oilsrdquo Journal of Bioscience and Bioengi-neering vol 92 no 5 pp 405ndash416 2001

[17] L Friesenhagen and H Lepper ldquoProcess for the productionof fatty acid esters of short-chain aliphatic alcohols from fatsandor oils containing free fatty acidsrdquoUS Patent 4608202 1986

[18] P Felizardo J MacHado D Vergueiro M J N Correia J PGomes and J M Bordado ldquoStudy on the glycerolysis reactionof high free fatty acid oils for use as biodiesel feedstockrdquo FuelProcessing Technology vol 92 no 6 pp 1225ndash1229 2011

[19] A Tafesh and S Basheer ldquoPretreatment methods in biodieselproduction processesrdquo in Pretreatment Techniques for Biofuelsand Biorefineries Z Fang Ed Green Energy and Technologypp 417ndash434 Springer Berlin Germany 2013

[20] D Kusdiana and S Saka ldquoEffects of water on biodiesel fuelproduction by supercritical methanol treatmentrdquo BioresourceTechnology vol 91 no 3 pp 289ndash295 2004

[21] K Komers F Skopal R Stloukal and J Machek ldquoKinetics andmechanism of the KOHmdashcatalyzed methanolysis of rapeseedoil for biodiesel productionrdquo European Journal of Lipid Scienceand Technology vol 104 pp 728ndash737 2002

[22] A K CokerModeling of Chemical Kinetics and Reactor DesignGulf Publishing Houston Tex USA 2001

[23] C D Holland and R G Anthony Fundamentals of ChemicalReaction Engineering Prentice-Hall 1979

[24] J K Rodrıguez-Guerrero M F Rubens and P T V RosaldquoProduction of biodiesel from castor oil using sub and super-critical ethanol effect of sodium hydroxide on the ethyl esterproductionrdquoThe Journal of Supercritical Fluids vol 83 pp 124ndash132 2013

[25] G Vicente M Martınez and J Aracil ldquoOptimisation ofintegrated biodiesel production Part I A study of the biodieselpurity and yieldrdquoBioresource Technology vol 98 no 9 pp 1724ndash1733 2007

[26] A Srivastava and R Prasad ldquoTriglycerides-based diesel fuelsrdquoRenewable and Sustainable Energy Reviews vol 4 no 2 pp 111ndash133 2000

[27] B Klofutar J Golob B Likozar C Klofutar E Zagar andI Poljansek ldquoThe transesterification of rapeseed and wastesunflower oils mass-transfer and kinetics in a laboratory batchreactor and in an industrial-scale reactorseparator setuprdquoBioresource Technology vol 101 no 10 pp 3333ndash3344 2010

[28] S D Crymble ldquoOptimization and Reaction Kinetics of the Pro-duction of Biodiesel from Castor Oil via Sodium Methoxide-Catalyzed Methanolysisrdquo Dave C Swalm School of ChemicalEngineering Mississippi State University Miss USA 2010

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International Journal of

International Journal of Chemical Engineering 3

Table1Re

actio

nrateconstantsd

atafor

transeste

rificatio

nreactio

nin

biod

ieselprodu

ction

Srnum

ber

12

34

56

78

910

119896+1

(Lm

olsdots)

00500

00920

01650

000

60000

6300021

00031

01672

02251

0634

119896minus1

(Lm

olsdots)

0110

001750

02710

00016

000

0700035

000

0009373

04711

0119896+2

(Lm

ols)

02150

05440

13050

004

42000

9200072

00123

03553

01317

7104

0119896minus2

(Lm

ols)

12280

24350

464

1000127

00023

00102

01224

02674

03917

49120

119896+3

(Lm

ols)

02420

03270

04340

00050

00070

00231

000

9219

608

0119

078

600

119896minus3

(Lm

ols)

00070

00110

00170

000

0300027

00035

000

0000077

00181

01210

Temperature

(∘ C)

5060

7065

6530

3060

6060

Molar

ratio

119872R

61

61

61

91

31

91

91

61

61

61

Catalystconcentration(w

t)

02

02

02

1515

1505

1010

10Oilfeed

stock

Soybean

Soybean

Soybean

Casto

rCa

stor

Casto

rCa

stor

Rapeseed

WasteSunfl

ower

Palm

Reference

[5]

[5]

[5]

[28]

[28]

[28]

[28]

[27]

[27]

[3]

4 International Journal of Chemical Engineering

developing the kinetic model of alkali-catalyzed transes-terification reaction [21] However the kinetics parameterfor alkali-catalyzed transesterification in the present workis developed by assuming that triglycerides were pretreatedearlier Also this work represents a preliminary design ofreactors for a biodiesel plant Therefore some importantissues such as the existence of competing reaction alongwith the transesterification such as saponification reactionand the presence of water in the oil the transport processheterogeneity of the reaction and loss of polarity of analkaline catalyst were not considered

The kinetic model was developed by first performingstoichiometric mole balance of each species in a plug flowreactor (PFR) using the reaction kinetics in (2) to (4)However since a simpler mole balance of each species in abatch reactor produces the same solution as in Section 3 thebatch reactor balance is used instead

Mole balance of T is as follows

minus

119889119862T119889119905

= 119896+1119862T119862A minus 119896

minus1119862D119862E1 (6)

Mole balance of D is as follows

minus

119889119862D119889119905

= minus (119896+1119862T119862A minus 119896

minus1119862D119862E1 minus 119896

+2119862D119862A + 119896

minus2119862M119862E2)

(7)

Mole balance of M is as follows

minus

119889119862M119889119905

= minus (119896+2119862D119862A minus 119896

minus2119862M119862E2 minus 119896

+3119862M119862A + 119896

minus3119862G119862E3)

(8)

Mole balance of E1 is as follows

minus

119889119862E1119889119905

= minus (119896+1119862T119862A minus 119896

minus1119862D119862E1) (9)

Mole balance of E2 is as follows

minus

119889119862E2119889119905

= minus (119896+2119862D119862A minus 119896

minus2119862M119862E2) (10)

Mole balance of E3 is as follows

minus

119889119862E3119889119905

= minus (119896+3119862M119862A minus 119896

minus3119862G119862E3) (11)

Mole balance of A (methanol) is as follows

minus

119889119862A119889119905

= 119896+1119862T119862A minus 119896

minus1119862D119862E1 + 119896

+2119862D119862A

minus 119896minus2119862M119862E2 + 119896

+3119862M119862A minus 119896

minus3119862G119862E3

(12)

Mole balance of G is as follows

minus

119889119862G119889119905

= minus (119896+3119862M119862A minus 119896

minus3119862G119862E3) (13)

Published reaction rate constants (119896+1ndash119896119909minus3

) are listed inTable 1 In this work methanol is assumed in excess whiletriglyceride is the limiting reactant

Closed form simultaneous solution of ordinary differen-tial equations (6) to (13) by analysis is possible if only theforward reactions are considered significant but the backwardreactions are neglected On the other hand if both forwardand reverse reactions are equally significant closed formsolution for (6) to (13) cannot be found and they have to besolved numerically using a 4th order Runge-Kutta algorithmwhich is available in MATLAB The solution generates themolar concentrations of all species 119862

119894 as functions of the

design variables that is the conversion of the limitingreactant 119883T and the molar ratio of the excess variable 119872

119877

Conversion is defined as

conversion =

loss of reactantfeed of reactant

(14)

For reactant T the conversion is

119883T =

119873T0 minus 119873T119873T0

= 1 minus

119873T0119881

119873T0119881= 1 minus

119862T119862T0

(15)

Selectivity is defined as the ratio of the desired product tothe amount of limiting reactant that has undergone chemicalchange [22] That is

Selectivity

=

amount of desired productamount of limiting reactant that has undergone chemical change

(16)

In this study the total methyl ester is defined as

Total methyl ester = methyl ester 1 +methyl ester 2

+methyl ester 3

(17)

The selectivity of the totalmethyl ester 119878E and of glycerol119878G defined as the moles of total methyl ester or glycerolproduced respectively per moles of the limiting reactantT that have reacted is then formulated as functions of theconversion of triglyceride119883T as shown in

119878E =

119862E1 + 119862E2 + 119862E3119862T119900119883T

119878G =

119862G119862T119900119883T

(18)

22 Selectivity of Methyl Esters and Glycerol in ContinuousStirred Tank Reactor The kinetic model for continuousstirred tank reactor (CSTR) is much simpler The stoichio-metric mole balance of each species in a CSTR using thereaction kinetics in (2) to (4) yields a set of nonlinearequations in (19) to (26)

Mole balance of T is as follows

119862T119900 minus 119862T =

119881

119865T(119896+1119862T119862A minus 119896

minus1119862D119862E1)

= 120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1)

(19)

International Journal of Chemical Engineering 5

Mole balance of D is as follows

119862D119900 minus 119862D

= minus120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1 minus 119896

+2119862D119862A + 119896

minus2119862M119862E2)

(20)

Mole balance of M is as follows

119862M119900 minus 119862M

= minus120591 (119896+2119862D119862A minus 119896

minus2119862M119862E2 minus 119896

+3119862M119862A + 119896

minus3119862G119862E3)

(21)

Mole balance of E1 is as follows

119862E1119900 minus 119862E1 = minus120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1) (22)

Mole balance of E2 is as follows

119862E2119900 minus 119862E2 = minus120591 (119896+2119862D119862A minus 119896

minus2119862M119862E2) (23)

Mole balance of E3 is as follows

119862E3119900 minus 119862E3 = minus120591 (119896+3119862M119862A minus 119896

minus3119862G119862E3) (24)

Mole balance of A (methanol) is as follows

119862A119900 minus 119862A

= 120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1 + 119896

+2119862D119862A minus 119896

minus2119862M119862E2

+119896+3119862M119862A minus 119896

minus3119862G119862E3)

(25)

Mole balance of G is as follows

119862G119900 minus 119862G = minus120591 (119896+3119862M119862A minus 119896

minus3119862G119862E3) (26)

Closed form simultaneous solution of nonlinear equa-tions (19) to (26) by analysis is not possible They have to besolved numerically using amatrix inversion algorithmwhichis available in MATLAB The solution generates the molarconcentrations of all species 119862

119894 as functions of the design

variables that is the conversion of the limiting reactant andthe molar ratio of the excess variable 119860

3 Solution of the PFR and CSTR

31 Removal of Temporal Dependence Equations (6) to (13)cannot be solved in their time dependent forms because of thesingle degree of freedom of the problem In order to solve theequations simultaneously the degree of freedom is reduced tozero by changing the independent variable from time to theconversion or concentration of the limiting reactant using thechain rule and the mole balance equation for T (6) Considerthe following

119889119862119894

119889119862T= (

119889119862119894

119889119905

)(

119889119905

119889119862T) (27)

Hence (7) to (13) can be rewritten with concentration ofT as their independent variable as follows

119889119862D119889119862T

= minus(1 minus

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119889119862M119889119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2 minus 120572

4119862M119862A + 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119889119862E1119889119862T

= minus1

119889119862E2119889119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119889119862E3119889119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119889119862A119889119862T

= 1 +

1205722119862D119862A minus 120572

3119862M119862E2 + 120572

4119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

119889119862G119889119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

(28)

where

1205721=

119896minus1

119896+1

1205722=

119896+2

119896+1

1205723=

119896minus2

119896+1

1205724=

119896+3

119896+1

1205725=

119896minus3

119896+1

(29)

Similarly (28) cannot be solved in their time dependentforms because of the single degree of freedom of the problemIn order to solve the equations simultaneously the degreeof freedom is reduced to zero by changing the independentvariable from time to the conversion or concentration of thelimiting reactant using algebraic manipulation and the molebalance equation for T (19) Consider the following

119862119894119900minus 119862119894

119862T119900 minus 119862T= minus(

119862119894119900minus 119862119894

120591

)(

120591

119862T119900 minus 119862T) (30)

Hence (28) can be rewritten with concentration of T astheir independent variable as follows

119862D119900 minus 119862D119862T119900 minus 119862T

= minus(1 minus

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119862M119900 minus 119862M119862T119900 minus 119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2 minus 120572

4119862M119862A + 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119862E1119900 minus 119862E1119862T119900 minus 119862T

= minus1

6 International Journal of Chemical Engineering

119862E2119900 minus 119862E2119862T119900 minus 119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119862E3119900 minus 119862E3119862T119900 minus 119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119862A119900 minus 119862A119862T119900 minus 119862T

= 1 +

1205722119862D119862A minus 120572

3119862M119862E2 + 120572

4119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

119862G119900 minus 119862G119862T119900 minus 119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

) (31)

Two main cases are considered the base case where thereactions (2) to (4) are irreversible and the alternative casewhere the reactions are reversible

32 Case 1 Base Case Irreversible Reactions In Case 1 thebase case is considered by assuming (2) to (4) to be irre-versible reactions In other words the forward reactions areso dominant that the reverse reaction can be neglected andthe overall effect is that the reactions are irreversible Theresults of the base case can then be compared with that of thealternative Case 2 where the reactions are all reversible inorder to verify the importance of the reverse reaction and itsimplication to the maximum attainable molar concentrationof methyl ester Since the reverse reactions are omitted thevalue of 120572

1 1205723 and 120572

5is zero Hence (28) for PFR can be

rewritten as follows

119889119862D119889119862T

= minus(1 minus

1205722119862D

119862T) (32)

119889119862M119889119862T

= minus(

1205722119862D minus 120572

4119862M

119862T) (33)

119889119862E1119889119862T

= minus1 (34)

119889119862E2119889119862T

= minus

1205722119862D

119862T (35)

119889119862E3119889119862T

= minus

1205724119862M119862T

(36)

119889119862A119889119862T

= 1 +

1205722119862D + 120572

4119862M

119862T (37)

119889119862G119889119862T

= minus

1205724119862M119862T

(38)

The solution of the set of ordinary differential equations(32) can be found analytically by using the integrating factormethod [23] The concentrations of all the species generated

by the solution are then expressed in terms of the triglyceridesconversion119883T as shown in

119862T = 119862T119900 (1 minus 119883T)

119862D =

119862T1199001205722minus 1

[(

119862T119862T119900

) minus (

119862T119862T119900

)

1205722

]

=

119862T1199001205722minus 1

[(1 minus 119883T) minus (1 minus 119883T)1205722

]

119862M = 119862T119900 [1205722

1 minus 1205722

[

(1 minus 119883T)

1 minus 1205724

minus

(1 minus 119883T)1205722

1205722minus 1205724

]

+

1205722(1 minus 119883T)

1205724

(1 minus 1205724) (1205722minus 1205724)

]

119862E1 = 119862T119900 (1 minus (

119862T119862T119900

)) = 119862T119900 (1 minus (1 minus 119883T)) = 119862T119900119883T

119862E2 = 119862T119900 1 minus

1205722

1205722minus 1

[(1 minus 119883T) minus(1 minus 119883T)

1205722

1205722

]

119862E3 = 1205724119862T119900 [

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

119862A = 119862T119900 119872119877+

1205722

(1 minus 1205722)

times [(

(1 minus 1205722)

1205722

+

21205724minus 1

(1 minus 1205724)

)119883T

minus (

21205724minus 1205722

1205722(1205722minus 1205724)

) [1 minus (1 minus 119883T)1205722

]

minus

(1 minus 1205722)

(1 minus 1205724) (1205722minus 1205724)

times [1 minus (1 minus 119883T)1205724

] ]

119862G = 1205724119862T119900 [

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(39)

For the CSTR (31) can be manipulated algebraically andrewritten with conversion of T as their independent variableas follows

119862D =

119862T119900119883T (1 minus 119883T)

(1 minus (1 minus 1205722)119883T)

(40)

International Journal of Chemical Engineering 7

119862M =

1205722119862T119900119883

2

T (1 minus 119883T)

(1 minus (1 minus 1205724)119883T) (1 minus (1 minus 120572

2)119883T)

(41)

119862E1 = 119862T119900119883T (42)

119862E2 =1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

(43)

119862E3 =12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(44)

119862A = 119862T119900 (119872119877minus 1 +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

)

(45)

119862G =

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(46)

33 Case 2 Alternative Case Reversible Reactions In Case 2an alternative case was considered by assuming that thereactions in (2) to (4) are reversible Together with the basecase where the reactions are irreversible it can be used todiscover the significance of the reverse and forward reactions

Since the values of all 120572119894rsquos in (28) for the PFR and

(31) for the CSTR are not zero no closed form solutionto them can be found because they are too complex foranalytical solution The solution of both sets of equationscan be achieved by numerical methods using a computersimulation software Equations (28) for the PFR are solvedby using the ordinary differential equation 45 (ODE 45) inMATLAB Concentration of each species is obtained usingRungge-Kutta numerical integration algorithm On the otherhand (31) for the CSTR are solved by using the simultaneousnonlinear equations solver in MATLAB Concentration ofeach species is obtained using the multivariable Newton-Raphson algorithm

34 Selectivity of Methyl Esters and Glycerol for Case 1 andCase 2 The net concentration of methyl esters is the sum ofconcentration of ester 1 ester 2 and ester 3 In Case 1 the netconcentration of methyl esters in the PFR is given by

119862E1 + 119862E2 + 119862E3

= 119862T119900 1 + 119883T minus

1205722

1205722minus 1

[(1 minus 119883T) minus(1 minus 119883T)

1205722

1205722

]

+1205724[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(47)

Similarly the net concentration of methyl esters in theCSTR for Case 1 is given by

119862E1 + 119862E2 + 119862E3

= 119862E1119900 + 119862E2119900 + 119862E3119900

+ [119862T119900119883T +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(48)

The selectivity of methyl esters in Case 1 for PFR is givenby

119878E =

119883T + 1

119883Tminus

1205722

1205722minus 1

[

(1 minus 119883T)

119883Tminus

(1 minus 119883T)1205722

1205722119883T

]

+1205724[

1205722

1 minus 1205722

[

1

1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722119883T

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724119883T

]

(49)

The selectivity of glycerol in Case 1 for PFR is given by

119878G =

1205724

119883T[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(50)

On the other hand the selectivity of methyl esters inCase 1 for CSTR is given by

119878E = [1 +

1205722119883T

(1 minus (1 minus 1205722)119883T)

+

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(51)

The selectivity of glycerol in Case 1 for CSTR is given by

119878G =

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(52)

For Case 2 there is no closed form expression for selec-tivity of methyl esters and glycerolThe selectivities of methylesters and glycerol have to be calculated using (18) fromthe concentration of the species generated by the numericalsolution

4 Results and Discussion

41 Comparison of Selectivities for Cases 1 and 2 This studyhas shown the development of kinetic parameters for deter-mining methyl esters and glycerol selectivity in a biodiesel

8 International Journal of Chemical Engineering

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

ity

Conversion of triglyceride XT

Case 1-T = 60∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 60∘C MR = 6 1 catalyst = 02 wt

Figure 1 Selectivity plots of Cases 1 and 2 at reaction temperature60∘C molar ratio 6 1 and catalyst concentration 02 wt

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

ity

Conversion of triglyceride XT

Case 1-T = 70∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 70∘C MR = 6 1 catalyst = 02 wt

Figure 2 Selectivity plots of Cases 1 and 2 at reaction temperature70∘C molar ratio 6 1 and catalyst concentration 02 wt

transesterification reaction it has also established severalmathematical equations for the same Furthermore a par-ticularly important parameter for designing a reactor thatis product selectivity was determined for each case andcondition For comparing the base case and an alternativecase datasets 2 and 3 were evaluated using each calculationschemesThe difference in the selectivity between Case 1 andCase 2 which were investigated under the same conditionsis very significant and is attributed to the reversibility factorof the reaction as illustrated in Figures 1 and 2The results ofthe base case show that when all the reactions are irreversibleit implies that the maximum attainable molar concentrationand selectivity ofmethyl ester have been reachedThis verifiesthe significant role of the forward reactions in (2)ndash(4)

For a simple reversible reaction we can see the effectsof thermodynamic parameter like temperature on thereversibility of the reaction whereas the reversibility ofa reaction is controlled by reaction equilibrium constant

Table 2 Selectivity at 07ndash09 triglycerides conversion for datasets(1ndash3) and (6-7)

Conversion119883T Dataset Methyl esters selectivityCase 1 Case 2

07

1 2610 25262 2643 25113 2630 24706 2610 26137 2493 2313

08

1 2766 26752 2784 26663 2769 26296 2764 27667 2682 2480

09

1 2895 28322 2903 28163 2892 27886 2893 28797 2852 2655

The reaction equilibrium constant 119870 is defined as theforward rate constant divided by the reverse rate constant andaffected by temperature [12] This transesterification reactionis a complex reaction which consists of three reversibleand consecutive reactions Therefore for simplification andpreliminary design purpose selectivity is effectively used todetermine the effect of temperature and role of catalyst onthe reversibility Figures 1 and 2 show significant changes ofthe selectivity plots for conversion of triglycerides from 07to 09 and the plots finally reach the equilibrium at the endof the reaction In order to access the role of temperature andamount of catalyst on the reversibility of transesterificationreaction Table 2 was constructed by observing the methylesters selectivity for conversion of triglycerides from 07 to09 It presents the difference in selectivity for Case 1 andCase 2 Datasets (1ndash3) are used to determine the effects ofdifferent temperatures on the reversibility of the transesterifi-cation reaction which represent a temperature of 50 60 and70 respectively Conversion of triglyceride at 09 is selectedfor analysis From this data we can see that the forwardreaction alone is able to provide better selectivity than reversereaction at any temperature Datasets (6-7) are used to ana-lyze the role catalyst on the reversibility of transesterificationreaction whereas datasets 6 and 7 represent the amount ofcatalyst of 15 and 05 respectively A significant role ofthe forward reaction once again was determined at a highercatalyst concentrationThe results obtained also indicate thata higher catalyst concentration controls the forward reactionsand gives preferably product selectivity

According to Narvaez et al [9] and Noureddini and Zhu[5] the forward reactions in a transesterification reaction arethe most important reactions However Diasakou et al [7]claimed that the reverse reactions during a transesterificationreaction do not influence the forward reactions In this studya lower concentration of methyl ester was found for Case 2

International Journal of Chemical Engineering 9

Table 3 Activation energy

Reaction Activation energy (calmol)T rarr D 13145D rarr T 9932D rarr M 19860M rarr D 14639M rarr G 6421G rarr M 9588

which affects the selectivity and methyl ester conversionwhich is likely due to the reverse nature of the reaction [4]This result suggests that for establishing the optimal chemicalprocess for biodiesel fuel production it can be assumed thatwhen irreversible reactions are employed better selectivitycan be obtained because of the absence of reverse reactions

42 Effects of Reaction Characteristics on Selectivity Thereactor design stage for a biodiesel plant utilizes methyl esterselectivity for the material balances and stream costs Attain-ing the appropriate operating conditions through productselectivity can eliminate material and energy recycling thusreducing costsThe effects of the reaction temperature molarratio of methanol to oil and the catalyst concentration on theselectivity of methyl esters and glycerol are analyzed for bothCase 1 and Case 2 in the following subsections

421 Effect of ReactionTemperature on Selectivity An investi-gation on the effect of temperature onmethyl ester selectivitywas conducted using datasets (1ndash3) where the molar ratio ofalcohol to oil and the catalyst concentration are fixed TheArrhenius equation was used for this investigation

119896 = 119896∘exp(minus

119864

119877119879

) (53)

According to (53) the reaction rate 119896 is an integralpart of the selectivity expressions It depends on the energyof activation (119864) obtained from the Arrhenius equation[22] For reactions at different temperatures fixed molarratios and catalyst concentrations the activation energy isconstant In this study the kinetic data used to analyzethe temperature effect were adapted from Noureddini andZhu [5] Because the data published in their research utilizethe average reaction rate constants at 50∘C and constantactivation energy (53) can bemanipulated to obtain the otherreaction rate constants (at 60∘C and 70∘C) listed in Table 1The results of the activation energy investigated in their studyare shown in Table 3

Figures 3 and 4 show the effects of the reaction tempera-ture on the selectivity ofmethyl esters and glycerol for Cases 1and 2 respectively The reaction temperature had a small butsubstantial effect on the selectivity The figures show thatthe selectivity of methyl esters is high at a high temperaturein the early conversion of T However in both figures theselectivities of E for both Cases 1 and 2 at 70∘C were foundto decrease toward the completion of the reaction As theboiling point of methanol is 647∘C an additional 5∘C has

0

02

04

06

08

1

12

00

05

10

15

20

25

30

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 3 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 1

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 4 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 2

the effect of lowering the product concentration and affectingthe selectivity of E at the equilibriumThis temperature effectchanges the slope of selectivity from a concave to a convexshape which is also related with the reaction rate constant atdifferent temperatures

According to Darnoko and Cheryan [2] the transester-ification reaction rates were increased at 65∘C as comparedwith those at 50∘C The results of their research also showedan enhanced methyl ester yield at 65∘C compared withthat at 50∘C which was because of the higher viscosity ofoil at 50∘C In addition 55∘C is a stable temperature thatcan maintain the oil liquidity This result indicates that anoptimum temperature promotes the formation of methylesters and thus contributes to a higher selectivity of biodieselproducts It can also be suggested that the reaction rateconstant 119896 which is greatly dependent on the temperatureand selectivity of E is greatly improved at the optimumtemperature

10 International Journal of Chemical Engineering

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 5 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 1

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 6 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 2

The findings confirm that methyl ester selectivity effectscan be realistically obtained at the optimum temperaturewhich is 60∘C in this study As the reactor optimizationrequires the relationship between the conversion and selec-tivity in both cases (Case 1 and Case 2) the selectivity withinthe studied temperature indicates that the biodiesel reactormay work more efficiently in converting T to E at 60∘C

422 Effect of Molar Ratio of Methanol to Oil on SelectivityAn investigation into the effects of the methanol-to-oil molarratio involves datasets 4 and 5 Selectivity plots of methylesters and glycerol are shown in Figures 5 and 6 For Cases 1and 2 the selectivity of methyl esters and glycerol was rela-tively affected by the molar ratio of methanol to oil It can beseen from the figures that the higher molar ratio of methanolto oil encourages the formation of transesterification reactionproducts thus contributing to a higher selectivity

The most striking result to emerge from the figures isthe change in the shape of the selectivity plot from concave

0

02

04

06

08

1

12

0 02 04 06 08 1

Sele

ctiv

ity

(a)(b)

(c)

Triglyceride conversion XT

Figure 7 Selectivity plots (a) methyl ester 1 (b) methyl ester 2 and(c) methyl ester 3 for dataset 4

to convex for a molar ratio of 9 1 An increasing selectivityof methyl ester can be found in an early conversion oftriglyceride but toward equilibrium the selectivity is foundto slightly decrease A possible explanation for this mightbe that the methyl ester concentration has both quadratic aswell as cubic effects that can be explained by (42)ndash(44) andFigure 7

According to (42) the selectivity of methyl ester 1 isconstant at 1 Equation (43) is a quadratic equation whichgives a parabolic shape to the plot of methyl ester 2 Equation(44) clearly illustrates the selectivity of methyl ester 3 whenthe equation is a cubic one In more detail the power of twois more dominant at an 119883T of less than 03 which meansthat the formation of E2 is more active under this conditionHowever we can see an active formation of E3 at an 119883Tof 05ndash1 when the power of three is dominant At the sametime E1 is formed linearly with a triglyceride conversionThe stepwise transesterification reaction in (2)ndash(4) shows thateach E is formed consecutivelyThismeans that to achieve themaximum yield the maximum selectivity at the maximum Tconversion is necessary and each E must be formed duringthe process Therefore it can be assumed that the selectivityof methyl ester is more greatly affected by the quadratic andcubic functions at a highermolar ratio ofmethanol to oil thanat a lower one

In addition Freedman et al [11] reported that the bestmethyl ester conversion is achieved at a molar ratio of 6 1with alkaline catalyst and that higher molar ratios do notincrease the productivity but do increase the cost of alcoholrecovery At a high molar excess of methanol a pseudo-first-order reaction appeared more likely than a second-order reaction However high molar ratio of methanol isused for noncatalytic and supercritical methanol reaction[6 11 20 24] Narvaez et al [9] stated that when an excessamount of methanol is used it can positively affect thereversible characteristic of the reaction and the displacementof the reaction toward the product As a consequence excessmethanol does not necessarily contribute to an increase in theconcentration of methyl ester and glycerol

International Journal of Chemical Engineering 11

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 8 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 9 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 2

423 Effect of Catalyst Concentration on Selectivity Apartfrom the temperature and molar ratio the parameters thataffect the selectivity are the same as those influencing thereaction rates namely the catalyst The effects of the catalystconcentration are studied through datasets 6 and 7 andthe selectivity plots can be seen in Figures 8 and 9 Whenanalyzing the figures it can be seen that the selectivity of bothproducts is higher at a higher catalyst concentration

Toward the equilibrium of the reaction the selectivitywas observed to increase at a higher catalyst concentra-tion thus contributing to an increased amount of methylester formation Vicente et al [25] stated that the largestmethyl ester conversions are obtained when a large catalystconcentration is employed (13) at a mild temperature(20ndash50∘C) This agrees with the resulting selectivity curvesplotted which indicates that the catalyst concentration hasa positive effect on the selectivity of methyl esters andglycerol However a greater application of an alkali catalystcan lead to the production of large amounts of soap andextra cost is required to remove the catalyst from the reactionsystem Srivastava and Prasad [26] have stated that a catalyst

0

02

04

06

08

1

12

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity

(a)

(c)(b)

Triglyceride conversion XT

Figure 10 Selectivity plots (a)methyl ester 1 (b)methyl ester 2 and(c) methyl ester 3 for dataset 6

concentration of 05ndash1 can yield up to a 99 methyl esterconversion

In Figures 8 and 9 there is a clear increasing trend of theselectivity ofmethyl ester for a 15 wt catalyst concentrationduring the early conversion of the reactant which decreasesat the end of the reactionThe same transition trend has beenfound when analyzing the influence of the molar ratio onmethyl ester selectivity A further detailed analysis showedthat the quadratic and cubic effects are more significantat a higher catalyst concentration than at a lower catalystconcentration As shown in Figure 10 the selectivity of E2 hasa quadratic plot whereas the selectivity of E3 has a parabolicshape Referring to (42)ndash(44) we can see that E1 is linearlyformed with a T conversion E2 is produced more at a Tconversion of lower than 035 where we can see that thepower of two in (43) is more dominant at this stage At aT conversion of over 05 the effect of the power of three in(44) is dominant causing a higher formation of E3 Becausethe transesterification reaction is a reversible and consecutiveequation the formation of three Es is important to achievea better selectivity With an optimum amount of catalyst thereactor becomesmore efficient in converting the reactant intothe products

43 Comparison ofMethyl Ester Selectivities fromDifferent OilFeedstocks To compare the selectivities of methyl esters andglycerol from different feedstocks datasets (8ndash10) were usedFigure 11 presents the selectivity ofmethyl esters derived fromrapeseed oil waste sunflower oil and palm oil for Case 1 andCase 2 As can be seen from the graph the methyl estersand glycerol were more likely to form if palm oil is used asthe feedstock compared to the other two oil feedstocks Thepresent finding also suggests that the selectivity of methylester was much lower when using low cost feedstock such aswaste sunflower oil Waste oil contains large amounts of freefatty acids (FFAs) (about 20) which affect the yield of fuelfrom that process The amount of FFAs in palm oil is 064[3] but for rapeseed oil the author used fresh oil [27] whichis estimated less than 1

12 International Journal of Chemical Engineering

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

PO-case 1 RO-case 1

WSO-case 1 WSO-case 2RO-case 2PO-case 2

Conversion of triglyceride XT

Sele

ctiv

ity o

f met

hyl e

sters

Figure 11 Selectivity plots of methyl ester from various feedstockfor Cases 1 and 2

As discussed before these free fatty acids will reactwith alkali catalysts to produce soaps that will inhibit thetransesterification reaction Soaps will allow emulsificationthat causes the phase separation of methyl ester and glycerolto be less sharp It produces water that can hydrolyze thetriglycerides and contribute to the formation of more soap[14] The effect of reversibility of transesterification can beseen significantly when analysing the selectivity of methylester derived from palm oil In Figure 11 methyl ester derivedfrom palm oil shows a higher selectivity plot for base caseThis finding suggests that forward reaction dominates thereaction and contributes to a better selectivity when lowFFAs feedstock is used in biodiesel production As there aremany low cost feedstocks available for biodiesel productiona pretreatment to these feedstocks can be carried out in orderto ensure the value of FFAs is within the allowable range

5 Conclusions

This paper has presented a comprehensive kinetic modelingof a transesterification reaction for biodiesel with homoge-neous alkaline catalyst The purpose of the study was todevelop the kinetic models of transesterification reactiondetermine the selectivity of methyl ester and glycerol andevaluate the significance of the reverse reactions in the trans-esterification reaction This study has shown that a processmodel solution was found for two types of common biodieselreactors The concentration of each species during transes-terification was found leading to a selectivity determinationduring the biodiesel production In addition the reversibleand irreversible effects of a transesterification reaction werediscovered The forward reaction is more dominant than thereverse reaction and the maximum selectivity can be foundif a base case of transesterification reaction is assumed tohave occurred in the biodiesel reactor system For the variousreaction characteristics under investigation the selectivities

are influenced by the temperature molar ratio of methanolto oil catalyst concentration and type of oil used as thefeedstock Furthermore an analysis of the selectivity plotsindicates an enhanced effect of the reaction characteristicson the selectivity This research has shown that the selectivityof methyl ester is maximized at 60∘C a 9 1 molar ratio ofmethanol to oil and a catalyst concentration of 15 Thisinvestigation into the effects of the molar ratio of methanolto oil and the catalyst concentration on the selectivity canbe made more interesting if several more curves are plottedat a molar ratio of methanol to oil between 3 1 to 9 1 anda catalyst concentration between 05 and 15 Howevera limitation of this research remains in the availability ofthe reaction rate constants under various reaction condi-tions In addition a comparison should be made throughmutual reaction conditionsThe findings from this study willenhance the concept of selectivity and its applications inthe evaluation of complex transesterification reactions whenthe goal is to attain the maximum production of methylesters and glycerol It is recommended that further researchis undertaken in exploring the selectivity data for specifyingthe reactor configurations and may be used in the synthesisof reactor network for biodiesel production

Nomenclature

119896+1 119896minus1 119896+2

119896minus2 119896+3 119896minus3

Reaction constant

119862T 119862D 119862M 119862G119862E1 119862E2 119862E3119862A 119862E

Molar concentration of triglyceridediglyceride monoglyceride glycerolester 1 ester 2 ester 3 methanol andmethyl ester

119883T Conversion of triglyceride119872119877 Molar ratio

119862T0 Initial molar concentration oftriglyceride

119878E 119878G Selectivity of methyl ester glycerol120572 Reaction rate constant factorwt Weight percentT TriglycerideD DiglycerideM MonoglycerideA MethanolG GlycerolE Methyl esterE1 Methyl ester 1E2 Methyl ester 2E3 Methyl ester 3PFR Plug flow reactorCSTR Continuous stirred tank reactor119873T0 Initial amount of triglyceride at 119905 = 0

119873T The amount of triglyceride present attime 119905

119881 VolumePO Palm oilRO Rapeseed oilWSO Waste sunflower oilNaOH Sodium hydroxide

International Journal of Chemical Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgment

Thework was carried out with the financial support from theMinistry of Education Malaysia

References

[1] A Demirbas ldquoBiodiesel from triglycerides via transesterifica-tionrdquo in Biodiesel pp 121ndash140 Springer London UK 2008

[2] D Darnoko and M Cheryan ldquoKinetics of palm oil transesteri-fication in a batch reactorrdquo JAOCS Journal of the American OilChemistsrsquo Society vol 77 no 12 pp 1263ndash1267 2000

[3] T Leevijit WWisutmethangoon G Prateepehaikul C Tongu-rai and M Allen ldquoA second order kinetics of palm oil transes-terification in a batch reactorrdquo in Proceedings of the Joint Inter-national Conference on Sustainable Energy and Environment pp277ndash281 2004

[4] S Jain andM P Sharma ldquoKinetics of acid base catalyzed trans-esterification of Jatropha curcas oilrdquo Bioresource Technology vol101 no 20 pp 7701ndash7706 2010

[5] H Noureddini and D Zhu ldquoKinetics of transesterification ofsoybean oilrdquo Journal of the American Oil Chemistsrsquo Society vol74 no 11 pp 1457ndash1463 1997

[6] D Kusdiana and S Saka ldquoKinetics of transesterification in rape-seed oil to biodiesel fuel as treated in supercritical methanolrdquoFuel vol 80 no 5 pp 693ndash698 2001

[7] M Diasakou A Louloudi and N Papayannakos ldquoKinetics ofthe non-catalytic transesterification of soybean oilrdquo Fuel vol 77no 12 pp 1297ndash1302 1998

[8] H Maeda S Hagiwara H Nabetani et al ldquoBiodiesel fuelsfrom palm oil via the non-catalytic transesterification in abubble column reactor at atmospheric pressure a kinetic studyrdquoRenewable Energy vol 33 no 7 pp 1629ndash1636 2008

[9] P C Narvaez S M Rincon and F J Sanchez ldquoKinetics of palmoil methanolysisrdquo Journal of the American Oil Chemistsrsquo Societyvol 84 pp 971ndash977 2007

[10] E Minami and S Saka ldquoKinetics of hydrolysis and methylesterification for biodiesel production in two-step supercriticalmethanol processrdquo Fuel vol 85 no 17-18 pp 2479ndash2483 2006

[11] B Freedman R O Butterfield and E H Pryde ldquoTransesteri-fication kinetics of soybean oil 1rdquo Journal of the American OilChemistsrsquo Society vol 63 no 10 pp 1375ndash1380 1986

[12] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

[13] J M Douglas Conceptual Design of Chemical ProcessesMcGraw Hill 1988

[14] J van Gerpen B Shanks R Pruszko D Clements and GKnothe Biodiesel Production Technology Subcontractor ReportNational Reanewable Energy Laboratory 2004

[15] H J Wright J B Segur H V Clark S K Coburn E ELangdon and R N DuPuis ldquoA report on ester interchangerdquoOilamp Soap vol 21 no 5 pp 145ndash148 1944

[16] H Fukuda A Kondo and H Noda ldquoBiodiesel fuel productionby transesterification of oilsrdquo Journal of Bioscience and Bioengi-neering vol 92 no 5 pp 405ndash416 2001

[17] L Friesenhagen and H Lepper ldquoProcess for the productionof fatty acid esters of short-chain aliphatic alcohols from fatsandor oils containing free fatty acidsrdquoUS Patent 4608202 1986

[18] P Felizardo J MacHado D Vergueiro M J N Correia J PGomes and J M Bordado ldquoStudy on the glycerolysis reactionof high free fatty acid oils for use as biodiesel feedstockrdquo FuelProcessing Technology vol 92 no 6 pp 1225ndash1229 2011

[19] A Tafesh and S Basheer ldquoPretreatment methods in biodieselproduction processesrdquo in Pretreatment Techniques for Biofuelsand Biorefineries Z Fang Ed Green Energy and Technologypp 417ndash434 Springer Berlin Germany 2013

[20] D Kusdiana and S Saka ldquoEffects of water on biodiesel fuelproduction by supercritical methanol treatmentrdquo BioresourceTechnology vol 91 no 3 pp 289ndash295 2004

[21] K Komers F Skopal R Stloukal and J Machek ldquoKinetics andmechanism of the KOHmdashcatalyzed methanolysis of rapeseedoil for biodiesel productionrdquo European Journal of Lipid Scienceand Technology vol 104 pp 728ndash737 2002

[22] A K CokerModeling of Chemical Kinetics and Reactor DesignGulf Publishing Houston Tex USA 2001

[23] C D Holland and R G Anthony Fundamentals of ChemicalReaction Engineering Prentice-Hall 1979

[24] J K Rodrıguez-Guerrero M F Rubens and P T V RosaldquoProduction of biodiesel from castor oil using sub and super-critical ethanol effect of sodium hydroxide on the ethyl esterproductionrdquoThe Journal of Supercritical Fluids vol 83 pp 124ndash132 2013

[25] G Vicente M Martınez and J Aracil ldquoOptimisation ofintegrated biodiesel production Part I A study of the biodieselpurity and yieldrdquoBioresource Technology vol 98 no 9 pp 1724ndash1733 2007

[26] A Srivastava and R Prasad ldquoTriglycerides-based diesel fuelsrdquoRenewable and Sustainable Energy Reviews vol 4 no 2 pp 111ndash133 2000

[27] B Klofutar J Golob B Likozar C Klofutar E Zagar andI Poljansek ldquoThe transesterification of rapeseed and wastesunflower oils mass-transfer and kinetics in a laboratory batchreactor and in an industrial-scale reactorseparator setuprdquoBioresource Technology vol 101 no 10 pp 3333ndash3344 2010

[28] S D Crymble ldquoOptimization and Reaction Kinetics of the Pro-duction of Biodiesel from Castor Oil via Sodium Methoxide-Catalyzed Methanolysisrdquo Dave C Swalm School of ChemicalEngineering Mississippi State University Miss USA 2010

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4 International Journal of Chemical Engineering

developing the kinetic model of alkali-catalyzed transes-terification reaction [21] However the kinetics parameterfor alkali-catalyzed transesterification in the present workis developed by assuming that triglycerides were pretreatedearlier Also this work represents a preliminary design ofreactors for a biodiesel plant Therefore some importantissues such as the existence of competing reaction alongwith the transesterification such as saponification reactionand the presence of water in the oil the transport processheterogeneity of the reaction and loss of polarity of analkaline catalyst were not considered

The kinetic model was developed by first performingstoichiometric mole balance of each species in a plug flowreactor (PFR) using the reaction kinetics in (2) to (4)However since a simpler mole balance of each species in abatch reactor produces the same solution as in Section 3 thebatch reactor balance is used instead

Mole balance of T is as follows

minus

119889119862T119889119905

= 119896+1119862T119862A minus 119896

minus1119862D119862E1 (6)

Mole balance of D is as follows

minus

119889119862D119889119905

= minus (119896+1119862T119862A minus 119896

minus1119862D119862E1 minus 119896

+2119862D119862A + 119896

minus2119862M119862E2)

(7)

Mole balance of M is as follows

minus

119889119862M119889119905

= minus (119896+2119862D119862A minus 119896

minus2119862M119862E2 minus 119896

+3119862M119862A + 119896

minus3119862G119862E3)

(8)

Mole balance of E1 is as follows

minus

119889119862E1119889119905

= minus (119896+1119862T119862A minus 119896

minus1119862D119862E1) (9)

Mole balance of E2 is as follows

minus

119889119862E2119889119905

= minus (119896+2119862D119862A minus 119896

minus2119862M119862E2) (10)

Mole balance of E3 is as follows

minus

119889119862E3119889119905

= minus (119896+3119862M119862A minus 119896

minus3119862G119862E3) (11)

Mole balance of A (methanol) is as follows

minus

119889119862A119889119905

= 119896+1119862T119862A minus 119896

minus1119862D119862E1 + 119896

+2119862D119862A

minus 119896minus2119862M119862E2 + 119896

+3119862M119862A minus 119896

minus3119862G119862E3

(12)

Mole balance of G is as follows

minus

119889119862G119889119905

= minus (119896+3119862M119862A minus 119896

minus3119862G119862E3) (13)

Published reaction rate constants (119896+1ndash119896119909minus3

) are listed inTable 1 In this work methanol is assumed in excess whiletriglyceride is the limiting reactant

Closed form simultaneous solution of ordinary differen-tial equations (6) to (13) by analysis is possible if only theforward reactions are considered significant but the backwardreactions are neglected On the other hand if both forwardand reverse reactions are equally significant closed formsolution for (6) to (13) cannot be found and they have to besolved numerically using a 4th order Runge-Kutta algorithmwhich is available in MATLAB The solution generates themolar concentrations of all species 119862

119894 as functions of the

design variables that is the conversion of the limitingreactant 119883T and the molar ratio of the excess variable 119872

119877

Conversion is defined as

conversion =

loss of reactantfeed of reactant

(14)

For reactant T the conversion is

119883T =

119873T0 minus 119873T119873T0

= 1 minus

119873T0119881

119873T0119881= 1 minus

119862T119862T0

(15)

Selectivity is defined as the ratio of the desired product tothe amount of limiting reactant that has undergone chemicalchange [22] That is

Selectivity

=

amount of desired productamount of limiting reactant that has undergone chemical change

(16)

In this study the total methyl ester is defined as

Total methyl ester = methyl ester 1 +methyl ester 2

+methyl ester 3

(17)

The selectivity of the totalmethyl ester 119878E and of glycerol119878G defined as the moles of total methyl ester or glycerolproduced respectively per moles of the limiting reactantT that have reacted is then formulated as functions of theconversion of triglyceride119883T as shown in

119878E =

119862E1 + 119862E2 + 119862E3119862T119900119883T

119878G =

119862G119862T119900119883T

(18)

22 Selectivity of Methyl Esters and Glycerol in ContinuousStirred Tank Reactor The kinetic model for continuousstirred tank reactor (CSTR) is much simpler The stoichio-metric mole balance of each species in a CSTR using thereaction kinetics in (2) to (4) yields a set of nonlinearequations in (19) to (26)

Mole balance of T is as follows

119862T119900 minus 119862T =

119881

119865T(119896+1119862T119862A minus 119896

minus1119862D119862E1)

= 120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1)

(19)

International Journal of Chemical Engineering 5

Mole balance of D is as follows

119862D119900 minus 119862D

= minus120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1 minus 119896

+2119862D119862A + 119896

minus2119862M119862E2)

(20)

Mole balance of M is as follows

119862M119900 minus 119862M

= minus120591 (119896+2119862D119862A minus 119896

minus2119862M119862E2 minus 119896

+3119862M119862A + 119896

minus3119862G119862E3)

(21)

Mole balance of E1 is as follows

119862E1119900 minus 119862E1 = minus120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1) (22)

Mole balance of E2 is as follows

119862E2119900 minus 119862E2 = minus120591 (119896+2119862D119862A minus 119896

minus2119862M119862E2) (23)

Mole balance of E3 is as follows

119862E3119900 minus 119862E3 = minus120591 (119896+3119862M119862A minus 119896

minus3119862G119862E3) (24)

Mole balance of A (methanol) is as follows

119862A119900 minus 119862A

= 120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1 + 119896

+2119862D119862A minus 119896

minus2119862M119862E2

+119896+3119862M119862A minus 119896

minus3119862G119862E3)

(25)

Mole balance of G is as follows

119862G119900 minus 119862G = minus120591 (119896+3119862M119862A minus 119896

minus3119862G119862E3) (26)

Closed form simultaneous solution of nonlinear equa-tions (19) to (26) by analysis is not possible They have to besolved numerically using amatrix inversion algorithmwhichis available in MATLAB The solution generates the molarconcentrations of all species 119862

119894 as functions of the design

variables that is the conversion of the limiting reactant andthe molar ratio of the excess variable 119860

3 Solution of the PFR and CSTR

31 Removal of Temporal Dependence Equations (6) to (13)cannot be solved in their time dependent forms because of thesingle degree of freedom of the problem In order to solve theequations simultaneously the degree of freedom is reduced tozero by changing the independent variable from time to theconversion or concentration of the limiting reactant using thechain rule and the mole balance equation for T (6) Considerthe following

119889119862119894

119889119862T= (

119889119862119894

119889119905

)(

119889119905

119889119862T) (27)

Hence (7) to (13) can be rewritten with concentration ofT as their independent variable as follows

119889119862D119889119862T

= minus(1 minus

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119889119862M119889119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2 minus 120572

4119862M119862A + 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119889119862E1119889119862T

= minus1

119889119862E2119889119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119889119862E3119889119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119889119862A119889119862T

= 1 +

1205722119862D119862A minus 120572

3119862M119862E2 + 120572

4119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

119889119862G119889119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

(28)

where

1205721=

119896minus1

119896+1

1205722=

119896+2

119896+1

1205723=

119896minus2

119896+1

1205724=

119896+3

119896+1

1205725=

119896minus3

119896+1

(29)

Similarly (28) cannot be solved in their time dependentforms because of the single degree of freedom of the problemIn order to solve the equations simultaneously the degreeof freedom is reduced to zero by changing the independentvariable from time to the conversion or concentration of thelimiting reactant using algebraic manipulation and the molebalance equation for T (19) Consider the following

119862119894119900minus 119862119894

119862T119900 minus 119862T= minus(

119862119894119900minus 119862119894

120591

)(

120591

119862T119900 minus 119862T) (30)

Hence (28) can be rewritten with concentration of T astheir independent variable as follows

119862D119900 minus 119862D119862T119900 minus 119862T

= minus(1 minus

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119862M119900 minus 119862M119862T119900 minus 119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2 minus 120572

4119862M119862A + 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119862E1119900 minus 119862E1119862T119900 minus 119862T

= minus1

6 International Journal of Chemical Engineering

119862E2119900 minus 119862E2119862T119900 minus 119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119862E3119900 minus 119862E3119862T119900 minus 119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119862A119900 minus 119862A119862T119900 minus 119862T

= 1 +

1205722119862D119862A minus 120572

3119862M119862E2 + 120572

4119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

119862G119900 minus 119862G119862T119900 minus 119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

) (31)

Two main cases are considered the base case where thereactions (2) to (4) are irreversible and the alternative casewhere the reactions are reversible

32 Case 1 Base Case Irreversible Reactions In Case 1 thebase case is considered by assuming (2) to (4) to be irre-versible reactions In other words the forward reactions areso dominant that the reverse reaction can be neglected andthe overall effect is that the reactions are irreversible Theresults of the base case can then be compared with that of thealternative Case 2 where the reactions are all reversible inorder to verify the importance of the reverse reaction and itsimplication to the maximum attainable molar concentrationof methyl ester Since the reverse reactions are omitted thevalue of 120572

1 1205723 and 120572

5is zero Hence (28) for PFR can be

rewritten as follows

119889119862D119889119862T

= minus(1 minus

1205722119862D

119862T) (32)

119889119862M119889119862T

= minus(

1205722119862D minus 120572

4119862M

119862T) (33)

119889119862E1119889119862T

= minus1 (34)

119889119862E2119889119862T

= minus

1205722119862D

119862T (35)

119889119862E3119889119862T

= minus

1205724119862M119862T

(36)

119889119862A119889119862T

= 1 +

1205722119862D + 120572

4119862M

119862T (37)

119889119862G119889119862T

= minus

1205724119862M119862T

(38)

The solution of the set of ordinary differential equations(32) can be found analytically by using the integrating factormethod [23] The concentrations of all the species generated

by the solution are then expressed in terms of the triglyceridesconversion119883T as shown in

119862T = 119862T119900 (1 minus 119883T)

119862D =

119862T1199001205722minus 1

[(

119862T119862T119900

) minus (

119862T119862T119900

)

1205722

]

=

119862T1199001205722minus 1

[(1 minus 119883T) minus (1 minus 119883T)1205722

]

119862M = 119862T119900 [1205722

1 minus 1205722

[

(1 minus 119883T)

1 minus 1205724

minus

(1 minus 119883T)1205722

1205722minus 1205724

]

+

1205722(1 minus 119883T)

1205724

(1 minus 1205724) (1205722minus 1205724)

]

119862E1 = 119862T119900 (1 minus (

119862T119862T119900

)) = 119862T119900 (1 minus (1 minus 119883T)) = 119862T119900119883T

119862E2 = 119862T119900 1 minus

1205722

1205722minus 1

[(1 minus 119883T) minus(1 minus 119883T)

1205722

1205722

]

119862E3 = 1205724119862T119900 [

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

119862A = 119862T119900 119872119877+

1205722

(1 minus 1205722)

times [(

(1 minus 1205722)

1205722

+

21205724minus 1

(1 minus 1205724)

)119883T

minus (

21205724minus 1205722

1205722(1205722minus 1205724)

) [1 minus (1 minus 119883T)1205722

]

minus

(1 minus 1205722)

(1 minus 1205724) (1205722minus 1205724)

times [1 minus (1 minus 119883T)1205724

] ]

119862G = 1205724119862T119900 [

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(39)

For the CSTR (31) can be manipulated algebraically andrewritten with conversion of T as their independent variableas follows

119862D =

119862T119900119883T (1 minus 119883T)

(1 minus (1 minus 1205722)119883T)

(40)

International Journal of Chemical Engineering 7

119862M =

1205722119862T119900119883

2

T (1 minus 119883T)

(1 minus (1 minus 1205724)119883T) (1 minus (1 minus 120572

2)119883T)

(41)

119862E1 = 119862T119900119883T (42)

119862E2 =1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

(43)

119862E3 =12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(44)

119862A = 119862T119900 (119872119877minus 1 +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

)

(45)

119862G =

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(46)

33 Case 2 Alternative Case Reversible Reactions In Case 2an alternative case was considered by assuming that thereactions in (2) to (4) are reversible Together with the basecase where the reactions are irreversible it can be used todiscover the significance of the reverse and forward reactions

Since the values of all 120572119894rsquos in (28) for the PFR and

(31) for the CSTR are not zero no closed form solutionto them can be found because they are too complex foranalytical solution The solution of both sets of equationscan be achieved by numerical methods using a computersimulation software Equations (28) for the PFR are solvedby using the ordinary differential equation 45 (ODE 45) inMATLAB Concentration of each species is obtained usingRungge-Kutta numerical integration algorithm On the otherhand (31) for the CSTR are solved by using the simultaneousnonlinear equations solver in MATLAB Concentration ofeach species is obtained using the multivariable Newton-Raphson algorithm

34 Selectivity of Methyl Esters and Glycerol for Case 1 andCase 2 The net concentration of methyl esters is the sum ofconcentration of ester 1 ester 2 and ester 3 In Case 1 the netconcentration of methyl esters in the PFR is given by

119862E1 + 119862E2 + 119862E3

= 119862T119900 1 + 119883T minus

1205722

1205722minus 1

[(1 minus 119883T) minus(1 minus 119883T)

1205722

1205722

]

+1205724[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(47)

Similarly the net concentration of methyl esters in theCSTR for Case 1 is given by

119862E1 + 119862E2 + 119862E3

= 119862E1119900 + 119862E2119900 + 119862E3119900

+ [119862T119900119883T +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(48)

The selectivity of methyl esters in Case 1 for PFR is givenby

119878E =

119883T + 1

119883Tminus

1205722

1205722minus 1

[

(1 minus 119883T)

119883Tminus

(1 minus 119883T)1205722

1205722119883T

]

+1205724[

1205722

1 minus 1205722

[

1

1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722119883T

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724119883T

]

(49)

The selectivity of glycerol in Case 1 for PFR is given by

119878G =

1205724

119883T[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(50)

On the other hand the selectivity of methyl esters inCase 1 for CSTR is given by

119878E = [1 +

1205722119883T

(1 minus (1 minus 1205722)119883T)

+

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(51)

The selectivity of glycerol in Case 1 for CSTR is given by

119878G =

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(52)

For Case 2 there is no closed form expression for selec-tivity of methyl esters and glycerolThe selectivities of methylesters and glycerol have to be calculated using (18) fromthe concentration of the species generated by the numericalsolution

4 Results and Discussion

41 Comparison of Selectivities for Cases 1 and 2 This studyhas shown the development of kinetic parameters for deter-mining methyl esters and glycerol selectivity in a biodiesel

8 International Journal of Chemical Engineering

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

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Conversion of triglyceride XT

Case 1-T = 60∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 60∘C MR = 6 1 catalyst = 02 wt

Figure 1 Selectivity plots of Cases 1 and 2 at reaction temperature60∘C molar ratio 6 1 and catalyst concentration 02 wt

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

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Conversion of triglyceride XT

Case 1-T = 70∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 70∘C MR = 6 1 catalyst = 02 wt

Figure 2 Selectivity plots of Cases 1 and 2 at reaction temperature70∘C molar ratio 6 1 and catalyst concentration 02 wt

transesterification reaction it has also established severalmathematical equations for the same Furthermore a par-ticularly important parameter for designing a reactor thatis product selectivity was determined for each case andcondition For comparing the base case and an alternativecase datasets 2 and 3 were evaluated using each calculationschemesThe difference in the selectivity between Case 1 andCase 2 which were investigated under the same conditionsis very significant and is attributed to the reversibility factorof the reaction as illustrated in Figures 1 and 2The results ofthe base case show that when all the reactions are irreversibleit implies that the maximum attainable molar concentrationand selectivity ofmethyl ester have been reachedThis verifiesthe significant role of the forward reactions in (2)ndash(4)

For a simple reversible reaction we can see the effectsof thermodynamic parameter like temperature on thereversibility of the reaction whereas the reversibility ofa reaction is controlled by reaction equilibrium constant

Table 2 Selectivity at 07ndash09 triglycerides conversion for datasets(1ndash3) and (6-7)

Conversion119883T Dataset Methyl esters selectivityCase 1 Case 2

07

1 2610 25262 2643 25113 2630 24706 2610 26137 2493 2313

08

1 2766 26752 2784 26663 2769 26296 2764 27667 2682 2480

09

1 2895 28322 2903 28163 2892 27886 2893 28797 2852 2655

The reaction equilibrium constant 119870 is defined as theforward rate constant divided by the reverse rate constant andaffected by temperature [12] This transesterification reactionis a complex reaction which consists of three reversibleand consecutive reactions Therefore for simplification andpreliminary design purpose selectivity is effectively used todetermine the effect of temperature and role of catalyst onthe reversibility Figures 1 and 2 show significant changes ofthe selectivity plots for conversion of triglycerides from 07to 09 and the plots finally reach the equilibrium at the endof the reaction In order to access the role of temperature andamount of catalyst on the reversibility of transesterificationreaction Table 2 was constructed by observing the methylesters selectivity for conversion of triglycerides from 07 to09 It presents the difference in selectivity for Case 1 andCase 2 Datasets (1ndash3) are used to determine the effects ofdifferent temperatures on the reversibility of the transesterifi-cation reaction which represent a temperature of 50 60 and70 respectively Conversion of triglyceride at 09 is selectedfor analysis From this data we can see that the forwardreaction alone is able to provide better selectivity than reversereaction at any temperature Datasets (6-7) are used to ana-lyze the role catalyst on the reversibility of transesterificationreaction whereas datasets 6 and 7 represent the amount ofcatalyst of 15 and 05 respectively A significant role ofthe forward reaction once again was determined at a highercatalyst concentrationThe results obtained also indicate thata higher catalyst concentration controls the forward reactionsand gives preferably product selectivity

According to Narvaez et al [9] and Noureddini and Zhu[5] the forward reactions in a transesterification reaction arethe most important reactions However Diasakou et al [7]claimed that the reverse reactions during a transesterificationreaction do not influence the forward reactions In this studya lower concentration of methyl ester was found for Case 2

International Journal of Chemical Engineering 9

Table 3 Activation energy

Reaction Activation energy (calmol)T rarr D 13145D rarr T 9932D rarr M 19860M rarr D 14639M rarr G 6421G rarr M 9588

which affects the selectivity and methyl ester conversionwhich is likely due to the reverse nature of the reaction [4]This result suggests that for establishing the optimal chemicalprocess for biodiesel fuel production it can be assumed thatwhen irreversible reactions are employed better selectivitycan be obtained because of the absence of reverse reactions

42 Effects of Reaction Characteristics on Selectivity Thereactor design stage for a biodiesel plant utilizes methyl esterselectivity for the material balances and stream costs Attain-ing the appropriate operating conditions through productselectivity can eliminate material and energy recycling thusreducing costsThe effects of the reaction temperature molarratio of methanol to oil and the catalyst concentration on theselectivity of methyl esters and glycerol are analyzed for bothCase 1 and Case 2 in the following subsections

421 Effect of ReactionTemperature on Selectivity An investi-gation on the effect of temperature onmethyl ester selectivitywas conducted using datasets (1ndash3) where the molar ratio ofalcohol to oil and the catalyst concentration are fixed TheArrhenius equation was used for this investigation

119896 = 119896∘exp(minus

119864

119877119879

) (53)

According to (53) the reaction rate 119896 is an integralpart of the selectivity expressions It depends on the energyof activation (119864) obtained from the Arrhenius equation[22] For reactions at different temperatures fixed molarratios and catalyst concentrations the activation energy isconstant In this study the kinetic data used to analyzethe temperature effect were adapted from Noureddini andZhu [5] Because the data published in their research utilizethe average reaction rate constants at 50∘C and constantactivation energy (53) can bemanipulated to obtain the otherreaction rate constants (at 60∘C and 70∘C) listed in Table 1The results of the activation energy investigated in their studyare shown in Table 3

Figures 3 and 4 show the effects of the reaction tempera-ture on the selectivity ofmethyl esters and glycerol for Cases 1and 2 respectively The reaction temperature had a small butsubstantial effect on the selectivity The figures show thatthe selectivity of methyl esters is high at a high temperaturein the early conversion of T However in both figures theselectivities of E for both Cases 1 and 2 at 70∘C were foundto decrease toward the completion of the reaction As theboiling point of methanol is 647∘C an additional 5∘C has

0

02

04

06

08

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12

00

05

10

15

20

25

30

0 02 04 06 08 1

Sele

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Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 3 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 1

Sele

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02

04

06

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1

12

0

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2

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0 02 04 06 08 1

Sele

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f gly

cero

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Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 4 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 2

the effect of lowering the product concentration and affectingthe selectivity of E at the equilibriumThis temperature effectchanges the slope of selectivity from a concave to a convexshape which is also related with the reaction rate constant atdifferent temperatures

According to Darnoko and Cheryan [2] the transester-ification reaction rates were increased at 65∘C as comparedwith those at 50∘C The results of their research also showedan enhanced methyl ester yield at 65∘C compared withthat at 50∘C which was because of the higher viscosity ofoil at 50∘C In addition 55∘C is a stable temperature thatcan maintain the oil liquidity This result indicates that anoptimum temperature promotes the formation of methylesters and thus contributes to a higher selectivity of biodieselproducts It can also be suggested that the reaction rateconstant 119896 which is greatly dependent on the temperatureand selectivity of E is greatly improved at the optimumtemperature

10 International Journal of Chemical Engineering

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0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 5 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 1

Sele

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0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 6 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 2

The findings confirm that methyl ester selectivity effectscan be realistically obtained at the optimum temperaturewhich is 60∘C in this study As the reactor optimizationrequires the relationship between the conversion and selec-tivity in both cases (Case 1 and Case 2) the selectivity withinthe studied temperature indicates that the biodiesel reactormay work more efficiently in converting T to E at 60∘C

422 Effect of Molar Ratio of Methanol to Oil on SelectivityAn investigation into the effects of the methanol-to-oil molarratio involves datasets 4 and 5 Selectivity plots of methylesters and glycerol are shown in Figures 5 and 6 For Cases 1and 2 the selectivity of methyl esters and glycerol was rela-tively affected by the molar ratio of methanol to oil It can beseen from the figures that the higher molar ratio of methanolto oil encourages the formation of transesterification reactionproducts thus contributing to a higher selectivity

The most striking result to emerge from the figures isthe change in the shape of the selectivity plot from concave

0

02

04

06

08

1

12

0 02 04 06 08 1

Sele

ctiv

ity

(a)(b)

(c)

Triglyceride conversion XT

Figure 7 Selectivity plots (a) methyl ester 1 (b) methyl ester 2 and(c) methyl ester 3 for dataset 4

to convex for a molar ratio of 9 1 An increasing selectivityof methyl ester can be found in an early conversion oftriglyceride but toward equilibrium the selectivity is foundto slightly decrease A possible explanation for this mightbe that the methyl ester concentration has both quadratic aswell as cubic effects that can be explained by (42)ndash(44) andFigure 7

According to (42) the selectivity of methyl ester 1 isconstant at 1 Equation (43) is a quadratic equation whichgives a parabolic shape to the plot of methyl ester 2 Equation(44) clearly illustrates the selectivity of methyl ester 3 whenthe equation is a cubic one In more detail the power of twois more dominant at an 119883T of less than 03 which meansthat the formation of E2 is more active under this conditionHowever we can see an active formation of E3 at an 119883Tof 05ndash1 when the power of three is dominant At the sametime E1 is formed linearly with a triglyceride conversionThe stepwise transesterification reaction in (2)ndash(4) shows thateach E is formed consecutivelyThismeans that to achieve themaximum yield the maximum selectivity at the maximum Tconversion is necessary and each E must be formed duringthe process Therefore it can be assumed that the selectivityof methyl ester is more greatly affected by the quadratic andcubic functions at a highermolar ratio ofmethanol to oil thanat a lower one

In addition Freedman et al [11] reported that the bestmethyl ester conversion is achieved at a molar ratio of 6 1with alkaline catalyst and that higher molar ratios do notincrease the productivity but do increase the cost of alcoholrecovery At a high molar excess of methanol a pseudo-first-order reaction appeared more likely than a second-order reaction However high molar ratio of methanol isused for noncatalytic and supercritical methanol reaction[6 11 20 24] Narvaez et al [9] stated that when an excessamount of methanol is used it can positively affect thereversible characteristic of the reaction and the displacementof the reaction toward the product As a consequence excessmethanol does not necessarily contribute to an increase in theconcentration of methyl ester and glycerol

International Journal of Chemical Engineering 11

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0

02

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12

0

05

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15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 8 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 1

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0

02

04

06

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1

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0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 9 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 2

423 Effect of Catalyst Concentration on Selectivity Apartfrom the temperature and molar ratio the parameters thataffect the selectivity are the same as those influencing thereaction rates namely the catalyst The effects of the catalystconcentration are studied through datasets 6 and 7 andthe selectivity plots can be seen in Figures 8 and 9 Whenanalyzing the figures it can be seen that the selectivity of bothproducts is higher at a higher catalyst concentration

Toward the equilibrium of the reaction the selectivitywas observed to increase at a higher catalyst concentra-tion thus contributing to an increased amount of methylester formation Vicente et al [25] stated that the largestmethyl ester conversions are obtained when a large catalystconcentration is employed (13) at a mild temperature(20ndash50∘C) This agrees with the resulting selectivity curvesplotted which indicates that the catalyst concentration hasa positive effect on the selectivity of methyl esters andglycerol However a greater application of an alkali catalystcan lead to the production of large amounts of soap andextra cost is required to remove the catalyst from the reactionsystem Srivastava and Prasad [26] have stated that a catalyst

0

02

04

06

08

1

12

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity

(a)

(c)(b)

Triglyceride conversion XT

Figure 10 Selectivity plots (a)methyl ester 1 (b)methyl ester 2 and(c) methyl ester 3 for dataset 6

concentration of 05ndash1 can yield up to a 99 methyl esterconversion

In Figures 8 and 9 there is a clear increasing trend of theselectivity ofmethyl ester for a 15 wt catalyst concentrationduring the early conversion of the reactant which decreasesat the end of the reactionThe same transition trend has beenfound when analyzing the influence of the molar ratio onmethyl ester selectivity A further detailed analysis showedthat the quadratic and cubic effects are more significantat a higher catalyst concentration than at a lower catalystconcentration As shown in Figure 10 the selectivity of E2 hasa quadratic plot whereas the selectivity of E3 has a parabolicshape Referring to (42)ndash(44) we can see that E1 is linearlyformed with a T conversion E2 is produced more at a Tconversion of lower than 035 where we can see that thepower of two in (43) is more dominant at this stage At aT conversion of over 05 the effect of the power of three in(44) is dominant causing a higher formation of E3 Becausethe transesterification reaction is a reversible and consecutiveequation the formation of three Es is important to achievea better selectivity With an optimum amount of catalyst thereactor becomesmore efficient in converting the reactant intothe products

43 Comparison ofMethyl Ester Selectivities fromDifferent OilFeedstocks To compare the selectivities of methyl esters andglycerol from different feedstocks datasets (8ndash10) were usedFigure 11 presents the selectivity ofmethyl esters derived fromrapeseed oil waste sunflower oil and palm oil for Case 1 andCase 2 As can be seen from the graph the methyl estersand glycerol were more likely to form if palm oil is used asthe feedstock compared to the other two oil feedstocks Thepresent finding also suggests that the selectivity of methylester was much lower when using low cost feedstock such aswaste sunflower oil Waste oil contains large amounts of freefatty acids (FFAs) (about 20) which affect the yield of fuelfrom that process The amount of FFAs in palm oil is 064[3] but for rapeseed oil the author used fresh oil [27] whichis estimated less than 1

12 International Journal of Chemical Engineering

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

PO-case 1 RO-case 1

WSO-case 1 WSO-case 2RO-case 2PO-case 2

Conversion of triglyceride XT

Sele

ctiv

ity o

f met

hyl e

sters

Figure 11 Selectivity plots of methyl ester from various feedstockfor Cases 1 and 2

As discussed before these free fatty acids will reactwith alkali catalysts to produce soaps that will inhibit thetransesterification reaction Soaps will allow emulsificationthat causes the phase separation of methyl ester and glycerolto be less sharp It produces water that can hydrolyze thetriglycerides and contribute to the formation of more soap[14] The effect of reversibility of transesterification can beseen significantly when analysing the selectivity of methylester derived from palm oil In Figure 11 methyl ester derivedfrom palm oil shows a higher selectivity plot for base caseThis finding suggests that forward reaction dominates thereaction and contributes to a better selectivity when lowFFAs feedstock is used in biodiesel production As there aremany low cost feedstocks available for biodiesel productiona pretreatment to these feedstocks can be carried out in orderto ensure the value of FFAs is within the allowable range

5 Conclusions

This paper has presented a comprehensive kinetic modelingof a transesterification reaction for biodiesel with homoge-neous alkaline catalyst The purpose of the study was todevelop the kinetic models of transesterification reactiondetermine the selectivity of methyl ester and glycerol andevaluate the significance of the reverse reactions in the trans-esterification reaction This study has shown that a processmodel solution was found for two types of common biodieselreactors The concentration of each species during transes-terification was found leading to a selectivity determinationduring the biodiesel production In addition the reversibleand irreversible effects of a transesterification reaction werediscovered The forward reaction is more dominant than thereverse reaction and the maximum selectivity can be foundif a base case of transesterification reaction is assumed tohave occurred in the biodiesel reactor system For the variousreaction characteristics under investigation the selectivities

are influenced by the temperature molar ratio of methanolto oil catalyst concentration and type of oil used as thefeedstock Furthermore an analysis of the selectivity plotsindicates an enhanced effect of the reaction characteristicson the selectivity This research has shown that the selectivityof methyl ester is maximized at 60∘C a 9 1 molar ratio ofmethanol to oil and a catalyst concentration of 15 Thisinvestigation into the effects of the molar ratio of methanolto oil and the catalyst concentration on the selectivity canbe made more interesting if several more curves are plottedat a molar ratio of methanol to oil between 3 1 to 9 1 anda catalyst concentration between 05 and 15 Howevera limitation of this research remains in the availability ofthe reaction rate constants under various reaction condi-tions In addition a comparison should be made throughmutual reaction conditionsThe findings from this study willenhance the concept of selectivity and its applications inthe evaluation of complex transesterification reactions whenthe goal is to attain the maximum production of methylesters and glycerol It is recommended that further researchis undertaken in exploring the selectivity data for specifyingthe reactor configurations and may be used in the synthesisof reactor network for biodiesel production

Nomenclature

119896+1 119896minus1 119896+2

119896minus2 119896+3 119896minus3

Reaction constant

119862T 119862D 119862M 119862G119862E1 119862E2 119862E3119862A 119862E

Molar concentration of triglyceridediglyceride monoglyceride glycerolester 1 ester 2 ester 3 methanol andmethyl ester

119883T Conversion of triglyceride119872119877 Molar ratio

119862T0 Initial molar concentration oftriglyceride

119878E 119878G Selectivity of methyl ester glycerol120572 Reaction rate constant factorwt Weight percentT TriglycerideD DiglycerideM MonoglycerideA MethanolG GlycerolE Methyl esterE1 Methyl ester 1E2 Methyl ester 2E3 Methyl ester 3PFR Plug flow reactorCSTR Continuous stirred tank reactor119873T0 Initial amount of triglyceride at 119905 = 0

119873T The amount of triglyceride present attime 119905

119881 VolumePO Palm oilRO Rapeseed oilWSO Waste sunflower oilNaOH Sodium hydroxide

International Journal of Chemical Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgment

Thework was carried out with the financial support from theMinistry of Education Malaysia

References

[1] A Demirbas ldquoBiodiesel from triglycerides via transesterifica-tionrdquo in Biodiesel pp 121ndash140 Springer London UK 2008

[2] D Darnoko and M Cheryan ldquoKinetics of palm oil transesteri-fication in a batch reactorrdquo JAOCS Journal of the American OilChemistsrsquo Society vol 77 no 12 pp 1263ndash1267 2000

[3] T Leevijit WWisutmethangoon G Prateepehaikul C Tongu-rai and M Allen ldquoA second order kinetics of palm oil transes-terification in a batch reactorrdquo in Proceedings of the Joint Inter-national Conference on Sustainable Energy and Environment pp277ndash281 2004

[4] S Jain andM P Sharma ldquoKinetics of acid base catalyzed trans-esterification of Jatropha curcas oilrdquo Bioresource Technology vol101 no 20 pp 7701ndash7706 2010

[5] H Noureddini and D Zhu ldquoKinetics of transesterification ofsoybean oilrdquo Journal of the American Oil Chemistsrsquo Society vol74 no 11 pp 1457ndash1463 1997

[6] D Kusdiana and S Saka ldquoKinetics of transesterification in rape-seed oil to biodiesel fuel as treated in supercritical methanolrdquoFuel vol 80 no 5 pp 693ndash698 2001

[7] M Diasakou A Louloudi and N Papayannakos ldquoKinetics ofthe non-catalytic transesterification of soybean oilrdquo Fuel vol 77no 12 pp 1297ndash1302 1998

[8] H Maeda S Hagiwara H Nabetani et al ldquoBiodiesel fuelsfrom palm oil via the non-catalytic transesterification in abubble column reactor at atmospheric pressure a kinetic studyrdquoRenewable Energy vol 33 no 7 pp 1629ndash1636 2008

[9] P C Narvaez S M Rincon and F J Sanchez ldquoKinetics of palmoil methanolysisrdquo Journal of the American Oil Chemistsrsquo Societyvol 84 pp 971ndash977 2007

[10] E Minami and S Saka ldquoKinetics of hydrolysis and methylesterification for biodiesel production in two-step supercriticalmethanol processrdquo Fuel vol 85 no 17-18 pp 2479ndash2483 2006

[11] B Freedman R O Butterfield and E H Pryde ldquoTransesteri-fication kinetics of soybean oil 1rdquo Journal of the American OilChemistsrsquo Society vol 63 no 10 pp 1375ndash1380 1986

[12] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

[13] J M Douglas Conceptual Design of Chemical ProcessesMcGraw Hill 1988

[14] J van Gerpen B Shanks R Pruszko D Clements and GKnothe Biodiesel Production Technology Subcontractor ReportNational Reanewable Energy Laboratory 2004

[15] H J Wright J B Segur H V Clark S K Coburn E ELangdon and R N DuPuis ldquoA report on ester interchangerdquoOilamp Soap vol 21 no 5 pp 145ndash148 1944

[16] H Fukuda A Kondo and H Noda ldquoBiodiesel fuel productionby transesterification of oilsrdquo Journal of Bioscience and Bioengi-neering vol 92 no 5 pp 405ndash416 2001

[17] L Friesenhagen and H Lepper ldquoProcess for the productionof fatty acid esters of short-chain aliphatic alcohols from fatsandor oils containing free fatty acidsrdquoUS Patent 4608202 1986

[18] P Felizardo J MacHado D Vergueiro M J N Correia J PGomes and J M Bordado ldquoStudy on the glycerolysis reactionof high free fatty acid oils for use as biodiesel feedstockrdquo FuelProcessing Technology vol 92 no 6 pp 1225ndash1229 2011

[19] A Tafesh and S Basheer ldquoPretreatment methods in biodieselproduction processesrdquo in Pretreatment Techniques for Biofuelsand Biorefineries Z Fang Ed Green Energy and Technologypp 417ndash434 Springer Berlin Germany 2013

[20] D Kusdiana and S Saka ldquoEffects of water on biodiesel fuelproduction by supercritical methanol treatmentrdquo BioresourceTechnology vol 91 no 3 pp 289ndash295 2004

[21] K Komers F Skopal R Stloukal and J Machek ldquoKinetics andmechanism of the KOHmdashcatalyzed methanolysis of rapeseedoil for biodiesel productionrdquo European Journal of Lipid Scienceand Technology vol 104 pp 728ndash737 2002

[22] A K CokerModeling of Chemical Kinetics and Reactor DesignGulf Publishing Houston Tex USA 2001

[23] C D Holland and R G Anthony Fundamentals of ChemicalReaction Engineering Prentice-Hall 1979

[24] J K Rodrıguez-Guerrero M F Rubens and P T V RosaldquoProduction of biodiesel from castor oil using sub and super-critical ethanol effect of sodium hydroxide on the ethyl esterproductionrdquoThe Journal of Supercritical Fluids vol 83 pp 124ndash132 2013

[25] G Vicente M Martınez and J Aracil ldquoOptimisation ofintegrated biodiesel production Part I A study of the biodieselpurity and yieldrdquoBioresource Technology vol 98 no 9 pp 1724ndash1733 2007

[26] A Srivastava and R Prasad ldquoTriglycerides-based diesel fuelsrdquoRenewable and Sustainable Energy Reviews vol 4 no 2 pp 111ndash133 2000

[27] B Klofutar J Golob B Likozar C Klofutar E Zagar andI Poljansek ldquoThe transesterification of rapeseed and wastesunflower oils mass-transfer and kinetics in a laboratory batchreactor and in an industrial-scale reactorseparator setuprdquoBioresource Technology vol 101 no 10 pp 3333ndash3344 2010

[28] S D Crymble ldquoOptimization and Reaction Kinetics of the Pro-duction of Biodiesel from Castor Oil via Sodium Methoxide-Catalyzed Methanolysisrdquo Dave C Swalm School of ChemicalEngineering Mississippi State University Miss USA 2010

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International Journal of

International Journal of Chemical Engineering 5

Mole balance of D is as follows

119862D119900 minus 119862D

= minus120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1 minus 119896

+2119862D119862A + 119896

minus2119862M119862E2)

(20)

Mole balance of M is as follows

119862M119900 minus 119862M

= minus120591 (119896+2119862D119862A minus 119896

minus2119862M119862E2 minus 119896

+3119862M119862A + 119896

minus3119862G119862E3)

(21)

Mole balance of E1 is as follows

119862E1119900 minus 119862E1 = minus120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1) (22)

Mole balance of E2 is as follows

119862E2119900 minus 119862E2 = minus120591 (119896+2119862D119862A minus 119896

minus2119862M119862E2) (23)

Mole balance of E3 is as follows

119862E3119900 minus 119862E3 = minus120591 (119896+3119862M119862A minus 119896

minus3119862G119862E3) (24)

Mole balance of A (methanol) is as follows

119862A119900 minus 119862A

= 120591 (119896+1119862T119862A minus 119896

minus1119862D119862E1 + 119896

+2119862D119862A minus 119896

minus2119862M119862E2

+119896+3119862M119862A minus 119896

minus3119862G119862E3)

(25)

Mole balance of G is as follows

119862G119900 minus 119862G = minus120591 (119896+3119862M119862A minus 119896

minus3119862G119862E3) (26)

Closed form simultaneous solution of nonlinear equa-tions (19) to (26) by analysis is not possible They have to besolved numerically using amatrix inversion algorithmwhichis available in MATLAB The solution generates the molarconcentrations of all species 119862

119894 as functions of the design

variables that is the conversion of the limiting reactant andthe molar ratio of the excess variable 119860

3 Solution of the PFR and CSTR

31 Removal of Temporal Dependence Equations (6) to (13)cannot be solved in their time dependent forms because of thesingle degree of freedom of the problem In order to solve theequations simultaneously the degree of freedom is reduced tozero by changing the independent variable from time to theconversion or concentration of the limiting reactant using thechain rule and the mole balance equation for T (6) Considerthe following

119889119862119894

119889119862T= (

119889119862119894

119889119905

)(

119889119905

119889119862T) (27)

Hence (7) to (13) can be rewritten with concentration ofT as their independent variable as follows

119889119862D119889119862T

= minus(1 minus

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119889119862M119889119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2 minus 120572

4119862M119862A + 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119889119862E1119889119862T

= minus1

119889119862E2119889119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119889119862E3119889119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119889119862A119889119862T

= 1 +

1205722119862D119862A minus 120572

3119862M119862E2 + 120572

4119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

119889119862G119889119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

(28)

where

1205721=

119896minus1

119896+1

1205722=

119896+2

119896+1

1205723=

119896minus2

119896+1

1205724=

119896+3

119896+1

1205725=

119896minus3

119896+1

(29)

Similarly (28) cannot be solved in their time dependentforms because of the single degree of freedom of the problemIn order to solve the equations simultaneously the degreeof freedom is reduced to zero by changing the independentvariable from time to the conversion or concentration of thelimiting reactant using algebraic manipulation and the molebalance equation for T (19) Consider the following

119862119894119900minus 119862119894

119862T119900 minus 119862T= minus(

119862119894119900minus 119862119894

120591

)(

120591

119862T119900 minus 119862T) (30)

Hence (28) can be rewritten with concentration of T astheir independent variable as follows

119862D119900 minus 119862D119862T119900 minus 119862T

= minus(1 minus

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119862M119900 minus 119862M119862T119900 minus 119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2 minus 120572

4119862M119862A + 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119862E1119900 minus 119862E1119862T119900 minus 119862T

= minus1

6 International Journal of Chemical Engineering

119862E2119900 minus 119862E2119862T119900 minus 119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119862E3119900 minus 119862E3119862T119900 minus 119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119862A119900 minus 119862A119862T119900 minus 119862T

= 1 +

1205722119862D119862A minus 120572

3119862M119862E2 + 120572

4119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

119862G119900 minus 119862G119862T119900 minus 119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

) (31)

Two main cases are considered the base case where thereactions (2) to (4) are irreversible and the alternative casewhere the reactions are reversible

32 Case 1 Base Case Irreversible Reactions In Case 1 thebase case is considered by assuming (2) to (4) to be irre-versible reactions In other words the forward reactions areso dominant that the reverse reaction can be neglected andthe overall effect is that the reactions are irreversible Theresults of the base case can then be compared with that of thealternative Case 2 where the reactions are all reversible inorder to verify the importance of the reverse reaction and itsimplication to the maximum attainable molar concentrationof methyl ester Since the reverse reactions are omitted thevalue of 120572

1 1205723 and 120572

5is zero Hence (28) for PFR can be

rewritten as follows

119889119862D119889119862T

= minus(1 minus

1205722119862D

119862T) (32)

119889119862M119889119862T

= minus(

1205722119862D minus 120572

4119862M

119862T) (33)

119889119862E1119889119862T

= minus1 (34)

119889119862E2119889119862T

= minus

1205722119862D

119862T (35)

119889119862E3119889119862T

= minus

1205724119862M119862T

(36)

119889119862A119889119862T

= 1 +

1205722119862D + 120572

4119862M

119862T (37)

119889119862G119889119862T

= minus

1205724119862M119862T

(38)

The solution of the set of ordinary differential equations(32) can be found analytically by using the integrating factormethod [23] The concentrations of all the species generated

by the solution are then expressed in terms of the triglyceridesconversion119883T as shown in

119862T = 119862T119900 (1 minus 119883T)

119862D =

119862T1199001205722minus 1

[(

119862T119862T119900

) minus (

119862T119862T119900

)

1205722

]

=

119862T1199001205722minus 1

[(1 minus 119883T) minus (1 minus 119883T)1205722

]

119862M = 119862T119900 [1205722

1 minus 1205722

[

(1 minus 119883T)

1 minus 1205724

minus

(1 minus 119883T)1205722

1205722minus 1205724

]

+

1205722(1 minus 119883T)

1205724

(1 minus 1205724) (1205722minus 1205724)

]

119862E1 = 119862T119900 (1 minus (

119862T119862T119900

)) = 119862T119900 (1 minus (1 minus 119883T)) = 119862T119900119883T

119862E2 = 119862T119900 1 minus

1205722

1205722minus 1

[(1 minus 119883T) minus(1 minus 119883T)

1205722

1205722

]

119862E3 = 1205724119862T119900 [

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

119862A = 119862T119900 119872119877+

1205722

(1 minus 1205722)

times [(

(1 minus 1205722)

1205722

+

21205724minus 1

(1 minus 1205724)

)119883T

minus (

21205724minus 1205722

1205722(1205722minus 1205724)

) [1 minus (1 minus 119883T)1205722

]

minus

(1 minus 1205722)

(1 minus 1205724) (1205722minus 1205724)

times [1 minus (1 minus 119883T)1205724

] ]

119862G = 1205724119862T119900 [

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(39)

For the CSTR (31) can be manipulated algebraically andrewritten with conversion of T as their independent variableas follows

119862D =

119862T119900119883T (1 minus 119883T)

(1 minus (1 minus 1205722)119883T)

(40)

International Journal of Chemical Engineering 7

119862M =

1205722119862T119900119883

2

T (1 minus 119883T)

(1 minus (1 minus 1205724)119883T) (1 minus (1 minus 120572

2)119883T)

(41)

119862E1 = 119862T119900119883T (42)

119862E2 =1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

(43)

119862E3 =12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(44)

119862A = 119862T119900 (119872119877minus 1 +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

)

(45)

119862G =

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(46)

33 Case 2 Alternative Case Reversible Reactions In Case 2an alternative case was considered by assuming that thereactions in (2) to (4) are reversible Together with the basecase where the reactions are irreversible it can be used todiscover the significance of the reverse and forward reactions

Since the values of all 120572119894rsquos in (28) for the PFR and

(31) for the CSTR are not zero no closed form solutionto them can be found because they are too complex foranalytical solution The solution of both sets of equationscan be achieved by numerical methods using a computersimulation software Equations (28) for the PFR are solvedby using the ordinary differential equation 45 (ODE 45) inMATLAB Concentration of each species is obtained usingRungge-Kutta numerical integration algorithm On the otherhand (31) for the CSTR are solved by using the simultaneousnonlinear equations solver in MATLAB Concentration ofeach species is obtained using the multivariable Newton-Raphson algorithm

34 Selectivity of Methyl Esters and Glycerol for Case 1 andCase 2 The net concentration of methyl esters is the sum ofconcentration of ester 1 ester 2 and ester 3 In Case 1 the netconcentration of methyl esters in the PFR is given by

119862E1 + 119862E2 + 119862E3

= 119862T119900 1 + 119883T minus

1205722

1205722minus 1

[(1 minus 119883T) minus(1 minus 119883T)

1205722

1205722

]

+1205724[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(47)

Similarly the net concentration of methyl esters in theCSTR for Case 1 is given by

119862E1 + 119862E2 + 119862E3

= 119862E1119900 + 119862E2119900 + 119862E3119900

+ [119862T119900119883T +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(48)

The selectivity of methyl esters in Case 1 for PFR is givenby

119878E =

119883T + 1

119883Tminus

1205722

1205722minus 1

[

(1 minus 119883T)

119883Tminus

(1 minus 119883T)1205722

1205722119883T

]

+1205724[

1205722

1 minus 1205722

[

1

1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722119883T

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724119883T

]

(49)

The selectivity of glycerol in Case 1 for PFR is given by

119878G =

1205724

119883T[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(50)

On the other hand the selectivity of methyl esters inCase 1 for CSTR is given by

119878E = [1 +

1205722119883T

(1 minus (1 minus 1205722)119883T)

+

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(51)

The selectivity of glycerol in Case 1 for CSTR is given by

119878G =

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(52)

For Case 2 there is no closed form expression for selec-tivity of methyl esters and glycerolThe selectivities of methylesters and glycerol have to be calculated using (18) fromthe concentration of the species generated by the numericalsolution

4 Results and Discussion

41 Comparison of Selectivities for Cases 1 and 2 This studyhas shown the development of kinetic parameters for deter-mining methyl esters and glycerol selectivity in a biodiesel

8 International Journal of Chemical Engineering

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

ity

Conversion of triglyceride XT

Case 1-T = 60∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 60∘C MR = 6 1 catalyst = 02 wt

Figure 1 Selectivity plots of Cases 1 and 2 at reaction temperature60∘C molar ratio 6 1 and catalyst concentration 02 wt

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

ity

Conversion of triglyceride XT

Case 1-T = 70∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 70∘C MR = 6 1 catalyst = 02 wt

Figure 2 Selectivity plots of Cases 1 and 2 at reaction temperature70∘C molar ratio 6 1 and catalyst concentration 02 wt

transesterification reaction it has also established severalmathematical equations for the same Furthermore a par-ticularly important parameter for designing a reactor thatis product selectivity was determined for each case andcondition For comparing the base case and an alternativecase datasets 2 and 3 were evaluated using each calculationschemesThe difference in the selectivity between Case 1 andCase 2 which were investigated under the same conditionsis very significant and is attributed to the reversibility factorof the reaction as illustrated in Figures 1 and 2The results ofthe base case show that when all the reactions are irreversibleit implies that the maximum attainable molar concentrationand selectivity ofmethyl ester have been reachedThis verifiesthe significant role of the forward reactions in (2)ndash(4)

For a simple reversible reaction we can see the effectsof thermodynamic parameter like temperature on thereversibility of the reaction whereas the reversibility ofa reaction is controlled by reaction equilibrium constant

Table 2 Selectivity at 07ndash09 triglycerides conversion for datasets(1ndash3) and (6-7)

Conversion119883T Dataset Methyl esters selectivityCase 1 Case 2

07

1 2610 25262 2643 25113 2630 24706 2610 26137 2493 2313

08

1 2766 26752 2784 26663 2769 26296 2764 27667 2682 2480

09

1 2895 28322 2903 28163 2892 27886 2893 28797 2852 2655

The reaction equilibrium constant 119870 is defined as theforward rate constant divided by the reverse rate constant andaffected by temperature [12] This transesterification reactionis a complex reaction which consists of three reversibleand consecutive reactions Therefore for simplification andpreliminary design purpose selectivity is effectively used todetermine the effect of temperature and role of catalyst onthe reversibility Figures 1 and 2 show significant changes ofthe selectivity plots for conversion of triglycerides from 07to 09 and the plots finally reach the equilibrium at the endof the reaction In order to access the role of temperature andamount of catalyst on the reversibility of transesterificationreaction Table 2 was constructed by observing the methylesters selectivity for conversion of triglycerides from 07 to09 It presents the difference in selectivity for Case 1 andCase 2 Datasets (1ndash3) are used to determine the effects ofdifferent temperatures on the reversibility of the transesterifi-cation reaction which represent a temperature of 50 60 and70 respectively Conversion of triglyceride at 09 is selectedfor analysis From this data we can see that the forwardreaction alone is able to provide better selectivity than reversereaction at any temperature Datasets (6-7) are used to ana-lyze the role catalyst on the reversibility of transesterificationreaction whereas datasets 6 and 7 represent the amount ofcatalyst of 15 and 05 respectively A significant role ofthe forward reaction once again was determined at a highercatalyst concentrationThe results obtained also indicate thata higher catalyst concentration controls the forward reactionsand gives preferably product selectivity

According to Narvaez et al [9] and Noureddini and Zhu[5] the forward reactions in a transesterification reaction arethe most important reactions However Diasakou et al [7]claimed that the reverse reactions during a transesterificationreaction do not influence the forward reactions In this studya lower concentration of methyl ester was found for Case 2

International Journal of Chemical Engineering 9

Table 3 Activation energy

Reaction Activation energy (calmol)T rarr D 13145D rarr T 9932D rarr M 19860M rarr D 14639M rarr G 6421G rarr M 9588

which affects the selectivity and methyl ester conversionwhich is likely due to the reverse nature of the reaction [4]This result suggests that for establishing the optimal chemicalprocess for biodiesel fuel production it can be assumed thatwhen irreversible reactions are employed better selectivitycan be obtained because of the absence of reverse reactions

42 Effects of Reaction Characteristics on Selectivity Thereactor design stage for a biodiesel plant utilizes methyl esterselectivity for the material balances and stream costs Attain-ing the appropriate operating conditions through productselectivity can eliminate material and energy recycling thusreducing costsThe effects of the reaction temperature molarratio of methanol to oil and the catalyst concentration on theselectivity of methyl esters and glycerol are analyzed for bothCase 1 and Case 2 in the following subsections

421 Effect of ReactionTemperature on Selectivity An investi-gation on the effect of temperature onmethyl ester selectivitywas conducted using datasets (1ndash3) where the molar ratio ofalcohol to oil and the catalyst concentration are fixed TheArrhenius equation was used for this investigation

119896 = 119896∘exp(minus

119864

119877119879

) (53)

According to (53) the reaction rate 119896 is an integralpart of the selectivity expressions It depends on the energyof activation (119864) obtained from the Arrhenius equation[22] For reactions at different temperatures fixed molarratios and catalyst concentrations the activation energy isconstant In this study the kinetic data used to analyzethe temperature effect were adapted from Noureddini andZhu [5] Because the data published in their research utilizethe average reaction rate constants at 50∘C and constantactivation energy (53) can bemanipulated to obtain the otherreaction rate constants (at 60∘C and 70∘C) listed in Table 1The results of the activation energy investigated in their studyare shown in Table 3

Figures 3 and 4 show the effects of the reaction tempera-ture on the selectivity ofmethyl esters and glycerol for Cases 1and 2 respectively The reaction temperature had a small butsubstantial effect on the selectivity The figures show thatthe selectivity of methyl esters is high at a high temperaturein the early conversion of T However in both figures theselectivities of E for both Cases 1 and 2 at 70∘C were foundto decrease toward the completion of the reaction As theboiling point of methanol is 647∘C an additional 5∘C has

0

02

04

06

08

1

12

00

05

10

15

20

25

30

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 3 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 1

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 4 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 2

the effect of lowering the product concentration and affectingthe selectivity of E at the equilibriumThis temperature effectchanges the slope of selectivity from a concave to a convexshape which is also related with the reaction rate constant atdifferent temperatures

According to Darnoko and Cheryan [2] the transester-ification reaction rates were increased at 65∘C as comparedwith those at 50∘C The results of their research also showedan enhanced methyl ester yield at 65∘C compared withthat at 50∘C which was because of the higher viscosity ofoil at 50∘C In addition 55∘C is a stable temperature thatcan maintain the oil liquidity This result indicates that anoptimum temperature promotes the formation of methylesters and thus contributes to a higher selectivity of biodieselproducts It can also be suggested that the reaction rateconstant 119896 which is greatly dependent on the temperatureand selectivity of E is greatly improved at the optimumtemperature

10 International Journal of Chemical Engineering

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 5 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 1

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 6 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 2

The findings confirm that methyl ester selectivity effectscan be realistically obtained at the optimum temperaturewhich is 60∘C in this study As the reactor optimizationrequires the relationship between the conversion and selec-tivity in both cases (Case 1 and Case 2) the selectivity withinthe studied temperature indicates that the biodiesel reactormay work more efficiently in converting T to E at 60∘C

422 Effect of Molar Ratio of Methanol to Oil on SelectivityAn investigation into the effects of the methanol-to-oil molarratio involves datasets 4 and 5 Selectivity plots of methylesters and glycerol are shown in Figures 5 and 6 For Cases 1and 2 the selectivity of methyl esters and glycerol was rela-tively affected by the molar ratio of methanol to oil It can beseen from the figures that the higher molar ratio of methanolto oil encourages the formation of transesterification reactionproducts thus contributing to a higher selectivity

The most striking result to emerge from the figures isthe change in the shape of the selectivity plot from concave

0

02

04

06

08

1

12

0 02 04 06 08 1

Sele

ctiv

ity

(a)(b)

(c)

Triglyceride conversion XT

Figure 7 Selectivity plots (a) methyl ester 1 (b) methyl ester 2 and(c) methyl ester 3 for dataset 4

to convex for a molar ratio of 9 1 An increasing selectivityof methyl ester can be found in an early conversion oftriglyceride but toward equilibrium the selectivity is foundto slightly decrease A possible explanation for this mightbe that the methyl ester concentration has both quadratic aswell as cubic effects that can be explained by (42)ndash(44) andFigure 7

According to (42) the selectivity of methyl ester 1 isconstant at 1 Equation (43) is a quadratic equation whichgives a parabolic shape to the plot of methyl ester 2 Equation(44) clearly illustrates the selectivity of methyl ester 3 whenthe equation is a cubic one In more detail the power of twois more dominant at an 119883T of less than 03 which meansthat the formation of E2 is more active under this conditionHowever we can see an active formation of E3 at an 119883Tof 05ndash1 when the power of three is dominant At the sametime E1 is formed linearly with a triglyceride conversionThe stepwise transesterification reaction in (2)ndash(4) shows thateach E is formed consecutivelyThismeans that to achieve themaximum yield the maximum selectivity at the maximum Tconversion is necessary and each E must be formed duringthe process Therefore it can be assumed that the selectivityof methyl ester is more greatly affected by the quadratic andcubic functions at a highermolar ratio ofmethanol to oil thanat a lower one

In addition Freedman et al [11] reported that the bestmethyl ester conversion is achieved at a molar ratio of 6 1with alkaline catalyst and that higher molar ratios do notincrease the productivity but do increase the cost of alcoholrecovery At a high molar excess of methanol a pseudo-first-order reaction appeared more likely than a second-order reaction However high molar ratio of methanol isused for noncatalytic and supercritical methanol reaction[6 11 20 24] Narvaez et al [9] stated that when an excessamount of methanol is used it can positively affect thereversible characteristic of the reaction and the displacementof the reaction toward the product As a consequence excessmethanol does not necessarily contribute to an increase in theconcentration of methyl ester and glycerol

International Journal of Chemical Engineering 11

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 8 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 9 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 2

423 Effect of Catalyst Concentration on Selectivity Apartfrom the temperature and molar ratio the parameters thataffect the selectivity are the same as those influencing thereaction rates namely the catalyst The effects of the catalystconcentration are studied through datasets 6 and 7 andthe selectivity plots can be seen in Figures 8 and 9 Whenanalyzing the figures it can be seen that the selectivity of bothproducts is higher at a higher catalyst concentration

Toward the equilibrium of the reaction the selectivitywas observed to increase at a higher catalyst concentra-tion thus contributing to an increased amount of methylester formation Vicente et al [25] stated that the largestmethyl ester conversions are obtained when a large catalystconcentration is employed (13) at a mild temperature(20ndash50∘C) This agrees with the resulting selectivity curvesplotted which indicates that the catalyst concentration hasa positive effect on the selectivity of methyl esters andglycerol However a greater application of an alkali catalystcan lead to the production of large amounts of soap andextra cost is required to remove the catalyst from the reactionsystem Srivastava and Prasad [26] have stated that a catalyst

0

02

04

06

08

1

12

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity

(a)

(c)(b)

Triglyceride conversion XT

Figure 10 Selectivity plots (a)methyl ester 1 (b)methyl ester 2 and(c) methyl ester 3 for dataset 6

concentration of 05ndash1 can yield up to a 99 methyl esterconversion

In Figures 8 and 9 there is a clear increasing trend of theselectivity ofmethyl ester for a 15 wt catalyst concentrationduring the early conversion of the reactant which decreasesat the end of the reactionThe same transition trend has beenfound when analyzing the influence of the molar ratio onmethyl ester selectivity A further detailed analysis showedthat the quadratic and cubic effects are more significantat a higher catalyst concentration than at a lower catalystconcentration As shown in Figure 10 the selectivity of E2 hasa quadratic plot whereas the selectivity of E3 has a parabolicshape Referring to (42)ndash(44) we can see that E1 is linearlyformed with a T conversion E2 is produced more at a Tconversion of lower than 035 where we can see that thepower of two in (43) is more dominant at this stage At aT conversion of over 05 the effect of the power of three in(44) is dominant causing a higher formation of E3 Becausethe transesterification reaction is a reversible and consecutiveequation the formation of three Es is important to achievea better selectivity With an optimum amount of catalyst thereactor becomesmore efficient in converting the reactant intothe products

43 Comparison ofMethyl Ester Selectivities fromDifferent OilFeedstocks To compare the selectivities of methyl esters andglycerol from different feedstocks datasets (8ndash10) were usedFigure 11 presents the selectivity ofmethyl esters derived fromrapeseed oil waste sunflower oil and palm oil for Case 1 andCase 2 As can be seen from the graph the methyl estersand glycerol were more likely to form if palm oil is used asthe feedstock compared to the other two oil feedstocks Thepresent finding also suggests that the selectivity of methylester was much lower when using low cost feedstock such aswaste sunflower oil Waste oil contains large amounts of freefatty acids (FFAs) (about 20) which affect the yield of fuelfrom that process The amount of FFAs in palm oil is 064[3] but for rapeseed oil the author used fresh oil [27] whichis estimated less than 1

12 International Journal of Chemical Engineering

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

PO-case 1 RO-case 1

WSO-case 1 WSO-case 2RO-case 2PO-case 2

Conversion of triglyceride XT

Sele

ctiv

ity o

f met

hyl e

sters

Figure 11 Selectivity plots of methyl ester from various feedstockfor Cases 1 and 2

As discussed before these free fatty acids will reactwith alkali catalysts to produce soaps that will inhibit thetransesterification reaction Soaps will allow emulsificationthat causes the phase separation of methyl ester and glycerolto be less sharp It produces water that can hydrolyze thetriglycerides and contribute to the formation of more soap[14] The effect of reversibility of transesterification can beseen significantly when analysing the selectivity of methylester derived from palm oil In Figure 11 methyl ester derivedfrom palm oil shows a higher selectivity plot for base caseThis finding suggests that forward reaction dominates thereaction and contributes to a better selectivity when lowFFAs feedstock is used in biodiesel production As there aremany low cost feedstocks available for biodiesel productiona pretreatment to these feedstocks can be carried out in orderto ensure the value of FFAs is within the allowable range

5 Conclusions

This paper has presented a comprehensive kinetic modelingof a transesterification reaction for biodiesel with homoge-neous alkaline catalyst The purpose of the study was todevelop the kinetic models of transesterification reactiondetermine the selectivity of methyl ester and glycerol andevaluate the significance of the reverse reactions in the trans-esterification reaction This study has shown that a processmodel solution was found for two types of common biodieselreactors The concentration of each species during transes-terification was found leading to a selectivity determinationduring the biodiesel production In addition the reversibleand irreversible effects of a transesterification reaction werediscovered The forward reaction is more dominant than thereverse reaction and the maximum selectivity can be foundif a base case of transesterification reaction is assumed tohave occurred in the biodiesel reactor system For the variousreaction characteristics under investigation the selectivities

are influenced by the temperature molar ratio of methanolto oil catalyst concentration and type of oil used as thefeedstock Furthermore an analysis of the selectivity plotsindicates an enhanced effect of the reaction characteristicson the selectivity This research has shown that the selectivityof methyl ester is maximized at 60∘C a 9 1 molar ratio ofmethanol to oil and a catalyst concentration of 15 Thisinvestigation into the effects of the molar ratio of methanolto oil and the catalyst concentration on the selectivity canbe made more interesting if several more curves are plottedat a molar ratio of methanol to oil between 3 1 to 9 1 anda catalyst concentration between 05 and 15 Howevera limitation of this research remains in the availability ofthe reaction rate constants under various reaction condi-tions In addition a comparison should be made throughmutual reaction conditionsThe findings from this study willenhance the concept of selectivity and its applications inthe evaluation of complex transesterification reactions whenthe goal is to attain the maximum production of methylesters and glycerol It is recommended that further researchis undertaken in exploring the selectivity data for specifyingthe reactor configurations and may be used in the synthesisof reactor network for biodiesel production

Nomenclature

119896+1 119896minus1 119896+2

119896minus2 119896+3 119896minus3

Reaction constant

119862T 119862D 119862M 119862G119862E1 119862E2 119862E3119862A 119862E

Molar concentration of triglyceridediglyceride monoglyceride glycerolester 1 ester 2 ester 3 methanol andmethyl ester

119883T Conversion of triglyceride119872119877 Molar ratio

119862T0 Initial molar concentration oftriglyceride

119878E 119878G Selectivity of methyl ester glycerol120572 Reaction rate constant factorwt Weight percentT TriglycerideD DiglycerideM MonoglycerideA MethanolG GlycerolE Methyl esterE1 Methyl ester 1E2 Methyl ester 2E3 Methyl ester 3PFR Plug flow reactorCSTR Continuous stirred tank reactor119873T0 Initial amount of triglyceride at 119905 = 0

119873T The amount of triglyceride present attime 119905

119881 VolumePO Palm oilRO Rapeseed oilWSO Waste sunflower oilNaOH Sodium hydroxide

International Journal of Chemical Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgment

Thework was carried out with the financial support from theMinistry of Education Malaysia

References

[1] A Demirbas ldquoBiodiesel from triglycerides via transesterifica-tionrdquo in Biodiesel pp 121ndash140 Springer London UK 2008

[2] D Darnoko and M Cheryan ldquoKinetics of palm oil transesteri-fication in a batch reactorrdquo JAOCS Journal of the American OilChemistsrsquo Society vol 77 no 12 pp 1263ndash1267 2000

[3] T Leevijit WWisutmethangoon G Prateepehaikul C Tongu-rai and M Allen ldquoA second order kinetics of palm oil transes-terification in a batch reactorrdquo in Proceedings of the Joint Inter-national Conference on Sustainable Energy and Environment pp277ndash281 2004

[4] S Jain andM P Sharma ldquoKinetics of acid base catalyzed trans-esterification of Jatropha curcas oilrdquo Bioresource Technology vol101 no 20 pp 7701ndash7706 2010

[5] H Noureddini and D Zhu ldquoKinetics of transesterification ofsoybean oilrdquo Journal of the American Oil Chemistsrsquo Society vol74 no 11 pp 1457ndash1463 1997

[6] D Kusdiana and S Saka ldquoKinetics of transesterification in rape-seed oil to biodiesel fuel as treated in supercritical methanolrdquoFuel vol 80 no 5 pp 693ndash698 2001

[7] M Diasakou A Louloudi and N Papayannakos ldquoKinetics ofthe non-catalytic transesterification of soybean oilrdquo Fuel vol 77no 12 pp 1297ndash1302 1998

[8] H Maeda S Hagiwara H Nabetani et al ldquoBiodiesel fuelsfrom palm oil via the non-catalytic transesterification in abubble column reactor at atmospheric pressure a kinetic studyrdquoRenewable Energy vol 33 no 7 pp 1629ndash1636 2008

[9] P C Narvaez S M Rincon and F J Sanchez ldquoKinetics of palmoil methanolysisrdquo Journal of the American Oil Chemistsrsquo Societyvol 84 pp 971ndash977 2007

[10] E Minami and S Saka ldquoKinetics of hydrolysis and methylesterification for biodiesel production in two-step supercriticalmethanol processrdquo Fuel vol 85 no 17-18 pp 2479ndash2483 2006

[11] B Freedman R O Butterfield and E H Pryde ldquoTransesteri-fication kinetics of soybean oil 1rdquo Journal of the American OilChemistsrsquo Society vol 63 no 10 pp 1375ndash1380 1986

[12] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

[13] J M Douglas Conceptual Design of Chemical ProcessesMcGraw Hill 1988

[14] J van Gerpen B Shanks R Pruszko D Clements and GKnothe Biodiesel Production Technology Subcontractor ReportNational Reanewable Energy Laboratory 2004

[15] H J Wright J B Segur H V Clark S K Coburn E ELangdon and R N DuPuis ldquoA report on ester interchangerdquoOilamp Soap vol 21 no 5 pp 145ndash148 1944

[16] H Fukuda A Kondo and H Noda ldquoBiodiesel fuel productionby transesterification of oilsrdquo Journal of Bioscience and Bioengi-neering vol 92 no 5 pp 405ndash416 2001

[17] L Friesenhagen and H Lepper ldquoProcess for the productionof fatty acid esters of short-chain aliphatic alcohols from fatsandor oils containing free fatty acidsrdquoUS Patent 4608202 1986

[18] P Felizardo J MacHado D Vergueiro M J N Correia J PGomes and J M Bordado ldquoStudy on the glycerolysis reactionof high free fatty acid oils for use as biodiesel feedstockrdquo FuelProcessing Technology vol 92 no 6 pp 1225ndash1229 2011

[19] A Tafesh and S Basheer ldquoPretreatment methods in biodieselproduction processesrdquo in Pretreatment Techniques for Biofuelsand Biorefineries Z Fang Ed Green Energy and Technologypp 417ndash434 Springer Berlin Germany 2013

[20] D Kusdiana and S Saka ldquoEffects of water on biodiesel fuelproduction by supercritical methanol treatmentrdquo BioresourceTechnology vol 91 no 3 pp 289ndash295 2004

[21] K Komers F Skopal R Stloukal and J Machek ldquoKinetics andmechanism of the KOHmdashcatalyzed methanolysis of rapeseedoil for biodiesel productionrdquo European Journal of Lipid Scienceand Technology vol 104 pp 728ndash737 2002

[22] A K CokerModeling of Chemical Kinetics and Reactor DesignGulf Publishing Houston Tex USA 2001

[23] C D Holland and R G Anthony Fundamentals of ChemicalReaction Engineering Prentice-Hall 1979

[24] J K Rodrıguez-Guerrero M F Rubens and P T V RosaldquoProduction of biodiesel from castor oil using sub and super-critical ethanol effect of sodium hydroxide on the ethyl esterproductionrdquoThe Journal of Supercritical Fluids vol 83 pp 124ndash132 2013

[25] G Vicente M Martınez and J Aracil ldquoOptimisation ofintegrated biodiesel production Part I A study of the biodieselpurity and yieldrdquoBioresource Technology vol 98 no 9 pp 1724ndash1733 2007

[26] A Srivastava and R Prasad ldquoTriglycerides-based diesel fuelsrdquoRenewable and Sustainable Energy Reviews vol 4 no 2 pp 111ndash133 2000

[27] B Klofutar J Golob B Likozar C Klofutar E Zagar andI Poljansek ldquoThe transesterification of rapeseed and wastesunflower oils mass-transfer and kinetics in a laboratory batchreactor and in an industrial-scale reactorseparator setuprdquoBioresource Technology vol 101 no 10 pp 3333ndash3344 2010

[28] S D Crymble ldquoOptimization and Reaction Kinetics of the Pro-duction of Biodiesel from Castor Oil via Sodium Methoxide-Catalyzed Methanolysisrdquo Dave C Swalm School of ChemicalEngineering Mississippi State University Miss USA 2010

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6 International Journal of Chemical Engineering

119862E2119900 minus 119862E2119862T119900 minus 119862T

= minus(

1205722119862D119862A minus 120572

3119862M119862E2

119862T119862A minus 1205721119862D119862E1

)

119862E3119900 minus 119862E3119862T119900 minus 119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

)

119862A119900 minus 119862A119862T119900 minus 119862T

= 1 +

1205722119862D119862A minus 120572

3119862M119862E2 + 120572

4119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

119862G119900 minus 119862G119862T119900 minus 119862T

= minus(

1205724119862M119862A minus 120572

5119862G119862E3

119862T119862A minus 1205721119862D119862E1

) (31)

Two main cases are considered the base case where thereactions (2) to (4) are irreversible and the alternative casewhere the reactions are reversible

32 Case 1 Base Case Irreversible Reactions In Case 1 thebase case is considered by assuming (2) to (4) to be irre-versible reactions In other words the forward reactions areso dominant that the reverse reaction can be neglected andthe overall effect is that the reactions are irreversible Theresults of the base case can then be compared with that of thealternative Case 2 where the reactions are all reversible inorder to verify the importance of the reverse reaction and itsimplication to the maximum attainable molar concentrationof methyl ester Since the reverse reactions are omitted thevalue of 120572

1 1205723 and 120572

5is zero Hence (28) for PFR can be

rewritten as follows

119889119862D119889119862T

= minus(1 minus

1205722119862D

119862T) (32)

119889119862M119889119862T

= minus(

1205722119862D minus 120572

4119862M

119862T) (33)

119889119862E1119889119862T

= minus1 (34)

119889119862E2119889119862T

= minus

1205722119862D

119862T (35)

119889119862E3119889119862T

= minus

1205724119862M119862T

(36)

119889119862A119889119862T

= 1 +

1205722119862D + 120572

4119862M

119862T (37)

119889119862G119889119862T

= minus

1205724119862M119862T

(38)

The solution of the set of ordinary differential equations(32) can be found analytically by using the integrating factormethod [23] The concentrations of all the species generated

by the solution are then expressed in terms of the triglyceridesconversion119883T as shown in

119862T = 119862T119900 (1 minus 119883T)

119862D =

119862T1199001205722minus 1

[(

119862T119862T119900

) minus (

119862T119862T119900

)

1205722

]

=

119862T1199001205722minus 1

[(1 minus 119883T) minus (1 minus 119883T)1205722

]

119862M = 119862T119900 [1205722

1 minus 1205722

[

(1 minus 119883T)

1 minus 1205724

minus

(1 minus 119883T)1205722

1205722minus 1205724

]

+

1205722(1 minus 119883T)

1205724

(1 minus 1205724) (1205722minus 1205724)

]

119862E1 = 119862T119900 (1 minus (

119862T119862T119900

)) = 119862T119900 (1 minus (1 minus 119883T)) = 119862T119900119883T

119862E2 = 119862T119900 1 minus

1205722

1205722minus 1

[(1 minus 119883T) minus(1 minus 119883T)

1205722

1205722

]

119862E3 = 1205724119862T119900 [

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

119862A = 119862T119900 119872119877+

1205722

(1 minus 1205722)

times [(

(1 minus 1205722)

1205722

+

21205724minus 1

(1 minus 1205724)

)119883T

minus (

21205724minus 1205722

1205722(1205722minus 1205724)

) [1 minus (1 minus 119883T)1205722

]

minus

(1 minus 1205722)

(1 minus 1205724) (1205722minus 1205724)

times [1 minus (1 minus 119883T)1205724

] ]

119862G = 1205724119862T119900 [

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(39)

For the CSTR (31) can be manipulated algebraically andrewritten with conversion of T as their independent variableas follows

119862D =

119862T119900119883T (1 minus 119883T)

(1 minus (1 minus 1205722)119883T)

(40)

International Journal of Chemical Engineering 7

119862M =

1205722119862T119900119883

2

T (1 minus 119883T)

(1 minus (1 minus 1205724)119883T) (1 minus (1 minus 120572

2)119883T)

(41)

119862E1 = 119862T119900119883T (42)

119862E2 =1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

(43)

119862E3 =12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(44)

119862A = 119862T119900 (119872119877minus 1 +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

)

(45)

119862G =

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(46)

33 Case 2 Alternative Case Reversible Reactions In Case 2an alternative case was considered by assuming that thereactions in (2) to (4) are reversible Together with the basecase where the reactions are irreversible it can be used todiscover the significance of the reverse and forward reactions

Since the values of all 120572119894rsquos in (28) for the PFR and

(31) for the CSTR are not zero no closed form solutionto them can be found because they are too complex foranalytical solution The solution of both sets of equationscan be achieved by numerical methods using a computersimulation software Equations (28) for the PFR are solvedby using the ordinary differential equation 45 (ODE 45) inMATLAB Concentration of each species is obtained usingRungge-Kutta numerical integration algorithm On the otherhand (31) for the CSTR are solved by using the simultaneousnonlinear equations solver in MATLAB Concentration ofeach species is obtained using the multivariable Newton-Raphson algorithm

34 Selectivity of Methyl Esters and Glycerol for Case 1 andCase 2 The net concentration of methyl esters is the sum ofconcentration of ester 1 ester 2 and ester 3 In Case 1 the netconcentration of methyl esters in the PFR is given by

119862E1 + 119862E2 + 119862E3

= 119862T119900 1 + 119883T minus

1205722

1205722minus 1

[(1 minus 119883T) minus(1 minus 119883T)

1205722

1205722

]

+1205724[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(47)

Similarly the net concentration of methyl esters in theCSTR for Case 1 is given by

119862E1 + 119862E2 + 119862E3

= 119862E1119900 + 119862E2119900 + 119862E3119900

+ [119862T119900119883T +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(48)

The selectivity of methyl esters in Case 1 for PFR is givenby

119878E =

119883T + 1

119883Tminus

1205722

1205722minus 1

[

(1 minus 119883T)

119883Tminus

(1 minus 119883T)1205722

1205722119883T

]

+1205724[

1205722

1 minus 1205722

[

1

1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722119883T

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724119883T

]

(49)

The selectivity of glycerol in Case 1 for PFR is given by

119878G =

1205724

119883T[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(50)

On the other hand the selectivity of methyl esters inCase 1 for CSTR is given by

119878E = [1 +

1205722119883T

(1 minus (1 minus 1205722)119883T)

+

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(51)

The selectivity of glycerol in Case 1 for CSTR is given by

119878G =

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(52)

For Case 2 there is no closed form expression for selec-tivity of methyl esters and glycerolThe selectivities of methylesters and glycerol have to be calculated using (18) fromthe concentration of the species generated by the numericalsolution

4 Results and Discussion

41 Comparison of Selectivities for Cases 1 and 2 This studyhas shown the development of kinetic parameters for deter-mining methyl esters and glycerol selectivity in a biodiesel

8 International Journal of Chemical Engineering

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

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Conversion of triglyceride XT

Case 1-T = 60∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 60∘C MR = 6 1 catalyst = 02 wt

Figure 1 Selectivity plots of Cases 1 and 2 at reaction temperature60∘C molar ratio 6 1 and catalyst concentration 02 wt

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

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Conversion of triglyceride XT

Case 1-T = 70∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 70∘C MR = 6 1 catalyst = 02 wt

Figure 2 Selectivity plots of Cases 1 and 2 at reaction temperature70∘C molar ratio 6 1 and catalyst concentration 02 wt

transesterification reaction it has also established severalmathematical equations for the same Furthermore a par-ticularly important parameter for designing a reactor thatis product selectivity was determined for each case andcondition For comparing the base case and an alternativecase datasets 2 and 3 were evaluated using each calculationschemesThe difference in the selectivity between Case 1 andCase 2 which were investigated under the same conditionsis very significant and is attributed to the reversibility factorof the reaction as illustrated in Figures 1 and 2The results ofthe base case show that when all the reactions are irreversibleit implies that the maximum attainable molar concentrationand selectivity ofmethyl ester have been reachedThis verifiesthe significant role of the forward reactions in (2)ndash(4)

For a simple reversible reaction we can see the effectsof thermodynamic parameter like temperature on thereversibility of the reaction whereas the reversibility ofa reaction is controlled by reaction equilibrium constant

Table 2 Selectivity at 07ndash09 triglycerides conversion for datasets(1ndash3) and (6-7)

Conversion119883T Dataset Methyl esters selectivityCase 1 Case 2

07

1 2610 25262 2643 25113 2630 24706 2610 26137 2493 2313

08

1 2766 26752 2784 26663 2769 26296 2764 27667 2682 2480

09

1 2895 28322 2903 28163 2892 27886 2893 28797 2852 2655

The reaction equilibrium constant 119870 is defined as theforward rate constant divided by the reverse rate constant andaffected by temperature [12] This transesterification reactionis a complex reaction which consists of three reversibleand consecutive reactions Therefore for simplification andpreliminary design purpose selectivity is effectively used todetermine the effect of temperature and role of catalyst onthe reversibility Figures 1 and 2 show significant changes ofthe selectivity plots for conversion of triglycerides from 07to 09 and the plots finally reach the equilibrium at the endof the reaction In order to access the role of temperature andamount of catalyst on the reversibility of transesterificationreaction Table 2 was constructed by observing the methylesters selectivity for conversion of triglycerides from 07 to09 It presents the difference in selectivity for Case 1 andCase 2 Datasets (1ndash3) are used to determine the effects ofdifferent temperatures on the reversibility of the transesterifi-cation reaction which represent a temperature of 50 60 and70 respectively Conversion of triglyceride at 09 is selectedfor analysis From this data we can see that the forwardreaction alone is able to provide better selectivity than reversereaction at any temperature Datasets (6-7) are used to ana-lyze the role catalyst on the reversibility of transesterificationreaction whereas datasets 6 and 7 represent the amount ofcatalyst of 15 and 05 respectively A significant role ofthe forward reaction once again was determined at a highercatalyst concentrationThe results obtained also indicate thata higher catalyst concentration controls the forward reactionsand gives preferably product selectivity

According to Narvaez et al [9] and Noureddini and Zhu[5] the forward reactions in a transesterification reaction arethe most important reactions However Diasakou et al [7]claimed that the reverse reactions during a transesterificationreaction do not influence the forward reactions In this studya lower concentration of methyl ester was found for Case 2

International Journal of Chemical Engineering 9

Table 3 Activation energy

Reaction Activation energy (calmol)T rarr D 13145D rarr T 9932D rarr M 19860M rarr D 14639M rarr G 6421G rarr M 9588

which affects the selectivity and methyl ester conversionwhich is likely due to the reverse nature of the reaction [4]This result suggests that for establishing the optimal chemicalprocess for biodiesel fuel production it can be assumed thatwhen irreversible reactions are employed better selectivitycan be obtained because of the absence of reverse reactions

42 Effects of Reaction Characteristics on Selectivity Thereactor design stage for a biodiesel plant utilizes methyl esterselectivity for the material balances and stream costs Attain-ing the appropriate operating conditions through productselectivity can eliminate material and energy recycling thusreducing costsThe effects of the reaction temperature molarratio of methanol to oil and the catalyst concentration on theselectivity of methyl esters and glycerol are analyzed for bothCase 1 and Case 2 in the following subsections

421 Effect of ReactionTemperature on Selectivity An investi-gation on the effect of temperature onmethyl ester selectivitywas conducted using datasets (1ndash3) where the molar ratio ofalcohol to oil and the catalyst concentration are fixed TheArrhenius equation was used for this investigation

119896 = 119896∘exp(minus

119864

119877119879

) (53)

According to (53) the reaction rate 119896 is an integralpart of the selectivity expressions It depends on the energyof activation (119864) obtained from the Arrhenius equation[22] For reactions at different temperatures fixed molarratios and catalyst concentrations the activation energy isconstant In this study the kinetic data used to analyzethe temperature effect were adapted from Noureddini andZhu [5] Because the data published in their research utilizethe average reaction rate constants at 50∘C and constantactivation energy (53) can bemanipulated to obtain the otherreaction rate constants (at 60∘C and 70∘C) listed in Table 1The results of the activation energy investigated in their studyare shown in Table 3

Figures 3 and 4 show the effects of the reaction tempera-ture on the selectivity ofmethyl esters and glycerol for Cases 1and 2 respectively The reaction temperature had a small butsubstantial effect on the selectivity The figures show thatthe selectivity of methyl esters is high at a high temperaturein the early conversion of T However in both figures theselectivities of E for both Cases 1 and 2 at 70∘C were foundto decrease toward the completion of the reaction As theboiling point of methanol is 647∘C an additional 5∘C has

0

02

04

06

08

1

12

00

05

10

15

20

25

30

0 02 04 06 08 1

Sele

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Sele

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Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 3 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 1

Sele

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0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 02 04 06 08 1

Sele

ctiv

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f gly

cero

l

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 4 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 2

the effect of lowering the product concentration and affectingthe selectivity of E at the equilibriumThis temperature effectchanges the slope of selectivity from a concave to a convexshape which is also related with the reaction rate constant atdifferent temperatures

According to Darnoko and Cheryan [2] the transester-ification reaction rates were increased at 65∘C as comparedwith those at 50∘C The results of their research also showedan enhanced methyl ester yield at 65∘C compared withthat at 50∘C which was because of the higher viscosity ofoil at 50∘C In addition 55∘C is a stable temperature thatcan maintain the oil liquidity This result indicates that anoptimum temperature promotes the formation of methylesters and thus contributes to a higher selectivity of biodieselproducts It can also be suggested that the reaction rateconstant 119896 which is greatly dependent on the temperatureand selectivity of E is greatly improved at the optimumtemperature

10 International Journal of Chemical Engineering

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0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 5 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 1

Sele

ctiv

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f gly

cero

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0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 6 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 2

The findings confirm that methyl ester selectivity effectscan be realistically obtained at the optimum temperaturewhich is 60∘C in this study As the reactor optimizationrequires the relationship between the conversion and selec-tivity in both cases (Case 1 and Case 2) the selectivity withinthe studied temperature indicates that the biodiesel reactormay work more efficiently in converting T to E at 60∘C

422 Effect of Molar Ratio of Methanol to Oil on SelectivityAn investigation into the effects of the methanol-to-oil molarratio involves datasets 4 and 5 Selectivity plots of methylesters and glycerol are shown in Figures 5 and 6 For Cases 1and 2 the selectivity of methyl esters and glycerol was rela-tively affected by the molar ratio of methanol to oil It can beseen from the figures that the higher molar ratio of methanolto oil encourages the formation of transesterification reactionproducts thus contributing to a higher selectivity

The most striking result to emerge from the figures isthe change in the shape of the selectivity plot from concave

0

02

04

06

08

1

12

0 02 04 06 08 1

Sele

ctiv

ity

(a)(b)

(c)

Triglyceride conversion XT

Figure 7 Selectivity plots (a) methyl ester 1 (b) methyl ester 2 and(c) methyl ester 3 for dataset 4

to convex for a molar ratio of 9 1 An increasing selectivityof methyl ester can be found in an early conversion oftriglyceride but toward equilibrium the selectivity is foundto slightly decrease A possible explanation for this mightbe that the methyl ester concentration has both quadratic aswell as cubic effects that can be explained by (42)ndash(44) andFigure 7

According to (42) the selectivity of methyl ester 1 isconstant at 1 Equation (43) is a quadratic equation whichgives a parabolic shape to the plot of methyl ester 2 Equation(44) clearly illustrates the selectivity of methyl ester 3 whenthe equation is a cubic one In more detail the power of twois more dominant at an 119883T of less than 03 which meansthat the formation of E2 is more active under this conditionHowever we can see an active formation of E3 at an 119883Tof 05ndash1 when the power of three is dominant At the sametime E1 is formed linearly with a triglyceride conversionThe stepwise transesterification reaction in (2)ndash(4) shows thateach E is formed consecutivelyThismeans that to achieve themaximum yield the maximum selectivity at the maximum Tconversion is necessary and each E must be formed duringthe process Therefore it can be assumed that the selectivityof methyl ester is more greatly affected by the quadratic andcubic functions at a highermolar ratio ofmethanol to oil thanat a lower one

In addition Freedman et al [11] reported that the bestmethyl ester conversion is achieved at a molar ratio of 6 1with alkaline catalyst and that higher molar ratios do notincrease the productivity but do increase the cost of alcoholrecovery At a high molar excess of methanol a pseudo-first-order reaction appeared more likely than a second-order reaction However high molar ratio of methanol isused for noncatalytic and supercritical methanol reaction[6 11 20 24] Narvaez et al [9] stated that when an excessamount of methanol is used it can positively affect thereversible characteristic of the reaction and the displacementof the reaction toward the product As a consequence excessmethanol does not necessarily contribute to an increase in theconcentration of methyl ester and glycerol

International Journal of Chemical Engineering 11

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0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 8 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 1

Sele

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0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 9 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 2

423 Effect of Catalyst Concentration on Selectivity Apartfrom the temperature and molar ratio the parameters thataffect the selectivity are the same as those influencing thereaction rates namely the catalyst The effects of the catalystconcentration are studied through datasets 6 and 7 andthe selectivity plots can be seen in Figures 8 and 9 Whenanalyzing the figures it can be seen that the selectivity of bothproducts is higher at a higher catalyst concentration

Toward the equilibrium of the reaction the selectivitywas observed to increase at a higher catalyst concentra-tion thus contributing to an increased amount of methylester formation Vicente et al [25] stated that the largestmethyl ester conversions are obtained when a large catalystconcentration is employed (13) at a mild temperature(20ndash50∘C) This agrees with the resulting selectivity curvesplotted which indicates that the catalyst concentration hasa positive effect on the selectivity of methyl esters andglycerol However a greater application of an alkali catalystcan lead to the production of large amounts of soap andextra cost is required to remove the catalyst from the reactionsystem Srivastava and Prasad [26] have stated that a catalyst

0

02

04

06

08

1

12

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity

(a)

(c)(b)

Triglyceride conversion XT

Figure 10 Selectivity plots (a)methyl ester 1 (b)methyl ester 2 and(c) methyl ester 3 for dataset 6

concentration of 05ndash1 can yield up to a 99 methyl esterconversion

In Figures 8 and 9 there is a clear increasing trend of theselectivity ofmethyl ester for a 15 wt catalyst concentrationduring the early conversion of the reactant which decreasesat the end of the reactionThe same transition trend has beenfound when analyzing the influence of the molar ratio onmethyl ester selectivity A further detailed analysis showedthat the quadratic and cubic effects are more significantat a higher catalyst concentration than at a lower catalystconcentration As shown in Figure 10 the selectivity of E2 hasa quadratic plot whereas the selectivity of E3 has a parabolicshape Referring to (42)ndash(44) we can see that E1 is linearlyformed with a T conversion E2 is produced more at a Tconversion of lower than 035 where we can see that thepower of two in (43) is more dominant at this stage At aT conversion of over 05 the effect of the power of three in(44) is dominant causing a higher formation of E3 Becausethe transesterification reaction is a reversible and consecutiveequation the formation of three Es is important to achievea better selectivity With an optimum amount of catalyst thereactor becomesmore efficient in converting the reactant intothe products

43 Comparison ofMethyl Ester Selectivities fromDifferent OilFeedstocks To compare the selectivities of methyl esters andglycerol from different feedstocks datasets (8ndash10) were usedFigure 11 presents the selectivity ofmethyl esters derived fromrapeseed oil waste sunflower oil and palm oil for Case 1 andCase 2 As can be seen from the graph the methyl estersand glycerol were more likely to form if palm oil is used asthe feedstock compared to the other two oil feedstocks Thepresent finding also suggests that the selectivity of methylester was much lower when using low cost feedstock such aswaste sunflower oil Waste oil contains large amounts of freefatty acids (FFAs) (about 20) which affect the yield of fuelfrom that process The amount of FFAs in palm oil is 064[3] but for rapeseed oil the author used fresh oil [27] whichis estimated less than 1

12 International Journal of Chemical Engineering

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05

1

15

2

25

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0 01 02 03 04 05 06 07 08 09 1

PO-case 1 RO-case 1

WSO-case 1 WSO-case 2RO-case 2PO-case 2

Conversion of triglyceride XT

Sele

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Figure 11 Selectivity plots of methyl ester from various feedstockfor Cases 1 and 2

As discussed before these free fatty acids will reactwith alkali catalysts to produce soaps that will inhibit thetransesterification reaction Soaps will allow emulsificationthat causes the phase separation of methyl ester and glycerolto be less sharp It produces water that can hydrolyze thetriglycerides and contribute to the formation of more soap[14] The effect of reversibility of transesterification can beseen significantly when analysing the selectivity of methylester derived from palm oil In Figure 11 methyl ester derivedfrom palm oil shows a higher selectivity plot for base caseThis finding suggests that forward reaction dominates thereaction and contributes to a better selectivity when lowFFAs feedstock is used in biodiesel production As there aremany low cost feedstocks available for biodiesel productiona pretreatment to these feedstocks can be carried out in orderto ensure the value of FFAs is within the allowable range

5 Conclusions

This paper has presented a comprehensive kinetic modelingof a transesterification reaction for biodiesel with homoge-neous alkaline catalyst The purpose of the study was todevelop the kinetic models of transesterification reactiondetermine the selectivity of methyl ester and glycerol andevaluate the significance of the reverse reactions in the trans-esterification reaction This study has shown that a processmodel solution was found for two types of common biodieselreactors The concentration of each species during transes-terification was found leading to a selectivity determinationduring the biodiesel production In addition the reversibleand irreversible effects of a transesterification reaction werediscovered The forward reaction is more dominant than thereverse reaction and the maximum selectivity can be foundif a base case of transesterification reaction is assumed tohave occurred in the biodiesel reactor system For the variousreaction characteristics under investigation the selectivities

are influenced by the temperature molar ratio of methanolto oil catalyst concentration and type of oil used as thefeedstock Furthermore an analysis of the selectivity plotsindicates an enhanced effect of the reaction characteristicson the selectivity This research has shown that the selectivityof methyl ester is maximized at 60∘C a 9 1 molar ratio ofmethanol to oil and a catalyst concentration of 15 Thisinvestigation into the effects of the molar ratio of methanolto oil and the catalyst concentration on the selectivity canbe made more interesting if several more curves are plottedat a molar ratio of methanol to oil between 3 1 to 9 1 anda catalyst concentration between 05 and 15 Howevera limitation of this research remains in the availability ofthe reaction rate constants under various reaction condi-tions In addition a comparison should be made throughmutual reaction conditionsThe findings from this study willenhance the concept of selectivity and its applications inthe evaluation of complex transesterification reactions whenthe goal is to attain the maximum production of methylesters and glycerol It is recommended that further researchis undertaken in exploring the selectivity data for specifyingthe reactor configurations and may be used in the synthesisof reactor network for biodiesel production

Nomenclature

119896+1 119896minus1 119896+2

119896minus2 119896+3 119896minus3

Reaction constant

119862T 119862D 119862M 119862G119862E1 119862E2 119862E3119862A 119862E

Molar concentration of triglyceridediglyceride monoglyceride glycerolester 1 ester 2 ester 3 methanol andmethyl ester

119883T Conversion of triglyceride119872119877 Molar ratio

119862T0 Initial molar concentration oftriglyceride

119878E 119878G Selectivity of methyl ester glycerol120572 Reaction rate constant factorwt Weight percentT TriglycerideD DiglycerideM MonoglycerideA MethanolG GlycerolE Methyl esterE1 Methyl ester 1E2 Methyl ester 2E3 Methyl ester 3PFR Plug flow reactorCSTR Continuous stirred tank reactor119873T0 Initial amount of triglyceride at 119905 = 0

119873T The amount of triglyceride present attime 119905

119881 VolumePO Palm oilRO Rapeseed oilWSO Waste sunflower oilNaOH Sodium hydroxide

International Journal of Chemical Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgment

Thework was carried out with the financial support from theMinistry of Education Malaysia

References

[1] A Demirbas ldquoBiodiesel from triglycerides via transesterifica-tionrdquo in Biodiesel pp 121ndash140 Springer London UK 2008

[2] D Darnoko and M Cheryan ldquoKinetics of palm oil transesteri-fication in a batch reactorrdquo JAOCS Journal of the American OilChemistsrsquo Society vol 77 no 12 pp 1263ndash1267 2000

[3] T Leevijit WWisutmethangoon G Prateepehaikul C Tongu-rai and M Allen ldquoA second order kinetics of palm oil transes-terification in a batch reactorrdquo in Proceedings of the Joint Inter-national Conference on Sustainable Energy and Environment pp277ndash281 2004

[4] S Jain andM P Sharma ldquoKinetics of acid base catalyzed trans-esterification of Jatropha curcas oilrdquo Bioresource Technology vol101 no 20 pp 7701ndash7706 2010

[5] H Noureddini and D Zhu ldquoKinetics of transesterification ofsoybean oilrdquo Journal of the American Oil Chemistsrsquo Society vol74 no 11 pp 1457ndash1463 1997

[6] D Kusdiana and S Saka ldquoKinetics of transesterification in rape-seed oil to biodiesel fuel as treated in supercritical methanolrdquoFuel vol 80 no 5 pp 693ndash698 2001

[7] M Diasakou A Louloudi and N Papayannakos ldquoKinetics ofthe non-catalytic transesterification of soybean oilrdquo Fuel vol 77no 12 pp 1297ndash1302 1998

[8] H Maeda S Hagiwara H Nabetani et al ldquoBiodiesel fuelsfrom palm oil via the non-catalytic transesterification in abubble column reactor at atmospheric pressure a kinetic studyrdquoRenewable Energy vol 33 no 7 pp 1629ndash1636 2008

[9] P C Narvaez S M Rincon and F J Sanchez ldquoKinetics of palmoil methanolysisrdquo Journal of the American Oil Chemistsrsquo Societyvol 84 pp 971ndash977 2007

[10] E Minami and S Saka ldquoKinetics of hydrolysis and methylesterification for biodiesel production in two-step supercriticalmethanol processrdquo Fuel vol 85 no 17-18 pp 2479ndash2483 2006

[11] B Freedman R O Butterfield and E H Pryde ldquoTransesteri-fication kinetics of soybean oil 1rdquo Journal of the American OilChemistsrsquo Society vol 63 no 10 pp 1375ndash1380 1986

[12] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

[13] J M Douglas Conceptual Design of Chemical ProcessesMcGraw Hill 1988

[14] J van Gerpen B Shanks R Pruszko D Clements and GKnothe Biodiesel Production Technology Subcontractor ReportNational Reanewable Energy Laboratory 2004

[15] H J Wright J B Segur H V Clark S K Coburn E ELangdon and R N DuPuis ldquoA report on ester interchangerdquoOilamp Soap vol 21 no 5 pp 145ndash148 1944

[16] H Fukuda A Kondo and H Noda ldquoBiodiesel fuel productionby transesterification of oilsrdquo Journal of Bioscience and Bioengi-neering vol 92 no 5 pp 405ndash416 2001

[17] L Friesenhagen and H Lepper ldquoProcess for the productionof fatty acid esters of short-chain aliphatic alcohols from fatsandor oils containing free fatty acidsrdquoUS Patent 4608202 1986

[18] P Felizardo J MacHado D Vergueiro M J N Correia J PGomes and J M Bordado ldquoStudy on the glycerolysis reactionof high free fatty acid oils for use as biodiesel feedstockrdquo FuelProcessing Technology vol 92 no 6 pp 1225ndash1229 2011

[19] A Tafesh and S Basheer ldquoPretreatment methods in biodieselproduction processesrdquo in Pretreatment Techniques for Biofuelsand Biorefineries Z Fang Ed Green Energy and Technologypp 417ndash434 Springer Berlin Germany 2013

[20] D Kusdiana and S Saka ldquoEffects of water on biodiesel fuelproduction by supercritical methanol treatmentrdquo BioresourceTechnology vol 91 no 3 pp 289ndash295 2004

[21] K Komers F Skopal R Stloukal and J Machek ldquoKinetics andmechanism of the KOHmdashcatalyzed methanolysis of rapeseedoil for biodiesel productionrdquo European Journal of Lipid Scienceand Technology vol 104 pp 728ndash737 2002

[22] A K CokerModeling of Chemical Kinetics and Reactor DesignGulf Publishing Houston Tex USA 2001

[23] C D Holland and R G Anthony Fundamentals of ChemicalReaction Engineering Prentice-Hall 1979

[24] J K Rodrıguez-Guerrero M F Rubens and P T V RosaldquoProduction of biodiesel from castor oil using sub and super-critical ethanol effect of sodium hydroxide on the ethyl esterproductionrdquoThe Journal of Supercritical Fluids vol 83 pp 124ndash132 2013

[25] G Vicente M Martınez and J Aracil ldquoOptimisation ofintegrated biodiesel production Part I A study of the biodieselpurity and yieldrdquoBioresource Technology vol 98 no 9 pp 1724ndash1733 2007

[26] A Srivastava and R Prasad ldquoTriglycerides-based diesel fuelsrdquoRenewable and Sustainable Energy Reviews vol 4 no 2 pp 111ndash133 2000

[27] B Klofutar J Golob B Likozar C Klofutar E Zagar andI Poljansek ldquoThe transesterification of rapeseed and wastesunflower oils mass-transfer and kinetics in a laboratory batchreactor and in an industrial-scale reactorseparator setuprdquoBioresource Technology vol 101 no 10 pp 3333ndash3344 2010

[28] S D Crymble ldquoOptimization and Reaction Kinetics of the Pro-duction of Biodiesel from Castor Oil via Sodium Methoxide-Catalyzed Methanolysisrdquo Dave C Swalm School of ChemicalEngineering Mississippi State University Miss USA 2010

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International Journal of

International Journal of Chemical Engineering 7

119862M =

1205722119862T119900119883

2

T (1 minus 119883T)

(1 minus (1 minus 1205724)119883T) (1 minus (1 minus 120572

2)119883T)

(41)

119862E1 = 119862T119900119883T (42)

119862E2 =1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

(43)

119862E3 =12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(44)

119862A = 119862T119900 (119872119877minus 1 +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

)

(45)

119862G =

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(46)

33 Case 2 Alternative Case Reversible Reactions In Case 2an alternative case was considered by assuming that thereactions in (2) to (4) are reversible Together with the basecase where the reactions are irreversible it can be used todiscover the significance of the reverse and forward reactions

Since the values of all 120572119894rsquos in (28) for the PFR and

(31) for the CSTR are not zero no closed form solutionto them can be found because they are too complex foranalytical solution The solution of both sets of equationscan be achieved by numerical methods using a computersimulation software Equations (28) for the PFR are solvedby using the ordinary differential equation 45 (ODE 45) inMATLAB Concentration of each species is obtained usingRungge-Kutta numerical integration algorithm On the otherhand (31) for the CSTR are solved by using the simultaneousnonlinear equations solver in MATLAB Concentration ofeach species is obtained using the multivariable Newton-Raphson algorithm

34 Selectivity of Methyl Esters and Glycerol for Case 1 andCase 2 The net concentration of methyl esters is the sum ofconcentration of ester 1 ester 2 and ester 3 In Case 1 the netconcentration of methyl esters in the PFR is given by

119862E1 + 119862E2 + 119862E3

= 119862T119900 1 + 119883T minus

1205722

1205722minus 1

[(1 minus 119883T) minus(1 minus 119883T)

1205722

1205722

]

+1205724[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(47)

Similarly the net concentration of methyl esters in theCSTR for Case 1 is given by

119862E1 + 119862E2 + 119862E3

= 119862E1119900 + 119862E2119900 + 119862E3119900

+ [119862T119900119883T +

1205722119862T119900119883

2

T(1 minus (1 minus 120572

2)119883T)

+

12057221205724119862T119900119883

3

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(48)

The selectivity of methyl esters in Case 1 for PFR is givenby

119878E =

119883T + 1

119883Tminus

1205722

1205722minus 1

[

(1 minus 119883T)

119883Tminus

(1 minus 119883T)1205722

1205722119883T

]

+1205724[

1205722

1 minus 1205722

[

1

1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722119883T

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724119883T

]

(49)

The selectivity of glycerol in Case 1 for PFR is given by

119878G =

1205724

119883T[

1205722

1 minus 1205722

[

119883T1 minus 1205724

minus

[1 minus (1 minus 119883T)1205722

]

(1205722minus 1205724) 1205722

]

+

1205722[1 minus (1 minus 119883T)

1205724

]

(1 minus 1205724) (1205722minus 1205724) 1205724

]

(50)

On the other hand the selectivity of methyl esters inCase 1 for CSTR is given by

119878E = [1 +

1205722119883T

(1 minus (1 minus 1205722)119883T)

+

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

]

(51)

The selectivity of glycerol in Case 1 for CSTR is given by

119878G =

120572212057241198832

T(1 minus (1 minus 120572

4)119883T) (1 minus (1 minus 120572

2)119883T)

(52)

For Case 2 there is no closed form expression for selec-tivity of methyl esters and glycerolThe selectivities of methylesters and glycerol have to be calculated using (18) fromthe concentration of the species generated by the numericalsolution

4 Results and Discussion

41 Comparison of Selectivities for Cases 1 and 2 This studyhas shown the development of kinetic parameters for deter-mining methyl esters and glycerol selectivity in a biodiesel

8 International Journal of Chemical Engineering

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

ity

Conversion of triglyceride XT

Case 1-T = 60∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 60∘C MR = 6 1 catalyst = 02 wt

Figure 1 Selectivity plots of Cases 1 and 2 at reaction temperature60∘C molar ratio 6 1 and catalyst concentration 02 wt

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

ity

Conversion of triglyceride XT

Case 1-T = 70∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 70∘C MR = 6 1 catalyst = 02 wt

Figure 2 Selectivity plots of Cases 1 and 2 at reaction temperature70∘C molar ratio 6 1 and catalyst concentration 02 wt

transesterification reaction it has also established severalmathematical equations for the same Furthermore a par-ticularly important parameter for designing a reactor thatis product selectivity was determined for each case andcondition For comparing the base case and an alternativecase datasets 2 and 3 were evaluated using each calculationschemesThe difference in the selectivity between Case 1 andCase 2 which were investigated under the same conditionsis very significant and is attributed to the reversibility factorof the reaction as illustrated in Figures 1 and 2The results ofthe base case show that when all the reactions are irreversibleit implies that the maximum attainable molar concentrationand selectivity ofmethyl ester have been reachedThis verifiesthe significant role of the forward reactions in (2)ndash(4)

For a simple reversible reaction we can see the effectsof thermodynamic parameter like temperature on thereversibility of the reaction whereas the reversibility ofa reaction is controlled by reaction equilibrium constant

Table 2 Selectivity at 07ndash09 triglycerides conversion for datasets(1ndash3) and (6-7)

Conversion119883T Dataset Methyl esters selectivityCase 1 Case 2

07

1 2610 25262 2643 25113 2630 24706 2610 26137 2493 2313

08

1 2766 26752 2784 26663 2769 26296 2764 27667 2682 2480

09

1 2895 28322 2903 28163 2892 27886 2893 28797 2852 2655

The reaction equilibrium constant 119870 is defined as theforward rate constant divided by the reverse rate constant andaffected by temperature [12] This transesterification reactionis a complex reaction which consists of three reversibleand consecutive reactions Therefore for simplification andpreliminary design purpose selectivity is effectively used todetermine the effect of temperature and role of catalyst onthe reversibility Figures 1 and 2 show significant changes ofthe selectivity plots for conversion of triglycerides from 07to 09 and the plots finally reach the equilibrium at the endof the reaction In order to access the role of temperature andamount of catalyst on the reversibility of transesterificationreaction Table 2 was constructed by observing the methylesters selectivity for conversion of triglycerides from 07 to09 It presents the difference in selectivity for Case 1 andCase 2 Datasets (1ndash3) are used to determine the effects ofdifferent temperatures on the reversibility of the transesterifi-cation reaction which represent a temperature of 50 60 and70 respectively Conversion of triglyceride at 09 is selectedfor analysis From this data we can see that the forwardreaction alone is able to provide better selectivity than reversereaction at any temperature Datasets (6-7) are used to ana-lyze the role catalyst on the reversibility of transesterificationreaction whereas datasets 6 and 7 represent the amount ofcatalyst of 15 and 05 respectively A significant role ofthe forward reaction once again was determined at a highercatalyst concentrationThe results obtained also indicate thata higher catalyst concentration controls the forward reactionsand gives preferably product selectivity

According to Narvaez et al [9] and Noureddini and Zhu[5] the forward reactions in a transesterification reaction arethe most important reactions However Diasakou et al [7]claimed that the reverse reactions during a transesterificationreaction do not influence the forward reactions In this studya lower concentration of methyl ester was found for Case 2

International Journal of Chemical Engineering 9

Table 3 Activation energy

Reaction Activation energy (calmol)T rarr D 13145D rarr T 9932D rarr M 19860M rarr D 14639M rarr G 6421G rarr M 9588

which affects the selectivity and methyl ester conversionwhich is likely due to the reverse nature of the reaction [4]This result suggests that for establishing the optimal chemicalprocess for biodiesel fuel production it can be assumed thatwhen irreversible reactions are employed better selectivitycan be obtained because of the absence of reverse reactions

42 Effects of Reaction Characteristics on Selectivity Thereactor design stage for a biodiesel plant utilizes methyl esterselectivity for the material balances and stream costs Attain-ing the appropriate operating conditions through productselectivity can eliminate material and energy recycling thusreducing costsThe effects of the reaction temperature molarratio of methanol to oil and the catalyst concentration on theselectivity of methyl esters and glycerol are analyzed for bothCase 1 and Case 2 in the following subsections

421 Effect of ReactionTemperature on Selectivity An investi-gation on the effect of temperature onmethyl ester selectivitywas conducted using datasets (1ndash3) where the molar ratio ofalcohol to oil and the catalyst concentration are fixed TheArrhenius equation was used for this investigation

119896 = 119896∘exp(minus

119864

119877119879

) (53)

According to (53) the reaction rate 119896 is an integralpart of the selectivity expressions It depends on the energyof activation (119864) obtained from the Arrhenius equation[22] For reactions at different temperatures fixed molarratios and catalyst concentrations the activation energy isconstant In this study the kinetic data used to analyzethe temperature effect were adapted from Noureddini andZhu [5] Because the data published in their research utilizethe average reaction rate constants at 50∘C and constantactivation energy (53) can bemanipulated to obtain the otherreaction rate constants (at 60∘C and 70∘C) listed in Table 1The results of the activation energy investigated in their studyare shown in Table 3

Figures 3 and 4 show the effects of the reaction tempera-ture on the selectivity ofmethyl esters and glycerol for Cases 1and 2 respectively The reaction temperature had a small butsubstantial effect on the selectivity The figures show thatthe selectivity of methyl esters is high at a high temperaturein the early conversion of T However in both figures theselectivities of E for both Cases 1 and 2 at 70∘C were foundto decrease toward the completion of the reaction As theboiling point of methanol is 647∘C an additional 5∘C has

0

02

04

06

08

1

12

00

05

10

15

20

25

30

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 3 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 1

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 4 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 2

the effect of lowering the product concentration and affectingthe selectivity of E at the equilibriumThis temperature effectchanges the slope of selectivity from a concave to a convexshape which is also related with the reaction rate constant atdifferent temperatures

According to Darnoko and Cheryan [2] the transester-ification reaction rates were increased at 65∘C as comparedwith those at 50∘C The results of their research also showedan enhanced methyl ester yield at 65∘C compared withthat at 50∘C which was because of the higher viscosity ofoil at 50∘C In addition 55∘C is a stable temperature thatcan maintain the oil liquidity This result indicates that anoptimum temperature promotes the formation of methylesters and thus contributes to a higher selectivity of biodieselproducts It can also be suggested that the reaction rateconstant 119896 which is greatly dependent on the temperatureand selectivity of E is greatly improved at the optimumtemperature

10 International Journal of Chemical Engineering

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 5 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 1

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 6 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 2

The findings confirm that methyl ester selectivity effectscan be realistically obtained at the optimum temperaturewhich is 60∘C in this study As the reactor optimizationrequires the relationship between the conversion and selec-tivity in both cases (Case 1 and Case 2) the selectivity withinthe studied temperature indicates that the biodiesel reactormay work more efficiently in converting T to E at 60∘C

422 Effect of Molar Ratio of Methanol to Oil on SelectivityAn investigation into the effects of the methanol-to-oil molarratio involves datasets 4 and 5 Selectivity plots of methylesters and glycerol are shown in Figures 5 and 6 For Cases 1and 2 the selectivity of methyl esters and glycerol was rela-tively affected by the molar ratio of methanol to oil It can beseen from the figures that the higher molar ratio of methanolto oil encourages the formation of transesterification reactionproducts thus contributing to a higher selectivity

The most striking result to emerge from the figures isthe change in the shape of the selectivity plot from concave

0

02

04

06

08

1

12

0 02 04 06 08 1

Sele

ctiv

ity

(a)(b)

(c)

Triglyceride conversion XT

Figure 7 Selectivity plots (a) methyl ester 1 (b) methyl ester 2 and(c) methyl ester 3 for dataset 4

to convex for a molar ratio of 9 1 An increasing selectivityof methyl ester can be found in an early conversion oftriglyceride but toward equilibrium the selectivity is foundto slightly decrease A possible explanation for this mightbe that the methyl ester concentration has both quadratic aswell as cubic effects that can be explained by (42)ndash(44) andFigure 7

According to (42) the selectivity of methyl ester 1 isconstant at 1 Equation (43) is a quadratic equation whichgives a parabolic shape to the plot of methyl ester 2 Equation(44) clearly illustrates the selectivity of methyl ester 3 whenthe equation is a cubic one In more detail the power of twois more dominant at an 119883T of less than 03 which meansthat the formation of E2 is more active under this conditionHowever we can see an active formation of E3 at an 119883Tof 05ndash1 when the power of three is dominant At the sametime E1 is formed linearly with a triglyceride conversionThe stepwise transesterification reaction in (2)ndash(4) shows thateach E is formed consecutivelyThismeans that to achieve themaximum yield the maximum selectivity at the maximum Tconversion is necessary and each E must be formed duringthe process Therefore it can be assumed that the selectivityof methyl ester is more greatly affected by the quadratic andcubic functions at a highermolar ratio ofmethanol to oil thanat a lower one

In addition Freedman et al [11] reported that the bestmethyl ester conversion is achieved at a molar ratio of 6 1with alkaline catalyst and that higher molar ratios do notincrease the productivity but do increase the cost of alcoholrecovery At a high molar excess of methanol a pseudo-first-order reaction appeared more likely than a second-order reaction However high molar ratio of methanol isused for noncatalytic and supercritical methanol reaction[6 11 20 24] Narvaez et al [9] stated that when an excessamount of methanol is used it can positively affect thereversible characteristic of the reaction and the displacementof the reaction toward the product As a consequence excessmethanol does not necessarily contribute to an increase in theconcentration of methyl ester and glycerol

International Journal of Chemical Engineering 11

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 8 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 9 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 2

423 Effect of Catalyst Concentration on Selectivity Apartfrom the temperature and molar ratio the parameters thataffect the selectivity are the same as those influencing thereaction rates namely the catalyst The effects of the catalystconcentration are studied through datasets 6 and 7 andthe selectivity plots can be seen in Figures 8 and 9 Whenanalyzing the figures it can be seen that the selectivity of bothproducts is higher at a higher catalyst concentration

Toward the equilibrium of the reaction the selectivitywas observed to increase at a higher catalyst concentra-tion thus contributing to an increased amount of methylester formation Vicente et al [25] stated that the largestmethyl ester conversions are obtained when a large catalystconcentration is employed (13) at a mild temperature(20ndash50∘C) This agrees with the resulting selectivity curvesplotted which indicates that the catalyst concentration hasa positive effect on the selectivity of methyl esters andglycerol However a greater application of an alkali catalystcan lead to the production of large amounts of soap andextra cost is required to remove the catalyst from the reactionsystem Srivastava and Prasad [26] have stated that a catalyst

0

02

04

06

08

1

12

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity

(a)

(c)(b)

Triglyceride conversion XT

Figure 10 Selectivity plots (a)methyl ester 1 (b)methyl ester 2 and(c) methyl ester 3 for dataset 6

concentration of 05ndash1 can yield up to a 99 methyl esterconversion

In Figures 8 and 9 there is a clear increasing trend of theselectivity ofmethyl ester for a 15 wt catalyst concentrationduring the early conversion of the reactant which decreasesat the end of the reactionThe same transition trend has beenfound when analyzing the influence of the molar ratio onmethyl ester selectivity A further detailed analysis showedthat the quadratic and cubic effects are more significantat a higher catalyst concentration than at a lower catalystconcentration As shown in Figure 10 the selectivity of E2 hasa quadratic plot whereas the selectivity of E3 has a parabolicshape Referring to (42)ndash(44) we can see that E1 is linearlyformed with a T conversion E2 is produced more at a Tconversion of lower than 035 where we can see that thepower of two in (43) is more dominant at this stage At aT conversion of over 05 the effect of the power of three in(44) is dominant causing a higher formation of E3 Becausethe transesterification reaction is a reversible and consecutiveequation the formation of three Es is important to achievea better selectivity With an optimum amount of catalyst thereactor becomesmore efficient in converting the reactant intothe products

43 Comparison ofMethyl Ester Selectivities fromDifferent OilFeedstocks To compare the selectivities of methyl esters andglycerol from different feedstocks datasets (8ndash10) were usedFigure 11 presents the selectivity ofmethyl esters derived fromrapeseed oil waste sunflower oil and palm oil for Case 1 andCase 2 As can be seen from the graph the methyl estersand glycerol were more likely to form if palm oil is used asthe feedstock compared to the other two oil feedstocks Thepresent finding also suggests that the selectivity of methylester was much lower when using low cost feedstock such aswaste sunflower oil Waste oil contains large amounts of freefatty acids (FFAs) (about 20) which affect the yield of fuelfrom that process The amount of FFAs in palm oil is 064[3] but for rapeseed oil the author used fresh oil [27] whichis estimated less than 1

12 International Journal of Chemical Engineering

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

PO-case 1 RO-case 1

WSO-case 1 WSO-case 2RO-case 2PO-case 2

Conversion of triglyceride XT

Sele

ctiv

ity o

f met

hyl e

sters

Figure 11 Selectivity plots of methyl ester from various feedstockfor Cases 1 and 2

As discussed before these free fatty acids will reactwith alkali catalysts to produce soaps that will inhibit thetransesterification reaction Soaps will allow emulsificationthat causes the phase separation of methyl ester and glycerolto be less sharp It produces water that can hydrolyze thetriglycerides and contribute to the formation of more soap[14] The effect of reversibility of transesterification can beseen significantly when analysing the selectivity of methylester derived from palm oil In Figure 11 methyl ester derivedfrom palm oil shows a higher selectivity plot for base caseThis finding suggests that forward reaction dominates thereaction and contributes to a better selectivity when lowFFAs feedstock is used in biodiesel production As there aremany low cost feedstocks available for biodiesel productiona pretreatment to these feedstocks can be carried out in orderto ensure the value of FFAs is within the allowable range

5 Conclusions

This paper has presented a comprehensive kinetic modelingof a transesterification reaction for biodiesel with homoge-neous alkaline catalyst The purpose of the study was todevelop the kinetic models of transesterification reactiondetermine the selectivity of methyl ester and glycerol andevaluate the significance of the reverse reactions in the trans-esterification reaction This study has shown that a processmodel solution was found for two types of common biodieselreactors The concentration of each species during transes-terification was found leading to a selectivity determinationduring the biodiesel production In addition the reversibleand irreversible effects of a transesterification reaction werediscovered The forward reaction is more dominant than thereverse reaction and the maximum selectivity can be foundif a base case of transesterification reaction is assumed tohave occurred in the biodiesel reactor system For the variousreaction characteristics under investigation the selectivities

are influenced by the temperature molar ratio of methanolto oil catalyst concentration and type of oil used as thefeedstock Furthermore an analysis of the selectivity plotsindicates an enhanced effect of the reaction characteristicson the selectivity This research has shown that the selectivityof methyl ester is maximized at 60∘C a 9 1 molar ratio ofmethanol to oil and a catalyst concentration of 15 Thisinvestigation into the effects of the molar ratio of methanolto oil and the catalyst concentration on the selectivity canbe made more interesting if several more curves are plottedat a molar ratio of methanol to oil between 3 1 to 9 1 anda catalyst concentration between 05 and 15 Howevera limitation of this research remains in the availability ofthe reaction rate constants under various reaction condi-tions In addition a comparison should be made throughmutual reaction conditionsThe findings from this study willenhance the concept of selectivity and its applications inthe evaluation of complex transesterification reactions whenthe goal is to attain the maximum production of methylesters and glycerol It is recommended that further researchis undertaken in exploring the selectivity data for specifyingthe reactor configurations and may be used in the synthesisof reactor network for biodiesel production

Nomenclature

119896+1 119896minus1 119896+2

119896minus2 119896+3 119896minus3

Reaction constant

119862T 119862D 119862M 119862G119862E1 119862E2 119862E3119862A 119862E

Molar concentration of triglyceridediglyceride monoglyceride glycerolester 1 ester 2 ester 3 methanol andmethyl ester

119883T Conversion of triglyceride119872119877 Molar ratio

119862T0 Initial molar concentration oftriglyceride

119878E 119878G Selectivity of methyl ester glycerol120572 Reaction rate constant factorwt Weight percentT TriglycerideD DiglycerideM MonoglycerideA MethanolG GlycerolE Methyl esterE1 Methyl ester 1E2 Methyl ester 2E3 Methyl ester 3PFR Plug flow reactorCSTR Continuous stirred tank reactor119873T0 Initial amount of triglyceride at 119905 = 0

119873T The amount of triglyceride present attime 119905

119881 VolumePO Palm oilRO Rapeseed oilWSO Waste sunflower oilNaOH Sodium hydroxide

International Journal of Chemical Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgment

Thework was carried out with the financial support from theMinistry of Education Malaysia

References

[1] A Demirbas ldquoBiodiesel from triglycerides via transesterifica-tionrdquo in Biodiesel pp 121ndash140 Springer London UK 2008

[2] D Darnoko and M Cheryan ldquoKinetics of palm oil transesteri-fication in a batch reactorrdquo JAOCS Journal of the American OilChemistsrsquo Society vol 77 no 12 pp 1263ndash1267 2000

[3] T Leevijit WWisutmethangoon G Prateepehaikul C Tongu-rai and M Allen ldquoA second order kinetics of palm oil transes-terification in a batch reactorrdquo in Proceedings of the Joint Inter-national Conference on Sustainable Energy and Environment pp277ndash281 2004

[4] S Jain andM P Sharma ldquoKinetics of acid base catalyzed trans-esterification of Jatropha curcas oilrdquo Bioresource Technology vol101 no 20 pp 7701ndash7706 2010

[5] H Noureddini and D Zhu ldquoKinetics of transesterification ofsoybean oilrdquo Journal of the American Oil Chemistsrsquo Society vol74 no 11 pp 1457ndash1463 1997

[6] D Kusdiana and S Saka ldquoKinetics of transesterification in rape-seed oil to biodiesel fuel as treated in supercritical methanolrdquoFuel vol 80 no 5 pp 693ndash698 2001

[7] M Diasakou A Louloudi and N Papayannakos ldquoKinetics ofthe non-catalytic transesterification of soybean oilrdquo Fuel vol 77no 12 pp 1297ndash1302 1998

[8] H Maeda S Hagiwara H Nabetani et al ldquoBiodiesel fuelsfrom palm oil via the non-catalytic transesterification in abubble column reactor at atmospheric pressure a kinetic studyrdquoRenewable Energy vol 33 no 7 pp 1629ndash1636 2008

[9] P C Narvaez S M Rincon and F J Sanchez ldquoKinetics of palmoil methanolysisrdquo Journal of the American Oil Chemistsrsquo Societyvol 84 pp 971ndash977 2007

[10] E Minami and S Saka ldquoKinetics of hydrolysis and methylesterification for biodiesel production in two-step supercriticalmethanol processrdquo Fuel vol 85 no 17-18 pp 2479ndash2483 2006

[11] B Freedman R O Butterfield and E H Pryde ldquoTransesteri-fication kinetics of soybean oil 1rdquo Journal of the American OilChemistsrsquo Society vol 63 no 10 pp 1375ndash1380 1986

[12] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

[13] J M Douglas Conceptual Design of Chemical ProcessesMcGraw Hill 1988

[14] J van Gerpen B Shanks R Pruszko D Clements and GKnothe Biodiesel Production Technology Subcontractor ReportNational Reanewable Energy Laboratory 2004

[15] H J Wright J B Segur H V Clark S K Coburn E ELangdon and R N DuPuis ldquoA report on ester interchangerdquoOilamp Soap vol 21 no 5 pp 145ndash148 1944

[16] H Fukuda A Kondo and H Noda ldquoBiodiesel fuel productionby transesterification of oilsrdquo Journal of Bioscience and Bioengi-neering vol 92 no 5 pp 405ndash416 2001

[17] L Friesenhagen and H Lepper ldquoProcess for the productionof fatty acid esters of short-chain aliphatic alcohols from fatsandor oils containing free fatty acidsrdquoUS Patent 4608202 1986

[18] P Felizardo J MacHado D Vergueiro M J N Correia J PGomes and J M Bordado ldquoStudy on the glycerolysis reactionof high free fatty acid oils for use as biodiesel feedstockrdquo FuelProcessing Technology vol 92 no 6 pp 1225ndash1229 2011

[19] A Tafesh and S Basheer ldquoPretreatment methods in biodieselproduction processesrdquo in Pretreatment Techniques for Biofuelsand Biorefineries Z Fang Ed Green Energy and Technologypp 417ndash434 Springer Berlin Germany 2013

[20] D Kusdiana and S Saka ldquoEffects of water on biodiesel fuelproduction by supercritical methanol treatmentrdquo BioresourceTechnology vol 91 no 3 pp 289ndash295 2004

[21] K Komers F Skopal R Stloukal and J Machek ldquoKinetics andmechanism of the KOHmdashcatalyzed methanolysis of rapeseedoil for biodiesel productionrdquo European Journal of Lipid Scienceand Technology vol 104 pp 728ndash737 2002

[22] A K CokerModeling of Chemical Kinetics and Reactor DesignGulf Publishing Houston Tex USA 2001

[23] C D Holland and R G Anthony Fundamentals of ChemicalReaction Engineering Prentice-Hall 1979

[24] J K Rodrıguez-Guerrero M F Rubens and P T V RosaldquoProduction of biodiesel from castor oil using sub and super-critical ethanol effect of sodium hydroxide on the ethyl esterproductionrdquoThe Journal of Supercritical Fluids vol 83 pp 124ndash132 2013

[25] G Vicente M Martınez and J Aracil ldquoOptimisation ofintegrated biodiesel production Part I A study of the biodieselpurity and yieldrdquoBioresource Technology vol 98 no 9 pp 1724ndash1733 2007

[26] A Srivastava and R Prasad ldquoTriglycerides-based diesel fuelsrdquoRenewable and Sustainable Energy Reviews vol 4 no 2 pp 111ndash133 2000

[27] B Klofutar J Golob B Likozar C Klofutar E Zagar andI Poljansek ldquoThe transesterification of rapeseed and wastesunflower oils mass-transfer and kinetics in a laboratory batchreactor and in an industrial-scale reactorseparator setuprdquoBioresource Technology vol 101 no 10 pp 3333ndash3344 2010

[28] S D Crymble ldquoOptimization and Reaction Kinetics of the Pro-duction of Biodiesel from Castor Oil via Sodium Methoxide-Catalyzed Methanolysisrdquo Dave C Swalm School of ChemicalEngineering Mississippi State University Miss USA 2010

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International Journal of

8 International Journal of Chemical Engineering

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

ity

Conversion of triglyceride XT

Case 1-T = 60∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 60∘C MR = 6 1 catalyst = 02 wt

Figure 1 Selectivity plots of Cases 1 and 2 at reaction temperature60∘C molar ratio 6 1 and catalyst concentration 02 wt

0

05

1

15

2

25

3

35

0 02 04 06 08 1

Sele

ctiv

ity

Conversion of triglyceride XT

Case 1-T = 70∘C MR = 6 1 catalyst = 02 wt

Case 2-T = 70∘C MR = 6 1 catalyst = 02 wt

Figure 2 Selectivity plots of Cases 1 and 2 at reaction temperature70∘C molar ratio 6 1 and catalyst concentration 02 wt

transesterification reaction it has also established severalmathematical equations for the same Furthermore a par-ticularly important parameter for designing a reactor thatis product selectivity was determined for each case andcondition For comparing the base case and an alternativecase datasets 2 and 3 were evaluated using each calculationschemesThe difference in the selectivity between Case 1 andCase 2 which were investigated under the same conditionsis very significant and is attributed to the reversibility factorof the reaction as illustrated in Figures 1 and 2The results ofthe base case show that when all the reactions are irreversibleit implies that the maximum attainable molar concentrationand selectivity ofmethyl ester have been reachedThis verifiesthe significant role of the forward reactions in (2)ndash(4)

For a simple reversible reaction we can see the effectsof thermodynamic parameter like temperature on thereversibility of the reaction whereas the reversibility ofa reaction is controlled by reaction equilibrium constant

Table 2 Selectivity at 07ndash09 triglycerides conversion for datasets(1ndash3) and (6-7)

Conversion119883T Dataset Methyl esters selectivityCase 1 Case 2

07

1 2610 25262 2643 25113 2630 24706 2610 26137 2493 2313

08

1 2766 26752 2784 26663 2769 26296 2764 27667 2682 2480

09

1 2895 28322 2903 28163 2892 27886 2893 28797 2852 2655

The reaction equilibrium constant 119870 is defined as theforward rate constant divided by the reverse rate constant andaffected by temperature [12] This transesterification reactionis a complex reaction which consists of three reversibleand consecutive reactions Therefore for simplification andpreliminary design purpose selectivity is effectively used todetermine the effect of temperature and role of catalyst onthe reversibility Figures 1 and 2 show significant changes ofthe selectivity plots for conversion of triglycerides from 07to 09 and the plots finally reach the equilibrium at the endof the reaction In order to access the role of temperature andamount of catalyst on the reversibility of transesterificationreaction Table 2 was constructed by observing the methylesters selectivity for conversion of triglycerides from 07 to09 It presents the difference in selectivity for Case 1 andCase 2 Datasets (1ndash3) are used to determine the effects ofdifferent temperatures on the reversibility of the transesterifi-cation reaction which represent a temperature of 50 60 and70 respectively Conversion of triglyceride at 09 is selectedfor analysis From this data we can see that the forwardreaction alone is able to provide better selectivity than reversereaction at any temperature Datasets (6-7) are used to ana-lyze the role catalyst on the reversibility of transesterificationreaction whereas datasets 6 and 7 represent the amount ofcatalyst of 15 and 05 respectively A significant role ofthe forward reaction once again was determined at a highercatalyst concentrationThe results obtained also indicate thata higher catalyst concentration controls the forward reactionsand gives preferably product selectivity

According to Narvaez et al [9] and Noureddini and Zhu[5] the forward reactions in a transesterification reaction arethe most important reactions However Diasakou et al [7]claimed that the reverse reactions during a transesterificationreaction do not influence the forward reactions In this studya lower concentration of methyl ester was found for Case 2

International Journal of Chemical Engineering 9

Table 3 Activation energy

Reaction Activation energy (calmol)T rarr D 13145D rarr T 9932D rarr M 19860M rarr D 14639M rarr G 6421G rarr M 9588

which affects the selectivity and methyl ester conversionwhich is likely due to the reverse nature of the reaction [4]This result suggests that for establishing the optimal chemicalprocess for biodiesel fuel production it can be assumed thatwhen irreversible reactions are employed better selectivitycan be obtained because of the absence of reverse reactions

42 Effects of Reaction Characteristics on Selectivity Thereactor design stage for a biodiesel plant utilizes methyl esterselectivity for the material balances and stream costs Attain-ing the appropriate operating conditions through productselectivity can eliminate material and energy recycling thusreducing costsThe effects of the reaction temperature molarratio of methanol to oil and the catalyst concentration on theselectivity of methyl esters and glycerol are analyzed for bothCase 1 and Case 2 in the following subsections

421 Effect of ReactionTemperature on Selectivity An investi-gation on the effect of temperature onmethyl ester selectivitywas conducted using datasets (1ndash3) where the molar ratio ofalcohol to oil and the catalyst concentration are fixed TheArrhenius equation was used for this investigation

119896 = 119896∘exp(minus

119864

119877119879

) (53)

According to (53) the reaction rate 119896 is an integralpart of the selectivity expressions It depends on the energyof activation (119864) obtained from the Arrhenius equation[22] For reactions at different temperatures fixed molarratios and catalyst concentrations the activation energy isconstant In this study the kinetic data used to analyzethe temperature effect were adapted from Noureddini andZhu [5] Because the data published in their research utilizethe average reaction rate constants at 50∘C and constantactivation energy (53) can bemanipulated to obtain the otherreaction rate constants (at 60∘C and 70∘C) listed in Table 1The results of the activation energy investigated in their studyare shown in Table 3

Figures 3 and 4 show the effects of the reaction tempera-ture on the selectivity ofmethyl esters and glycerol for Cases 1and 2 respectively The reaction temperature had a small butsubstantial effect on the selectivity The figures show thatthe selectivity of methyl esters is high at a high temperaturein the early conversion of T However in both figures theselectivities of E for both Cases 1 and 2 at 70∘C were foundto decrease toward the completion of the reaction As theboiling point of methanol is 647∘C an additional 5∘C has

0

02

04

06

08

1

12

00

05

10

15

20

25

30

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 3 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 1

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 4 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 2

the effect of lowering the product concentration and affectingthe selectivity of E at the equilibriumThis temperature effectchanges the slope of selectivity from a concave to a convexshape which is also related with the reaction rate constant atdifferent temperatures

According to Darnoko and Cheryan [2] the transester-ification reaction rates were increased at 65∘C as comparedwith those at 50∘C The results of their research also showedan enhanced methyl ester yield at 65∘C compared withthat at 50∘C which was because of the higher viscosity ofoil at 50∘C In addition 55∘C is a stable temperature thatcan maintain the oil liquidity This result indicates that anoptimum temperature promotes the formation of methylesters and thus contributes to a higher selectivity of biodieselproducts It can also be suggested that the reaction rateconstant 119896 which is greatly dependent on the temperatureand selectivity of E is greatly improved at the optimumtemperature

10 International Journal of Chemical Engineering

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 5 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 1

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 6 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 2

The findings confirm that methyl ester selectivity effectscan be realistically obtained at the optimum temperaturewhich is 60∘C in this study As the reactor optimizationrequires the relationship between the conversion and selec-tivity in both cases (Case 1 and Case 2) the selectivity withinthe studied temperature indicates that the biodiesel reactormay work more efficiently in converting T to E at 60∘C

422 Effect of Molar Ratio of Methanol to Oil on SelectivityAn investigation into the effects of the methanol-to-oil molarratio involves datasets 4 and 5 Selectivity plots of methylesters and glycerol are shown in Figures 5 and 6 For Cases 1and 2 the selectivity of methyl esters and glycerol was rela-tively affected by the molar ratio of methanol to oil It can beseen from the figures that the higher molar ratio of methanolto oil encourages the formation of transesterification reactionproducts thus contributing to a higher selectivity

The most striking result to emerge from the figures isthe change in the shape of the selectivity plot from concave

0

02

04

06

08

1

12

0 02 04 06 08 1

Sele

ctiv

ity

(a)(b)

(c)

Triglyceride conversion XT

Figure 7 Selectivity plots (a) methyl ester 1 (b) methyl ester 2 and(c) methyl ester 3 for dataset 4

to convex for a molar ratio of 9 1 An increasing selectivityof methyl ester can be found in an early conversion oftriglyceride but toward equilibrium the selectivity is foundto slightly decrease A possible explanation for this mightbe that the methyl ester concentration has both quadratic aswell as cubic effects that can be explained by (42)ndash(44) andFigure 7

According to (42) the selectivity of methyl ester 1 isconstant at 1 Equation (43) is a quadratic equation whichgives a parabolic shape to the plot of methyl ester 2 Equation(44) clearly illustrates the selectivity of methyl ester 3 whenthe equation is a cubic one In more detail the power of twois more dominant at an 119883T of less than 03 which meansthat the formation of E2 is more active under this conditionHowever we can see an active formation of E3 at an 119883Tof 05ndash1 when the power of three is dominant At the sametime E1 is formed linearly with a triglyceride conversionThe stepwise transesterification reaction in (2)ndash(4) shows thateach E is formed consecutivelyThismeans that to achieve themaximum yield the maximum selectivity at the maximum Tconversion is necessary and each E must be formed duringthe process Therefore it can be assumed that the selectivityof methyl ester is more greatly affected by the quadratic andcubic functions at a highermolar ratio ofmethanol to oil thanat a lower one

In addition Freedman et al [11] reported that the bestmethyl ester conversion is achieved at a molar ratio of 6 1with alkaline catalyst and that higher molar ratios do notincrease the productivity but do increase the cost of alcoholrecovery At a high molar excess of methanol a pseudo-first-order reaction appeared more likely than a second-order reaction However high molar ratio of methanol isused for noncatalytic and supercritical methanol reaction[6 11 20 24] Narvaez et al [9] stated that when an excessamount of methanol is used it can positively affect thereversible characteristic of the reaction and the displacementof the reaction toward the product As a consequence excessmethanol does not necessarily contribute to an increase in theconcentration of methyl ester and glycerol

International Journal of Chemical Engineering 11

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 8 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 9 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 2

423 Effect of Catalyst Concentration on Selectivity Apartfrom the temperature and molar ratio the parameters thataffect the selectivity are the same as those influencing thereaction rates namely the catalyst The effects of the catalystconcentration are studied through datasets 6 and 7 andthe selectivity plots can be seen in Figures 8 and 9 Whenanalyzing the figures it can be seen that the selectivity of bothproducts is higher at a higher catalyst concentration

Toward the equilibrium of the reaction the selectivitywas observed to increase at a higher catalyst concentra-tion thus contributing to an increased amount of methylester formation Vicente et al [25] stated that the largestmethyl ester conversions are obtained when a large catalystconcentration is employed (13) at a mild temperature(20ndash50∘C) This agrees with the resulting selectivity curvesplotted which indicates that the catalyst concentration hasa positive effect on the selectivity of methyl esters andglycerol However a greater application of an alkali catalystcan lead to the production of large amounts of soap andextra cost is required to remove the catalyst from the reactionsystem Srivastava and Prasad [26] have stated that a catalyst

0

02

04

06

08

1

12

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity

(a)

(c)(b)

Triglyceride conversion XT

Figure 10 Selectivity plots (a)methyl ester 1 (b)methyl ester 2 and(c) methyl ester 3 for dataset 6

concentration of 05ndash1 can yield up to a 99 methyl esterconversion

In Figures 8 and 9 there is a clear increasing trend of theselectivity ofmethyl ester for a 15 wt catalyst concentrationduring the early conversion of the reactant which decreasesat the end of the reactionThe same transition trend has beenfound when analyzing the influence of the molar ratio onmethyl ester selectivity A further detailed analysis showedthat the quadratic and cubic effects are more significantat a higher catalyst concentration than at a lower catalystconcentration As shown in Figure 10 the selectivity of E2 hasa quadratic plot whereas the selectivity of E3 has a parabolicshape Referring to (42)ndash(44) we can see that E1 is linearlyformed with a T conversion E2 is produced more at a Tconversion of lower than 035 where we can see that thepower of two in (43) is more dominant at this stage At aT conversion of over 05 the effect of the power of three in(44) is dominant causing a higher formation of E3 Becausethe transesterification reaction is a reversible and consecutiveequation the formation of three Es is important to achievea better selectivity With an optimum amount of catalyst thereactor becomesmore efficient in converting the reactant intothe products

43 Comparison ofMethyl Ester Selectivities fromDifferent OilFeedstocks To compare the selectivities of methyl esters andglycerol from different feedstocks datasets (8ndash10) were usedFigure 11 presents the selectivity ofmethyl esters derived fromrapeseed oil waste sunflower oil and palm oil for Case 1 andCase 2 As can be seen from the graph the methyl estersand glycerol were more likely to form if palm oil is used asthe feedstock compared to the other two oil feedstocks Thepresent finding also suggests that the selectivity of methylester was much lower when using low cost feedstock such aswaste sunflower oil Waste oil contains large amounts of freefatty acids (FFAs) (about 20) which affect the yield of fuelfrom that process The amount of FFAs in palm oil is 064[3] but for rapeseed oil the author used fresh oil [27] whichis estimated less than 1

12 International Journal of Chemical Engineering

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

PO-case 1 RO-case 1

WSO-case 1 WSO-case 2RO-case 2PO-case 2

Conversion of triglyceride XT

Sele

ctiv

ity o

f met

hyl e

sters

Figure 11 Selectivity plots of methyl ester from various feedstockfor Cases 1 and 2

As discussed before these free fatty acids will reactwith alkali catalysts to produce soaps that will inhibit thetransesterification reaction Soaps will allow emulsificationthat causes the phase separation of methyl ester and glycerolto be less sharp It produces water that can hydrolyze thetriglycerides and contribute to the formation of more soap[14] The effect of reversibility of transesterification can beseen significantly when analysing the selectivity of methylester derived from palm oil In Figure 11 methyl ester derivedfrom palm oil shows a higher selectivity plot for base caseThis finding suggests that forward reaction dominates thereaction and contributes to a better selectivity when lowFFAs feedstock is used in biodiesel production As there aremany low cost feedstocks available for biodiesel productiona pretreatment to these feedstocks can be carried out in orderto ensure the value of FFAs is within the allowable range

5 Conclusions

This paper has presented a comprehensive kinetic modelingof a transesterification reaction for biodiesel with homoge-neous alkaline catalyst The purpose of the study was todevelop the kinetic models of transesterification reactiondetermine the selectivity of methyl ester and glycerol andevaluate the significance of the reverse reactions in the trans-esterification reaction This study has shown that a processmodel solution was found for two types of common biodieselreactors The concentration of each species during transes-terification was found leading to a selectivity determinationduring the biodiesel production In addition the reversibleand irreversible effects of a transesterification reaction werediscovered The forward reaction is more dominant than thereverse reaction and the maximum selectivity can be foundif a base case of transesterification reaction is assumed tohave occurred in the biodiesel reactor system For the variousreaction characteristics under investigation the selectivities

are influenced by the temperature molar ratio of methanolto oil catalyst concentration and type of oil used as thefeedstock Furthermore an analysis of the selectivity plotsindicates an enhanced effect of the reaction characteristicson the selectivity This research has shown that the selectivityof methyl ester is maximized at 60∘C a 9 1 molar ratio ofmethanol to oil and a catalyst concentration of 15 Thisinvestigation into the effects of the molar ratio of methanolto oil and the catalyst concentration on the selectivity canbe made more interesting if several more curves are plottedat a molar ratio of methanol to oil between 3 1 to 9 1 anda catalyst concentration between 05 and 15 Howevera limitation of this research remains in the availability ofthe reaction rate constants under various reaction condi-tions In addition a comparison should be made throughmutual reaction conditionsThe findings from this study willenhance the concept of selectivity and its applications inthe evaluation of complex transesterification reactions whenthe goal is to attain the maximum production of methylesters and glycerol It is recommended that further researchis undertaken in exploring the selectivity data for specifyingthe reactor configurations and may be used in the synthesisof reactor network for biodiesel production

Nomenclature

119896+1 119896minus1 119896+2

119896minus2 119896+3 119896minus3

Reaction constant

119862T 119862D 119862M 119862G119862E1 119862E2 119862E3119862A 119862E

Molar concentration of triglyceridediglyceride monoglyceride glycerolester 1 ester 2 ester 3 methanol andmethyl ester

119883T Conversion of triglyceride119872119877 Molar ratio

119862T0 Initial molar concentration oftriglyceride

119878E 119878G Selectivity of methyl ester glycerol120572 Reaction rate constant factorwt Weight percentT TriglycerideD DiglycerideM MonoglycerideA MethanolG GlycerolE Methyl esterE1 Methyl ester 1E2 Methyl ester 2E3 Methyl ester 3PFR Plug flow reactorCSTR Continuous stirred tank reactor119873T0 Initial amount of triglyceride at 119905 = 0

119873T The amount of triglyceride present attime 119905

119881 VolumePO Palm oilRO Rapeseed oilWSO Waste sunflower oilNaOH Sodium hydroxide

International Journal of Chemical Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgment

Thework was carried out with the financial support from theMinistry of Education Malaysia

References

[1] A Demirbas ldquoBiodiesel from triglycerides via transesterifica-tionrdquo in Biodiesel pp 121ndash140 Springer London UK 2008

[2] D Darnoko and M Cheryan ldquoKinetics of palm oil transesteri-fication in a batch reactorrdquo JAOCS Journal of the American OilChemistsrsquo Society vol 77 no 12 pp 1263ndash1267 2000

[3] T Leevijit WWisutmethangoon G Prateepehaikul C Tongu-rai and M Allen ldquoA second order kinetics of palm oil transes-terification in a batch reactorrdquo in Proceedings of the Joint Inter-national Conference on Sustainable Energy and Environment pp277ndash281 2004

[4] S Jain andM P Sharma ldquoKinetics of acid base catalyzed trans-esterification of Jatropha curcas oilrdquo Bioresource Technology vol101 no 20 pp 7701ndash7706 2010

[5] H Noureddini and D Zhu ldquoKinetics of transesterification ofsoybean oilrdquo Journal of the American Oil Chemistsrsquo Society vol74 no 11 pp 1457ndash1463 1997

[6] D Kusdiana and S Saka ldquoKinetics of transesterification in rape-seed oil to biodiesel fuel as treated in supercritical methanolrdquoFuel vol 80 no 5 pp 693ndash698 2001

[7] M Diasakou A Louloudi and N Papayannakos ldquoKinetics ofthe non-catalytic transesterification of soybean oilrdquo Fuel vol 77no 12 pp 1297ndash1302 1998

[8] H Maeda S Hagiwara H Nabetani et al ldquoBiodiesel fuelsfrom palm oil via the non-catalytic transesterification in abubble column reactor at atmospheric pressure a kinetic studyrdquoRenewable Energy vol 33 no 7 pp 1629ndash1636 2008

[9] P C Narvaez S M Rincon and F J Sanchez ldquoKinetics of palmoil methanolysisrdquo Journal of the American Oil Chemistsrsquo Societyvol 84 pp 971ndash977 2007

[10] E Minami and S Saka ldquoKinetics of hydrolysis and methylesterification for biodiesel production in two-step supercriticalmethanol processrdquo Fuel vol 85 no 17-18 pp 2479ndash2483 2006

[11] B Freedman R O Butterfield and E H Pryde ldquoTransesteri-fication kinetics of soybean oil 1rdquo Journal of the American OilChemistsrsquo Society vol 63 no 10 pp 1375ndash1380 1986

[12] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

[13] J M Douglas Conceptual Design of Chemical ProcessesMcGraw Hill 1988

[14] J van Gerpen B Shanks R Pruszko D Clements and GKnothe Biodiesel Production Technology Subcontractor ReportNational Reanewable Energy Laboratory 2004

[15] H J Wright J B Segur H V Clark S K Coburn E ELangdon and R N DuPuis ldquoA report on ester interchangerdquoOilamp Soap vol 21 no 5 pp 145ndash148 1944

[16] H Fukuda A Kondo and H Noda ldquoBiodiesel fuel productionby transesterification of oilsrdquo Journal of Bioscience and Bioengi-neering vol 92 no 5 pp 405ndash416 2001

[17] L Friesenhagen and H Lepper ldquoProcess for the productionof fatty acid esters of short-chain aliphatic alcohols from fatsandor oils containing free fatty acidsrdquoUS Patent 4608202 1986

[18] P Felizardo J MacHado D Vergueiro M J N Correia J PGomes and J M Bordado ldquoStudy on the glycerolysis reactionof high free fatty acid oils for use as biodiesel feedstockrdquo FuelProcessing Technology vol 92 no 6 pp 1225ndash1229 2011

[19] A Tafesh and S Basheer ldquoPretreatment methods in biodieselproduction processesrdquo in Pretreatment Techniques for Biofuelsand Biorefineries Z Fang Ed Green Energy and Technologypp 417ndash434 Springer Berlin Germany 2013

[20] D Kusdiana and S Saka ldquoEffects of water on biodiesel fuelproduction by supercritical methanol treatmentrdquo BioresourceTechnology vol 91 no 3 pp 289ndash295 2004

[21] K Komers F Skopal R Stloukal and J Machek ldquoKinetics andmechanism of the KOHmdashcatalyzed methanolysis of rapeseedoil for biodiesel productionrdquo European Journal of Lipid Scienceand Technology vol 104 pp 728ndash737 2002

[22] A K CokerModeling of Chemical Kinetics and Reactor DesignGulf Publishing Houston Tex USA 2001

[23] C D Holland and R G Anthony Fundamentals of ChemicalReaction Engineering Prentice-Hall 1979

[24] J K Rodrıguez-Guerrero M F Rubens and P T V RosaldquoProduction of biodiesel from castor oil using sub and super-critical ethanol effect of sodium hydroxide on the ethyl esterproductionrdquoThe Journal of Supercritical Fluids vol 83 pp 124ndash132 2013

[25] G Vicente M Martınez and J Aracil ldquoOptimisation ofintegrated biodiesel production Part I A study of the biodieselpurity and yieldrdquoBioresource Technology vol 98 no 9 pp 1724ndash1733 2007

[26] A Srivastava and R Prasad ldquoTriglycerides-based diesel fuelsrdquoRenewable and Sustainable Energy Reviews vol 4 no 2 pp 111ndash133 2000

[27] B Klofutar J Golob B Likozar C Klofutar E Zagar andI Poljansek ldquoThe transesterification of rapeseed and wastesunflower oils mass-transfer and kinetics in a laboratory batchreactor and in an industrial-scale reactorseparator setuprdquoBioresource Technology vol 101 no 10 pp 3333ndash3344 2010

[28] S D Crymble ldquoOptimization and Reaction Kinetics of the Pro-duction of Biodiesel from Castor Oil via Sodium Methoxide-Catalyzed Methanolysisrdquo Dave C Swalm School of ChemicalEngineering Mississippi State University Miss USA 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Chemical Engineering 9

Table 3 Activation energy

Reaction Activation energy (calmol)T rarr D 13145D rarr T 9932D rarr M 19860M rarr D 14639M rarr G 6421G rarr M 9588

which affects the selectivity and methyl ester conversionwhich is likely due to the reverse nature of the reaction [4]This result suggests that for establishing the optimal chemicalprocess for biodiesel fuel production it can be assumed thatwhen irreversible reactions are employed better selectivitycan be obtained because of the absence of reverse reactions

42 Effects of Reaction Characteristics on Selectivity Thereactor design stage for a biodiesel plant utilizes methyl esterselectivity for the material balances and stream costs Attain-ing the appropriate operating conditions through productselectivity can eliminate material and energy recycling thusreducing costsThe effects of the reaction temperature molarratio of methanol to oil and the catalyst concentration on theselectivity of methyl esters and glycerol are analyzed for bothCase 1 and Case 2 in the following subsections

421 Effect of ReactionTemperature on Selectivity An investi-gation on the effect of temperature onmethyl ester selectivitywas conducted using datasets (1ndash3) where the molar ratio ofalcohol to oil and the catalyst concentration are fixed TheArrhenius equation was used for this investigation

119896 = 119896∘exp(minus

119864

119877119879

) (53)

According to (53) the reaction rate 119896 is an integralpart of the selectivity expressions It depends on the energyof activation (119864) obtained from the Arrhenius equation[22] For reactions at different temperatures fixed molarratios and catalyst concentrations the activation energy isconstant In this study the kinetic data used to analyzethe temperature effect were adapted from Noureddini andZhu [5] Because the data published in their research utilizethe average reaction rate constants at 50∘C and constantactivation energy (53) can bemanipulated to obtain the otherreaction rate constants (at 60∘C and 70∘C) listed in Table 1The results of the activation energy investigated in their studyare shown in Table 3

Figures 3 and 4 show the effects of the reaction tempera-ture on the selectivity ofmethyl esters and glycerol for Cases 1and 2 respectively The reaction temperature had a small butsubstantial effect on the selectivity The figures show thatthe selectivity of methyl esters is high at a high temperaturein the early conversion of T However in both figures theselectivities of E for both Cases 1 and 2 at 70∘C were foundto decrease toward the completion of the reaction As theboiling point of methanol is 647∘C an additional 5∘C has

0

02

04

06

08

1

12

00

05

10

15

20

25

30

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 3 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 1

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 02 04 06 08 1

Sele

ctiv

ity o

f gly

cero

l

Conversion of triglyceride XT

SE at 50∘C

SE at 60∘C

SE at 70∘C

SG at 50∘C

SG at 60∘C

SG at 70∘C

Figure 4 Selectivity of methyl ester at various temperatures andfixed molar ratio and catalyst concentration for Case 2

the effect of lowering the product concentration and affectingthe selectivity of E at the equilibriumThis temperature effectchanges the slope of selectivity from a concave to a convexshape which is also related with the reaction rate constant atdifferent temperatures

According to Darnoko and Cheryan [2] the transester-ification reaction rates were increased at 65∘C as comparedwith those at 50∘C The results of their research also showedan enhanced methyl ester yield at 65∘C compared withthat at 50∘C which was because of the higher viscosity ofoil at 50∘C In addition 55∘C is a stable temperature thatcan maintain the oil liquidity This result indicates that anoptimum temperature promotes the formation of methylesters and thus contributes to a higher selectivity of biodieselproducts It can also be suggested that the reaction rateconstant 119896 which is greatly dependent on the temperatureand selectivity of E is greatly improved at the optimumtemperature

10 International Journal of Chemical Engineering

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 5 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 1

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 6 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 2

The findings confirm that methyl ester selectivity effectscan be realistically obtained at the optimum temperaturewhich is 60∘C in this study As the reactor optimizationrequires the relationship between the conversion and selec-tivity in both cases (Case 1 and Case 2) the selectivity withinthe studied temperature indicates that the biodiesel reactormay work more efficiently in converting T to E at 60∘C

422 Effect of Molar Ratio of Methanol to Oil on SelectivityAn investigation into the effects of the methanol-to-oil molarratio involves datasets 4 and 5 Selectivity plots of methylesters and glycerol are shown in Figures 5 and 6 For Cases 1and 2 the selectivity of methyl esters and glycerol was rela-tively affected by the molar ratio of methanol to oil It can beseen from the figures that the higher molar ratio of methanolto oil encourages the formation of transesterification reactionproducts thus contributing to a higher selectivity

The most striking result to emerge from the figures isthe change in the shape of the selectivity plot from concave

0

02

04

06

08

1

12

0 02 04 06 08 1

Sele

ctiv

ity

(a)(b)

(c)

Triglyceride conversion XT

Figure 7 Selectivity plots (a) methyl ester 1 (b) methyl ester 2 and(c) methyl ester 3 for dataset 4

to convex for a molar ratio of 9 1 An increasing selectivityof methyl ester can be found in an early conversion oftriglyceride but toward equilibrium the selectivity is foundto slightly decrease A possible explanation for this mightbe that the methyl ester concentration has both quadratic aswell as cubic effects that can be explained by (42)ndash(44) andFigure 7

According to (42) the selectivity of methyl ester 1 isconstant at 1 Equation (43) is a quadratic equation whichgives a parabolic shape to the plot of methyl ester 2 Equation(44) clearly illustrates the selectivity of methyl ester 3 whenthe equation is a cubic one In more detail the power of twois more dominant at an 119883T of less than 03 which meansthat the formation of E2 is more active under this conditionHowever we can see an active formation of E3 at an 119883Tof 05ndash1 when the power of three is dominant At the sametime E1 is formed linearly with a triglyceride conversionThe stepwise transesterification reaction in (2)ndash(4) shows thateach E is formed consecutivelyThismeans that to achieve themaximum yield the maximum selectivity at the maximum Tconversion is necessary and each E must be formed duringthe process Therefore it can be assumed that the selectivityof methyl ester is more greatly affected by the quadratic andcubic functions at a highermolar ratio ofmethanol to oil thanat a lower one

In addition Freedman et al [11] reported that the bestmethyl ester conversion is achieved at a molar ratio of 6 1with alkaline catalyst and that higher molar ratios do notincrease the productivity but do increase the cost of alcoholrecovery At a high molar excess of methanol a pseudo-first-order reaction appeared more likely than a second-order reaction However high molar ratio of methanol isused for noncatalytic and supercritical methanol reaction[6 11 20 24] Narvaez et al [9] stated that when an excessamount of methanol is used it can positively affect thereversible characteristic of the reaction and the displacementof the reaction toward the product As a consequence excessmethanol does not necessarily contribute to an increase in theconcentration of methyl ester and glycerol

International Journal of Chemical Engineering 11

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 8 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 9 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 2

423 Effect of Catalyst Concentration on Selectivity Apartfrom the temperature and molar ratio the parameters thataffect the selectivity are the same as those influencing thereaction rates namely the catalyst The effects of the catalystconcentration are studied through datasets 6 and 7 andthe selectivity plots can be seen in Figures 8 and 9 Whenanalyzing the figures it can be seen that the selectivity of bothproducts is higher at a higher catalyst concentration

Toward the equilibrium of the reaction the selectivitywas observed to increase at a higher catalyst concentra-tion thus contributing to an increased amount of methylester formation Vicente et al [25] stated that the largestmethyl ester conversions are obtained when a large catalystconcentration is employed (13) at a mild temperature(20ndash50∘C) This agrees with the resulting selectivity curvesplotted which indicates that the catalyst concentration hasa positive effect on the selectivity of methyl esters andglycerol However a greater application of an alkali catalystcan lead to the production of large amounts of soap andextra cost is required to remove the catalyst from the reactionsystem Srivastava and Prasad [26] have stated that a catalyst

0

02

04

06

08

1

12

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity

(a)

(c)(b)

Triglyceride conversion XT

Figure 10 Selectivity plots (a)methyl ester 1 (b)methyl ester 2 and(c) methyl ester 3 for dataset 6

concentration of 05ndash1 can yield up to a 99 methyl esterconversion

In Figures 8 and 9 there is a clear increasing trend of theselectivity ofmethyl ester for a 15 wt catalyst concentrationduring the early conversion of the reactant which decreasesat the end of the reactionThe same transition trend has beenfound when analyzing the influence of the molar ratio onmethyl ester selectivity A further detailed analysis showedthat the quadratic and cubic effects are more significantat a higher catalyst concentration than at a lower catalystconcentration As shown in Figure 10 the selectivity of E2 hasa quadratic plot whereas the selectivity of E3 has a parabolicshape Referring to (42)ndash(44) we can see that E1 is linearlyformed with a T conversion E2 is produced more at a Tconversion of lower than 035 where we can see that thepower of two in (43) is more dominant at this stage At aT conversion of over 05 the effect of the power of three in(44) is dominant causing a higher formation of E3 Becausethe transesterification reaction is a reversible and consecutiveequation the formation of three Es is important to achievea better selectivity With an optimum amount of catalyst thereactor becomesmore efficient in converting the reactant intothe products

43 Comparison ofMethyl Ester Selectivities fromDifferent OilFeedstocks To compare the selectivities of methyl esters andglycerol from different feedstocks datasets (8ndash10) were usedFigure 11 presents the selectivity ofmethyl esters derived fromrapeseed oil waste sunflower oil and palm oil for Case 1 andCase 2 As can be seen from the graph the methyl estersand glycerol were more likely to form if palm oil is used asthe feedstock compared to the other two oil feedstocks Thepresent finding also suggests that the selectivity of methylester was much lower when using low cost feedstock such aswaste sunflower oil Waste oil contains large amounts of freefatty acids (FFAs) (about 20) which affect the yield of fuelfrom that process The amount of FFAs in palm oil is 064[3] but for rapeseed oil the author used fresh oil [27] whichis estimated less than 1

12 International Journal of Chemical Engineering

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

PO-case 1 RO-case 1

WSO-case 1 WSO-case 2RO-case 2PO-case 2

Conversion of triglyceride XT

Sele

ctiv

ity o

f met

hyl e

sters

Figure 11 Selectivity plots of methyl ester from various feedstockfor Cases 1 and 2

As discussed before these free fatty acids will reactwith alkali catalysts to produce soaps that will inhibit thetransesterification reaction Soaps will allow emulsificationthat causes the phase separation of methyl ester and glycerolto be less sharp It produces water that can hydrolyze thetriglycerides and contribute to the formation of more soap[14] The effect of reversibility of transesterification can beseen significantly when analysing the selectivity of methylester derived from palm oil In Figure 11 methyl ester derivedfrom palm oil shows a higher selectivity plot for base caseThis finding suggests that forward reaction dominates thereaction and contributes to a better selectivity when lowFFAs feedstock is used in biodiesel production As there aremany low cost feedstocks available for biodiesel productiona pretreatment to these feedstocks can be carried out in orderto ensure the value of FFAs is within the allowable range

5 Conclusions

This paper has presented a comprehensive kinetic modelingof a transesterification reaction for biodiesel with homoge-neous alkaline catalyst The purpose of the study was todevelop the kinetic models of transesterification reactiondetermine the selectivity of methyl ester and glycerol andevaluate the significance of the reverse reactions in the trans-esterification reaction This study has shown that a processmodel solution was found for two types of common biodieselreactors The concentration of each species during transes-terification was found leading to a selectivity determinationduring the biodiesel production In addition the reversibleand irreversible effects of a transesterification reaction werediscovered The forward reaction is more dominant than thereverse reaction and the maximum selectivity can be foundif a base case of transesterification reaction is assumed tohave occurred in the biodiesel reactor system For the variousreaction characteristics under investigation the selectivities

are influenced by the temperature molar ratio of methanolto oil catalyst concentration and type of oil used as thefeedstock Furthermore an analysis of the selectivity plotsindicates an enhanced effect of the reaction characteristicson the selectivity This research has shown that the selectivityof methyl ester is maximized at 60∘C a 9 1 molar ratio ofmethanol to oil and a catalyst concentration of 15 Thisinvestigation into the effects of the molar ratio of methanolto oil and the catalyst concentration on the selectivity canbe made more interesting if several more curves are plottedat a molar ratio of methanol to oil between 3 1 to 9 1 anda catalyst concentration between 05 and 15 Howevera limitation of this research remains in the availability ofthe reaction rate constants under various reaction condi-tions In addition a comparison should be made throughmutual reaction conditionsThe findings from this study willenhance the concept of selectivity and its applications inthe evaluation of complex transesterification reactions whenthe goal is to attain the maximum production of methylesters and glycerol It is recommended that further researchis undertaken in exploring the selectivity data for specifyingthe reactor configurations and may be used in the synthesisof reactor network for biodiesel production

Nomenclature

119896+1 119896minus1 119896+2

119896minus2 119896+3 119896minus3

Reaction constant

119862T 119862D 119862M 119862G119862E1 119862E2 119862E3119862A 119862E

Molar concentration of triglyceridediglyceride monoglyceride glycerolester 1 ester 2 ester 3 methanol andmethyl ester

119883T Conversion of triglyceride119872119877 Molar ratio

119862T0 Initial molar concentration oftriglyceride

119878E 119878G Selectivity of methyl ester glycerol120572 Reaction rate constant factorwt Weight percentT TriglycerideD DiglycerideM MonoglycerideA MethanolG GlycerolE Methyl esterE1 Methyl ester 1E2 Methyl ester 2E3 Methyl ester 3PFR Plug flow reactorCSTR Continuous stirred tank reactor119873T0 Initial amount of triglyceride at 119905 = 0

119873T The amount of triglyceride present attime 119905

119881 VolumePO Palm oilRO Rapeseed oilWSO Waste sunflower oilNaOH Sodium hydroxide

International Journal of Chemical Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgment

Thework was carried out with the financial support from theMinistry of Education Malaysia

References

[1] A Demirbas ldquoBiodiesel from triglycerides via transesterifica-tionrdquo in Biodiesel pp 121ndash140 Springer London UK 2008

[2] D Darnoko and M Cheryan ldquoKinetics of palm oil transesteri-fication in a batch reactorrdquo JAOCS Journal of the American OilChemistsrsquo Society vol 77 no 12 pp 1263ndash1267 2000

[3] T Leevijit WWisutmethangoon G Prateepehaikul C Tongu-rai and M Allen ldquoA second order kinetics of palm oil transes-terification in a batch reactorrdquo in Proceedings of the Joint Inter-national Conference on Sustainable Energy and Environment pp277ndash281 2004

[4] S Jain andM P Sharma ldquoKinetics of acid base catalyzed trans-esterification of Jatropha curcas oilrdquo Bioresource Technology vol101 no 20 pp 7701ndash7706 2010

[5] H Noureddini and D Zhu ldquoKinetics of transesterification ofsoybean oilrdquo Journal of the American Oil Chemistsrsquo Society vol74 no 11 pp 1457ndash1463 1997

[6] D Kusdiana and S Saka ldquoKinetics of transesterification in rape-seed oil to biodiesel fuel as treated in supercritical methanolrdquoFuel vol 80 no 5 pp 693ndash698 2001

[7] M Diasakou A Louloudi and N Papayannakos ldquoKinetics ofthe non-catalytic transesterification of soybean oilrdquo Fuel vol 77no 12 pp 1297ndash1302 1998

[8] H Maeda S Hagiwara H Nabetani et al ldquoBiodiesel fuelsfrom palm oil via the non-catalytic transesterification in abubble column reactor at atmospheric pressure a kinetic studyrdquoRenewable Energy vol 33 no 7 pp 1629ndash1636 2008

[9] P C Narvaez S M Rincon and F J Sanchez ldquoKinetics of palmoil methanolysisrdquo Journal of the American Oil Chemistsrsquo Societyvol 84 pp 971ndash977 2007

[10] E Minami and S Saka ldquoKinetics of hydrolysis and methylesterification for biodiesel production in two-step supercriticalmethanol processrdquo Fuel vol 85 no 17-18 pp 2479ndash2483 2006

[11] B Freedman R O Butterfield and E H Pryde ldquoTransesteri-fication kinetics of soybean oil 1rdquo Journal of the American OilChemistsrsquo Society vol 63 no 10 pp 1375ndash1380 1986

[12] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

[13] J M Douglas Conceptual Design of Chemical ProcessesMcGraw Hill 1988

[14] J van Gerpen B Shanks R Pruszko D Clements and GKnothe Biodiesel Production Technology Subcontractor ReportNational Reanewable Energy Laboratory 2004

[15] H J Wright J B Segur H V Clark S K Coburn E ELangdon and R N DuPuis ldquoA report on ester interchangerdquoOilamp Soap vol 21 no 5 pp 145ndash148 1944

[16] H Fukuda A Kondo and H Noda ldquoBiodiesel fuel productionby transesterification of oilsrdquo Journal of Bioscience and Bioengi-neering vol 92 no 5 pp 405ndash416 2001

[17] L Friesenhagen and H Lepper ldquoProcess for the productionof fatty acid esters of short-chain aliphatic alcohols from fatsandor oils containing free fatty acidsrdquoUS Patent 4608202 1986

[18] P Felizardo J MacHado D Vergueiro M J N Correia J PGomes and J M Bordado ldquoStudy on the glycerolysis reactionof high free fatty acid oils for use as biodiesel feedstockrdquo FuelProcessing Technology vol 92 no 6 pp 1225ndash1229 2011

[19] A Tafesh and S Basheer ldquoPretreatment methods in biodieselproduction processesrdquo in Pretreatment Techniques for Biofuelsand Biorefineries Z Fang Ed Green Energy and Technologypp 417ndash434 Springer Berlin Germany 2013

[20] D Kusdiana and S Saka ldquoEffects of water on biodiesel fuelproduction by supercritical methanol treatmentrdquo BioresourceTechnology vol 91 no 3 pp 289ndash295 2004

[21] K Komers F Skopal R Stloukal and J Machek ldquoKinetics andmechanism of the KOHmdashcatalyzed methanolysis of rapeseedoil for biodiesel productionrdquo European Journal of Lipid Scienceand Technology vol 104 pp 728ndash737 2002

[22] A K CokerModeling of Chemical Kinetics and Reactor DesignGulf Publishing Houston Tex USA 2001

[23] C D Holland and R G Anthony Fundamentals of ChemicalReaction Engineering Prentice-Hall 1979

[24] J K Rodrıguez-Guerrero M F Rubens and P T V RosaldquoProduction of biodiesel from castor oil using sub and super-critical ethanol effect of sodium hydroxide on the ethyl esterproductionrdquoThe Journal of Supercritical Fluids vol 83 pp 124ndash132 2013

[25] G Vicente M Martınez and J Aracil ldquoOptimisation ofintegrated biodiesel production Part I A study of the biodieselpurity and yieldrdquoBioresource Technology vol 98 no 9 pp 1724ndash1733 2007

[26] A Srivastava and R Prasad ldquoTriglycerides-based diesel fuelsrdquoRenewable and Sustainable Energy Reviews vol 4 no 2 pp 111ndash133 2000

[27] B Klofutar J Golob B Likozar C Klofutar E Zagar andI Poljansek ldquoThe transesterification of rapeseed and wastesunflower oils mass-transfer and kinetics in a laboratory batchreactor and in an industrial-scale reactorseparator setuprdquoBioresource Technology vol 101 no 10 pp 3333ndash3344 2010

[28] S D Crymble ldquoOptimization and Reaction Kinetics of the Pro-duction of Biodiesel from Castor Oil via Sodium Methoxide-Catalyzed Methanolysisrdquo Dave C Swalm School of ChemicalEngineering Mississippi State University Miss USA 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 International Journal of Chemical Engineering

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 5 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 1

Sele

ctiv

ity o

f gly

cero

l

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity o

f met

hyl e

sters

Conversion of triglyceride XT

SE for MR 9 1 SG for MR 9 1SG for MR 3 1SE for MR 3 1

Figure 6 Selectivity ofmethyl ester at variousmolar ratios constanttemperature of 65∘C and catalyst concentration of 15 wt forCase 2

The findings confirm that methyl ester selectivity effectscan be realistically obtained at the optimum temperaturewhich is 60∘C in this study As the reactor optimizationrequires the relationship between the conversion and selec-tivity in both cases (Case 1 and Case 2) the selectivity withinthe studied temperature indicates that the biodiesel reactormay work more efficiently in converting T to E at 60∘C

422 Effect of Molar Ratio of Methanol to Oil on SelectivityAn investigation into the effects of the methanol-to-oil molarratio involves datasets 4 and 5 Selectivity plots of methylesters and glycerol are shown in Figures 5 and 6 For Cases 1and 2 the selectivity of methyl esters and glycerol was rela-tively affected by the molar ratio of methanol to oil It can beseen from the figures that the higher molar ratio of methanolto oil encourages the formation of transesterification reactionproducts thus contributing to a higher selectivity

The most striking result to emerge from the figures isthe change in the shape of the selectivity plot from concave

0

02

04

06

08

1

12

0 02 04 06 08 1

Sele

ctiv

ity

(a)(b)

(c)

Triglyceride conversion XT

Figure 7 Selectivity plots (a) methyl ester 1 (b) methyl ester 2 and(c) methyl ester 3 for dataset 4

to convex for a molar ratio of 9 1 An increasing selectivityof methyl ester can be found in an early conversion oftriglyceride but toward equilibrium the selectivity is foundto slightly decrease A possible explanation for this mightbe that the methyl ester concentration has both quadratic aswell as cubic effects that can be explained by (42)ndash(44) andFigure 7

According to (42) the selectivity of methyl ester 1 isconstant at 1 Equation (43) is a quadratic equation whichgives a parabolic shape to the plot of methyl ester 2 Equation(44) clearly illustrates the selectivity of methyl ester 3 whenthe equation is a cubic one In more detail the power of twois more dominant at an 119883T of less than 03 which meansthat the formation of E2 is more active under this conditionHowever we can see an active formation of E3 at an 119883Tof 05ndash1 when the power of three is dominant At the sametime E1 is formed linearly with a triglyceride conversionThe stepwise transesterification reaction in (2)ndash(4) shows thateach E is formed consecutivelyThismeans that to achieve themaximum yield the maximum selectivity at the maximum Tconversion is necessary and each E must be formed duringthe process Therefore it can be assumed that the selectivityof methyl ester is more greatly affected by the quadratic andcubic functions at a highermolar ratio ofmethanol to oil thanat a lower one

In addition Freedman et al [11] reported that the bestmethyl ester conversion is achieved at a molar ratio of 6 1with alkaline catalyst and that higher molar ratios do notincrease the productivity but do increase the cost of alcoholrecovery At a high molar excess of methanol a pseudo-first-order reaction appeared more likely than a second-order reaction However high molar ratio of methanol isused for noncatalytic and supercritical methanol reaction[6 11 20 24] Narvaez et al [9] stated that when an excessamount of methanol is used it can positively affect thereversible characteristic of the reaction and the displacementof the reaction toward the product As a consequence excessmethanol does not necessarily contribute to an increase in theconcentration of methyl ester and glycerol

International Journal of Chemical Engineering 11

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 8 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 9 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 2

423 Effect of Catalyst Concentration on Selectivity Apartfrom the temperature and molar ratio the parameters thataffect the selectivity are the same as those influencing thereaction rates namely the catalyst The effects of the catalystconcentration are studied through datasets 6 and 7 andthe selectivity plots can be seen in Figures 8 and 9 Whenanalyzing the figures it can be seen that the selectivity of bothproducts is higher at a higher catalyst concentration

Toward the equilibrium of the reaction the selectivitywas observed to increase at a higher catalyst concentra-tion thus contributing to an increased amount of methylester formation Vicente et al [25] stated that the largestmethyl ester conversions are obtained when a large catalystconcentration is employed (13) at a mild temperature(20ndash50∘C) This agrees with the resulting selectivity curvesplotted which indicates that the catalyst concentration hasa positive effect on the selectivity of methyl esters andglycerol However a greater application of an alkali catalystcan lead to the production of large amounts of soap andextra cost is required to remove the catalyst from the reactionsystem Srivastava and Prasad [26] have stated that a catalyst

0

02

04

06

08

1

12

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity

(a)

(c)(b)

Triglyceride conversion XT

Figure 10 Selectivity plots (a)methyl ester 1 (b)methyl ester 2 and(c) methyl ester 3 for dataset 6

concentration of 05ndash1 can yield up to a 99 methyl esterconversion

In Figures 8 and 9 there is a clear increasing trend of theselectivity ofmethyl ester for a 15 wt catalyst concentrationduring the early conversion of the reactant which decreasesat the end of the reactionThe same transition trend has beenfound when analyzing the influence of the molar ratio onmethyl ester selectivity A further detailed analysis showedthat the quadratic and cubic effects are more significantat a higher catalyst concentration than at a lower catalystconcentration As shown in Figure 10 the selectivity of E2 hasa quadratic plot whereas the selectivity of E3 has a parabolicshape Referring to (42)ndash(44) we can see that E1 is linearlyformed with a T conversion E2 is produced more at a Tconversion of lower than 035 where we can see that thepower of two in (43) is more dominant at this stage At aT conversion of over 05 the effect of the power of three in(44) is dominant causing a higher formation of E3 Becausethe transesterification reaction is a reversible and consecutiveequation the formation of three Es is important to achievea better selectivity With an optimum amount of catalyst thereactor becomesmore efficient in converting the reactant intothe products

43 Comparison ofMethyl Ester Selectivities fromDifferent OilFeedstocks To compare the selectivities of methyl esters andglycerol from different feedstocks datasets (8ndash10) were usedFigure 11 presents the selectivity ofmethyl esters derived fromrapeseed oil waste sunflower oil and palm oil for Case 1 andCase 2 As can be seen from the graph the methyl estersand glycerol were more likely to form if palm oil is used asthe feedstock compared to the other two oil feedstocks Thepresent finding also suggests that the selectivity of methylester was much lower when using low cost feedstock such aswaste sunflower oil Waste oil contains large amounts of freefatty acids (FFAs) (about 20) which affect the yield of fuelfrom that process The amount of FFAs in palm oil is 064[3] but for rapeseed oil the author used fresh oil [27] whichis estimated less than 1

12 International Journal of Chemical Engineering

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

PO-case 1 RO-case 1

WSO-case 1 WSO-case 2RO-case 2PO-case 2

Conversion of triglyceride XT

Sele

ctiv

ity o

f met

hyl e

sters

Figure 11 Selectivity plots of methyl ester from various feedstockfor Cases 1 and 2

As discussed before these free fatty acids will reactwith alkali catalysts to produce soaps that will inhibit thetransesterification reaction Soaps will allow emulsificationthat causes the phase separation of methyl ester and glycerolto be less sharp It produces water that can hydrolyze thetriglycerides and contribute to the formation of more soap[14] The effect of reversibility of transesterification can beseen significantly when analysing the selectivity of methylester derived from palm oil In Figure 11 methyl ester derivedfrom palm oil shows a higher selectivity plot for base caseThis finding suggests that forward reaction dominates thereaction and contributes to a better selectivity when lowFFAs feedstock is used in biodiesel production As there aremany low cost feedstocks available for biodiesel productiona pretreatment to these feedstocks can be carried out in orderto ensure the value of FFAs is within the allowable range

5 Conclusions

This paper has presented a comprehensive kinetic modelingof a transesterification reaction for biodiesel with homoge-neous alkaline catalyst The purpose of the study was todevelop the kinetic models of transesterification reactiondetermine the selectivity of methyl ester and glycerol andevaluate the significance of the reverse reactions in the trans-esterification reaction This study has shown that a processmodel solution was found for two types of common biodieselreactors The concentration of each species during transes-terification was found leading to a selectivity determinationduring the biodiesel production In addition the reversibleand irreversible effects of a transesterification reaction werediscovered The forward reaction is more dominant than thereverse reaction and the maximum selectivity can be foundif a base case of transesterification reaction is assumed tohave occurred in the biodiesel reactor system For the variousreaction characteristics under investigation the selectivities

are influenced by the temperature molar ratio of methanolto oil catalyst concentration and type of oil used as thefeedstock Furthermore an analysis of the selectivity plotsindicates an enhanced effect of the reaction characteristicson the selectivity This research has shown that the selectivityof methyl ester is maximized at 60∘C a 9 1 molar ratio ofmethanol to oil and a catalyst concentration of 15 Thisinvestigation into the effects of the molar ratio of methanolto oil and the catalyst concentration on the selectivity canbe made more interesting if several more curves are plottedat a molar ratio of methanol to oil between 3 1 to 9 1 anda catalyst concentration between 05 and 15 Howevera limitation of this research remains in the availability ofthe reaction rate constants under various reaction condi-tions In addition a comparison should be made throughmutual reaction conditionsThe findings from this study willenhance the concept of selectivity and its applications inthe evaluation of complex transesterification reactions whenthe goal is to attain the maximum production of methylesters and glycerol It is recommended that further researchis undertaken in exploring the selectivity data for specifyingthe reactor configurations and may be used in the synthesisof reactor network for biodiesel production

Nomenclature

119896+1 119896minus1 119896+2

119896minus2 119896+3 119896minus3

Reaction constant

119862T 119862D 119862M 119862G119862E1 119862E2 119862E3119862A 119862E

Molar concentration of triglyceridediglyceride monoglyceride glycerolester 1 ester 2 ester 3 methanol andmethyl ester

119883T Conversion of triglyceride119872119877 Molar ratio

119862T0 Initial molar concentration oftriglyceride

119878E 119878G Selectivity of methyl ester glycerol120572 Reaction rate constant factorwt Weight percentT TriglycerideD DiglycerideM MonoglycerideA MethanolG GlycerolE Methyl esterE1 Methyl ester 1E2 Methyl ester 2E3 Methyl ester 3PFR Plug flow reactorCSTR Continuous stirred tank reactor119873T0 Initial amount of triglyceride at 119905 = 0

119873T The amount of triglyceride present attime 119905

119881 VolumePO Palm oilRO Rapeseed oilWSO Waste sunflower oilNaOH Sodium hydroxide

International Journal of Chemical Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgment

Thework was carried out with the financial support from theMinistry of Education Malaysia

References

[1] A Demirbas ldquoBiodiesel from triglycerides via transesterifica-tionrdquo in Biodiesel pp 121ndash140 Springer London UK 2008

[2] D Darnoko and M Cheryan ldquoKinetics of palm oil transesteri-fication in a batch reactorrdquo JAOCS Journal of the American OilChemistsrsquo Society vol 77 no 12 pp 1263ndash1267 2000

[3] T Leevijit WWisutmethangoon G Prateepehaikul C Tongu-rai and M Allen ldquoA second order kinetics of palm oil transes-terification in a batch reactorrdquo in Proceedings of the Joint Inter-national Conference on Sustainable Energy and Environment pp277ndash281 2004

[4] S Jain andM P Sharma ldquoKinetics of acid base catalyzed trans-esterification of Jatropha curcas oilrdquo Bioresource Technology vol101 no 20 pp 7701ndash7706 2010

[5] H Noureddini and D Zhu ldquoKinetics of transesterification ofsoybean oilrdquo Journal of the American Oil Chemistsrsquo Society vol74 no 11 pp 1457ndash1463 1997

[6] D Kusdiana and S Saka ldquoKinetics of transesterification in rape-seed oil to biodiesel fuel as treated in supercritical methanolrdquoFuel vol 80 no 5 pp 693ndash698 2001

[7] M Diasakou A Louloudi and N Papayannakos ldquoKinetics ofthe non-catalytic transesterification of soybean oilrdquo Fuel vol 77no 12 pp 1297ndash1302 1998

[8] H Maeda S Hagiwara H Nabetani et al ldquoBiodiesel fuelsfrom palm oil via the non-catalytic transesterification in abubble column reactor at atmospheric pressure a kinetic studyrdquoRenewable Energy vol 33 no 7 pp 1629ndash1636 2008

[9] P C Narvaez S M Rincon and F J Sanchez ldquoKinetics of palmoil methanolysisrdquo Journal of the American Oil Chemistsrsquo Societyvol 84 pp 971ndash977 2007

[10] E Minami and S Saka ldquoKinetics of hydrolysis and methylesterification for biodiesel production in two-step supercriticalmethanol processrdquo Fuel vol 85 no 17-18 pp 2479ndash2483 2006

[11] B Freedman R O Butterfield and E H Pryde ldquoTransesteri-fication kinetics of soybean oil 1rdquo Journal of the American OilChemistsrsquo Society vol 63 no 10 pp 1375ndash1380 1986

[12] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

[13] J M Douglas Conceptual Design of Chemical ProcessesMcGraw Hill 1988

[14] J van Gerpen B Shanks R Pruszko D Clements and GKnothe Biodiesel Production Technology Subcontractor ReportNational Reanewable Energy Laboratory 2004

[15] H J Wright J B Segur H V Clark S K Coburn E ELangdon and R N DuPuis ldquoA report on ester interchangerdquoOilamp Soap vol 21 no 5 pp 145ndash148 1944

[16] H Fukuda A Kondo and H Noda ldquoBiodiesel fuel productionby transesterification of oilsrdquo Journal of Bioscience and Bioengi-neering vol 92 no 5 pp 405ndash416 2001

[17] L Friesenhagen and H Lepper ldquoProcess for the productionof fatty acid esters of short-chain aliphatic alcohols from fatsandor oils containing free fatty acidsrdquoUS Patent 4608202 1986

[18] P Felizardo J MacHado D Vergueiro M J N Correia J PGomes and J M Bordado ldquoStudy on the glycerolysis reactionof high free fatty acid oils for use as biodiesel feedstockrdquo FuelProcessing Technology vol 92 no 6 pp 1225ndash1229 2011

[19] A Tafesh and S Basheer ldquoPretreatment methods in biodieselproduction processesrdquo in Pretreatment Techniques for Biofuelsand Biorefineries Z Fang Ed Green Energy and Technologypp 417ndash434 Springer Berlin Germany 2013

[20] D Kusdiana and S Saka ldquoEffects of water on biodiesel fuelproduction by supercritical methanol treatmentrdquo BioresourceTechnology vol 91 no 3 pp 289ndash295 2004

[21] K Komers F Skopal R Stloukal and J Machek ldquoKinetics andmechanism of the KOHmdashcatalyzed methanolysis of rapeseedoil for biodiesel productionrdquo European Journal of Lipid Scienceand Technology vol 104 pp 728ndash737 2002

[22] A K CokerModeling of Chemical Kinetics and Reactor DesignGulf Publishing Houston Tex USA 2001

[23] C D Holland and R G Anthony Fundamentals of ChemicalReaction Engineering Prentice-Hall 1979

[24] J K Rodrıguez-Guerrero M F Rubens and P T V RosaldquoProduction of biodiesel from castor oil using sub and super-critical ethanol effect of sodium hydroxide on the ethyl esterproductionrdquoThe Journal of Supercritical Fluids vol 83 pp 124ndash132 2013

[25] G Vicente M Martınez and J Aracil ldquoOptimisation ofintegrated biodiesel production Part I A study of the biodieselpurity and yieldrdquoBioresource Technology vol 98 no 9 pp 1724ndash1733 2007

[26] A Srivastava and R Prasad ldquoTriglycerides-based diesel fuelsrdquoRenewable and Sustainable Energy Reviews vol 4 no 2 pp 111ndash133 2000

[27] B Klofutar J Golob B Likozar C Klofutar E Zagar andI Poljansek ldquoThe transesterification of rapeseed and wastesunflower oils mass-transfer and kinetics in a laboratory batchreactor and in an industrial-scale reactorseparator setuprdquoBioresource Technology vol 101 no 10 pp 3333ndash3344 2010

[28] S D Crymble ldquoOptimization and Reaction Kinetics of the Pro-duction of Biodiesel from Castor Oil via Sodium Methoxide-Catalyzed Methanolysisrdquo Dave C Swalm School of ChemicalEngineering Mississippi State University Miss USA 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Chemical Engineering 11

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 8 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 1

Sele

ctiv

ity o

f gly

cero

l

Sele

ctiv

ity o

f met

hyl e

sters

0

02

04

06

08

1

12

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1Conversion of triglyceride XT

SE for 15 wt catalystSE for 05 wt catalyst

SG for 15 wt catalystSG for 05 wt catalyst

Figure 9 Selectivity of methyl ester at various catalyst concentra-tions constant temperature of 30∘C and molar ratio 9 1 for Case 2

423 Effect of Catalyst Concentration on Selectivity Apartfrom the temperature and molar ratio the parameters thataffect the selectivity are the same as those influencing thereaction rates namely the catalyst The effects of the catalystconcentration are studied through datasets 6 and 7 andthe selectivity plots can be seen in Figures 8 and 9 Whenanalyzing the figures it can be seen that the selectivity of bothproducts is higher at a higher catalyst concentration

Toward the equilibrium of the reaction the selectivitywas observed to increase at a higher catalyst concentra-tion thus contributing to an increased amount of methylester formation Vicente et al [25] stated that the largestmethyl ester conversions are obtained when a large catalystconcentration is employed (13) at a mild temperature(20ndash50∘C) This agrees with the resulting selectivity curvesplotted which indicates that the catalyst concentration hasa positive effect on the selectivity of methyl esters andglycerol However a greater application of an alkali catalystcan lead to the production of large amounts of soap andextra cost is required to remove the catalyst from the reactionsystem Srivastava and Prasad [26] have stated that a catalyst

0

02

04

06

08

1

12

0 01 02 03 04 05 06 07 08 09 1

Sele

ctiv

ity

(a)

(c)(b)

Triglyceride conversion XT

Figure 10 Selectivity plots (a)methyl ester 1 (b)methyl ester 2 and(c) methyl ester 3 for dataset 6

concentration of 05ndash1 can yield up to a 99 methyl esterconversion

In Figures 8 and 9 there is a clear increasing trend of theselectivity ofmethyl ester for a 15 wt catalyst concentrationduring the early conversion of the reactant which decreasesat the end of the reactionThe same transition trend has beenfound when analyzing the influence of the molar ratio onmethyl ester selectivity A further detailed analysis showedthat the quadratic and cubic effects are more significantat a higher catalyst concentration than at a lower catalystconcentration As shown in Figure 10 the selectivity of E2 hasa quadratic plot whereas the selectivity of E3 has a parabolicshape Referring to (42)ndash(44) we can see that E1 is linearlyformed with a T conversion E2 is produced more at a Tconversion of lower than 035 where we can see that thepower of two in (43) is more dominant at this stage At aT conversion of over 05 the effect of the power of three in(44) is dominant causing a higher formation of E3 Becausethe transesterification reaction is a reversible and consecutiveequation the formation of three Es is important to achievea better selectivity With an optimum amount of catalyst thereactor becomesmore efficient in converting the reactant intothe products

43 Comparison ofMethyl Ester Selectivities fromDifferent OilFeedstocks To compare the selectivities of methyl esters andglycerol from different feedstocks datasets (8ndash10) were usedFigure 11 presents the selectivity ofmethyl esters derived fromrapeseed oil waste sunflower oil and palm oil for Case 1 andCase 2 As can be seen from the graph the methyl estersand glycerol were more likely to form if palm oil is used asthe feedstock compared to the other two oil feedstocks Thepresent finding also suggests that the selectivity of methylester was much lower when using low cost feedstock such aswaste sunflower oil Waste oil contains large amounts of freefatty acids (FFAs) (about 20) which affect the yield of fuelfrom that process The amount of FFAs in palm oil is 064[3] but for rapeseed oil the author used fresh oil [27] whichis estimated less than 1

12 International Journal of Chemical Engineering

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

PO-case 1 RO-case 1

WSO-case 1 WSO-case 2RO-case 2PO-case 2

Conversion of triglyceride XT

Sele

ctiv

ity o

f met

hyl e

sters

Figure 11 Selectivity plots of methyl ester from various feedstockfor Cases 1 and 2

As discussed before these free fatty acids will reactwith alkali catalysts to produce soaps that will inhibit thetransesterification reaction Soaps will allow emulsificationthat causes the phase separation of methyl ester and glycerolto be less sharp It produces water that can hydrolyze thetriglycerides and contribute to the formation of more soap[14] The effect of reversibility of transesterification can beseen significantly when analysing the selectivity of methylester derived from palm oil In Figure 11 methyl ester derivedfrom palm oil shows a higher selectivity plot for base caseThis finding suggests that forward reaction dominates thereaction and contributes to a better selectivity when lowFFAs feedstock is used in biodiesel production As there aremany low cost feedstocks available for biodiesel productiona pretreatment to these feedstocks can be carried out in orderto ensure the value of FFAs is within the allowable range

5 Conclusions

This paper has presented a comprehensive kinetic modelingof a transesterification reaction for biodiesel with homoge-neous alkaline catalyst The purpose of the study was todevelop the kinetic models of transesterification reactiondetermine the selectivity of methyl ester and glycerol andevaluate the significance of the reverse reactions in the trans-esterification reaction This study has shown that a processmodel solution was found for two types of common biodieselreactors The concentration of each species during transes-terification was found leading to a selectivity determinationduring the biodiesel production In addition the reversibleand irreversible effects of a transesterification reaction werediscovered The forward reaction is more dominant than thereverse reaction and the maximum selectivity can be foundif a base case of transesterification reaction is assumed tohave occurred in the biodiesel reactor system For the variousreaction characteristics under investigation the selectivities

are influenced by the temperature molar ratio of methanolto oil catalyst concentration and type of oil used as thefeedstock Furthermore an analysis of the selectivity plotsindicates an enhanced effect of the reaction characteristicson the selectivity This research has shown that the selectivityof methyl ester is maximized at 60∘C a 9 1 molar ratio ofmethanol to oil and a catalyst concentration of 15 Thisinvestigation into the effects of the molar ratio of methanolto oil and the catalyst concentration on the selectivity canbe made more interesting if several more curves are plottedat a molar ratio of methanol to oil between 3 1 to 9 1 anda catalyst concentration between 05 and 15 Howevera limitation of this research remains in the availability ofthe reaction rate constants under various reaction condi-tions In addition a comparison should be made throughmutual reaction conditionsThe findings from this study willenhance the concept of selectivity and its applications inthe evaluation of complex transesterification reactions whenthe goal is to attain the maximum production of methylesters and glycerol It is recommended that further researchis undertaken in exploring the selectivity data for specifyingthe reactor configurations and may be used in the synthesisof reactor network for biodiesel production

Nomenclature

119896+1 119896minus1 119896+2

119896minus2 119896+3 119896minus3

Reaction constant

119862T 119862D 119862M 119862G119862E1 119862E2 119862E3119862A 119862E

Molar concentration of triglyceridediglyceride monoglyceride glycerolester 1 ester 2 ester 3 methanol andmethyl ester

119883T Conversion of triglyceride119872119877 Molar ratio

119862T0 Initial molar concentration oftriglyceride

119878E 119878G Selectivity of methyl ester glycerol120572 Reaction rate constant factorwt Weight percentT TriglycerideD DiglycerideM MonoglycerideA MethanolG GlycerolE Methyl esterE1 Methyl ester 1E2 Methyl ester 2E3 Methyl ester 3PFR Plug flow reactorCSTR Continuous stirred tank reactor119873T0 Initial amount of triglyceride at 119905 = 0

119873T The amount of triglyceride present attime 119905

119881 VolumePO Palm oilRO Rapeseed oilWSO Waste sunflower oilNaOH Sodium hydroxide

International Journal of Chemical Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgment

Thework was carried out with the financial support from theMinistry of Education Malaysia

References

[1] A Demirbas ldquoBiodiesel from triglycerides via transesterifica-tionrdquo in Biodiesel pp 121ndash140 Springer London UK 2008

[2] D Darnoko and M Cheryan ldquoKinetics of palm oil transesteri-fication in a batch reactorrdquo JAOCS Journal of the American OilChemistsrsquo Society vol 77 no 12 pp 1263ndash1267 2000

[3] T Leevijit WWisutmethangoon G Prateepehaikul C Tongu-rai and M Allen ldquoA second order kinetics of palm oil transes-terification in a batch reactorrdquo in Proceedings of the Joint Inter-national Conference on Sustainable Energy and Environment pp277ndash281 2004

[4] S Jain andM P Sharma ldquoKinetics of acid base catalyzed trans-esterification of Jatropha curcas oilrdquo Bioresource Technology vol101 no 20 pp 7701ndash7706 2010

[5] H Noureddini and D Zhu ldquoKinetics of transesterification ofsoybean oilrdquo Journal of the American Oil Chemistsrsquo Society vol74 no 11 pp 1457ndash1463 1997

[6] D Kusdiana and S Saka ldquoKinetics of transesterification in rape-seed oil to biodiesel fuel as treated in supercritical methanolrdquoFuel vol 80 no 5 pp 693ndash698 2001

[7] M Diasakou A Louloudi and N Papayannakos ldquoKinetics ofthe non-catalytic transesterification of soybean oilrdquo Fuel vol 77no 12 pp 1297ndash1302 1998

[8] H Maeda S Hagiwara H Nabetani et al ldquoBiodiesel fuelsfrom palm oil via the non-catalytic transesterification in abubble column reactor at atmospheric pressure a kinetic studyrdquoRenewable Energy vol 33 no 7 pp 1629ndash1636 2008

[9] P C Narvaez S M Rincon and F J Sanchez ldquoKinetics of palmoil methanolysisrdquo Journal of the American Oil Chemistsrsquo Societyvol 84 pp 971ndash977 2007

[10] E Minami and S Saka ldquoKinetics of hydrolysis and methylesterification for biodiesel production in two-step supercriticalmethanol processrdquo Fuel vol 85 no 17-18 pp 2479ndash2483 2006

[11] B Freedman R O Butterfield and E H Pryde ldquoTransesteri-fication kinetics of soybean oil 1rdquo Journal of the American OilChemistsrsquo Society vol 63 no 10 pp 1375ndash1380 1986

[12] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

[13] J M Douglas Conceptual Design of Chemical ProcessesMcGraw Hill 1988

[14] J van Gerpen B Shanks R Pruszko D Clements and GKnothe Biodiesel Production Technology Subcontractor ReportNational Reanewable Energy Laboratory 2004

[15] H J Wright J B Segur H V Clark S K Coburn E ELangdon and R N DuPuis ldquoA report on ester interchangerdquoOilamp Soap vol 21 no 5 pp 145ndash148 1944

[16] H Fukuda A Kondo and H Noda ldquoBiodiesel fuel productionby transesterification of oilsrdquo Journal of Bioscience and Bioengi-neering vol 92 no 5 pp 405ndash416 2001

[17] L Friesenhagen and H Lepper ldquoProcess for the productionof fatty acid esters of short-chain aliphatic alcohols from fatsandor oils containing free fatty acidsrdquoUS Patent 4608202 1986

[18] P Felizardo J MacHado D Vergueiro M J N Correia J PGomes and J M Bordado ldquoStudy on the glycerolysis reactionof high free fatty acid oils for use as biodiesel feedstockrdquo FuelProcessing Technology vol 92 no 6 pp 1225ndash1229 2011

[19] A Tafesh and S Basheer ldquoPretreatment methods in biodieselproduction processesrdquo in Pretreatment Techniques for Biofuelsand Biorefineries Z Fang Ed Green Energy and Technologypp 417ndash434 Springer Berlin Germany 2013

[20] D Kusdiana and S Saka ldquoEffects of water on biodiesel fuelproduction by supercritical methanol treatmentrdquo BioresourceTechnology vol 91 no 3 pp 289ndash295 2004

[21] K Komers F Skopal R Stloukal and J Machek ldquoKinetics andmechanism of the KOHmdashcatalyzed methanolysis of rapeseedoil for biodiesel productionrdquo European Journal of Lipid Scienceand Technology vol 104 pp 728ndash737 2002

[22] A K CokerModeling of Chemical Kinetics and Reactor DesignGulf Publishing Houston Tex USA 2001

[23] C D Holland and R G Anthony Fundamentals of ChemicalReaction Engineering Prentice-Hall 1979

[24] J K Rodrıguez-Guerrero M F Rubens and P T V RosaldquoProduction of biodiesel from castor oil using sub and super-critical ethanol effect of sodium hydroxide on the ethyl esterproductionrdquoThe Journal of Supercritical Fluids vol 83 pp 124ndash132 2013

[25] G Vicente M Martınez and J Aracil ldquoOptimisation ofintegrated biodiesel production Part I A study of the biodieselpurity and yieldrdquoBioresource Technology vol 98 no 9 pp 1724ndash1733 2007

[26] A Srivastava and R Prasad ldquoTriglycerides-based diesel fuelsrdquoRenewable and Sustainable Energy Reviews vol 4 no 2 pp 111ndash133 2000

[27] B Klofutar J Golob B Likozar C Klofutar E Zagar andI Poljansek ldquoThe transesterification of rapeseed and wastesunflower oils mass-transfer and kinetics in a laboratory batchreactor and in an industrial-scale reactorseparator setuprdquoBioresource Technology vol 101 no 10 pp 3333ndash3344 2010

[28] S D Crymble ldquoOptimization and Reaction Kinetics of the Pro-duction of Biodiesel from Castor Oil via Sodium Methoxide-Catalyzed Methanolysisrdquo Dave C Swalm School of ChemicalEngineering Mississippi State University Miss USA 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 International Journal of Chemical Engineering

0

05

1

15

2

25

3

0 01 02 03 04 05 06 07 08 09 1

PO-case 1 RO-case 1

WSO-case 1 WSO-case 2RO-case 2PO-case 2

Conversion of triglyceride XT

Sele

ctiv

ity o

f met

hyl e

sters

Figure 11 Selectivity plots of methyl ester from various feedstockfor Cases 1 and 2

As discussed before these free fatty acids will reactwith alkali catalysts to produce soaps that will inhibit thetransesterification reaction Soaps will allow emulsificationthat causes the phase separation of methyl ester and glycerolto be less sharp It produces water that can hydrolyze thetriglycerides and contribute to the formation of more soap[14] The effect of reversibility of transesterification can beseen significantly when analysing the selectivity of methylester derived from palm oil In Figure 11 methyl ester derivedfrom palm oil shows a higher selectivity plot for base caseThis finding suggests that forward reaction dominates thereaction and contributes to a better selectivity when lowFFAs feedstock is used in biodiesel production As there aremany low cost feedstocks available for biodiesel productiona pretreatment to these feedstocks can be carried out in orderto ensure the value of FFAs is within the allowable range

5 Conclusions

This paper has presented a comprehensive kinetic modelingof a transesterification reaction for biodiesel with homoge-neous alkaline catalyst The purpose of the study was todevelop the kinetic models of transesterification reactiondetermine the selectivity of methyl ester and glycerol andevaluate the significance of the reverse reactions in the trans-esterification reaction This study has shown that a processmodel solution was found for two types of common biodieselreactors The concentration of each species during transes-terification was found leading to a selectivity determinationduring the biodiesel production In addition the reversibleand irreversible effects of a transesterification reaction werediscovered The forward reaction is more dominant than thereverse reaction and the maximum selectivity can be foundif a base case of transesterification reaction is assumed tohave occurred in the biodiesel reactor system For the variousreaction characteristics under investigation the selectivities

are influenced by the temperature molar ratio of methanolto oil catalyst concentration and type of oil used as thefeedstock Furthermore an analysis of the selectivity plotsindicates an enhanced effect of the reaction characteristicson the selectivity This research has shown that the selectivityof methyl ester is maximized at 60∘C a 9 1 molar ratio ofmethanol to oil and a catalyst concentration of 15 Thisinvestigation into the effects of the molar ratio of methanolto oil and the catalyst concentration on the selectivity canbe made more interesting if several more curves are plottedat a molar ratio of methanol to oil between 3 1 to 9 1 anda catalyst concentration between 05 and 15 Howevera limitation of this research remains in the availability ofthe reaction rate constants under various reaction condi-tions In addition a comparison should be made throughmutual reaction conditionsThe findings from this study willenhance the concept of selectivity and its applications inthe evaluation of complex transesterification reactions whenthe goal is to attain the maximum production of methylesters and glycerol It is recommended that further researchis undertaken in exploring the selectivity data for specifyingthe reactor configurations and may be used in the synthesisof reactor network for biodiesel production

Nomenclature

119896+1 119896minus1 119896+2

119896minus2 119896+3 119896minus3

Reaction constant

119862T 119862D 119862M 119862G119862E1 119862E2 119862E3119862A 119862E

Molar concentration of triglyceridediglyceride monoglyceride glycerolester 1 ester 2 ester 3 methanol andmethyl ester

119883T Conversion of triglyceride119872119877 Molar ratio

119862T0 Initial molar concentration oftriglyceride

119878E 119878G Selectivity of methyl ester glycerol120572 Reaction rate constant factorwt Weight percentT TriglycerideD DiglycerideM MonoglycerideA MethanolG GlycerolE Methyl esterE1 Methyl ester 1E2 Methyl ester 2E3 Methyl ester 3PFR Plug flow reactorCSTR Continuous stirred tank reactor119873T0 Initial amount of triglyceride at 119905 = 0

119873T The amount of triglyceride present attime 119905

119881 VolumePO Palm oilRO Rapeseed oilWSO Waste sunflower oilNaOH Sodium hydroxide

International Journal of Chemical Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgment

Thework was carried out with the financial support from theMinistry of Education Malaysia

References

[1] A Demirbas ldquoBiodiesel from triglycerides via transesterifica-tionrdquo in Biodiesel pp 121ndash140 Springer London UK 2008

[2] D Darnoko and M Cheryan ldquoKinetics of palm oil transesteri-fication in a batch reactorrdquo JAOCS Journal of the American OilChemistsrsquo Society vol 77 no 12 pp 1263ndash1267 2000

[3] T Leevijit WWisutmethangoon G Prateepehaikul C Tongu-rai and M Allen ldquoA second order kinetics of palm oil transes-terification in a batch reactorrdquo in Proceedings of the Joint Inter-national Conference on Sustainable Energy and Environment pp277ndash281 2004

[4] S Jain andM P Sharma ldquoKinetics of acid base catalyzed trans-esterification of Jatropha curcas oilrdquo Bioresource Technology vol101 no 20 pp 7701ndash7706 2010

[5] H Noureddini and D Zhu ldquoKinetics of transesterification ofsoybean oilrdquo Journal of the American Oil Chemistsrsquo Society vol74 no 11 pp 1457ndash1463 1997

[6] D Kusdiana and S Saka ldquoKinetics of transesterification in rape-seed oil to biodiesel fuel as treated in supercritical methanolrdquoFuel vol 80 no 5 pp 693ndash698 2001

[7] M Diasakou A Louloudi and N Papayannakos ldquoKinetics ofthe non-catalytic transesterification of soybean oilrdquo Fuel vol 77no 12 pp 1297ndash1302 1998

[8] H Maeda S Hagiwara H Nabetani et al ldquoBiodiesel fuelsfrom palm oil via the non-catalytic transesterification in abubble column reactor at atmospheric pressure a kinetic studyrdquoRenewable Energy vol 33 no 7 pp 1629ndash1636 2008

[9] P C Narvaez S M Rincon and F J Sanchez ldquoKinetics of palmoil methanolysisrdquo Journal of the American Oil Chemistsrsquo Societyvol 84 pp 971ndash977 2007

[10] E Minami and S Saka ldquoKinetics of hydrolysis and methylesterification for biodiesel production in two-step supercriticalmethanol processrdquo Fuel vol 85 no 17-18 pp 2479ndash2483 2006

[11] B Freedman R O Butterfield and E H Pryde ldquoTransesteri-fication kinetics of soybean oil 1rdquo Journal of the American OilChemistsrsquo Society vol 63 no 10 pp 1375ndash1380 1986

[12] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

[13] J M Douglas Conceptual Design of Chemical ProcessesMcGraw Hill 1988

[14] J van Gerpen B Shanks R Pruszko D Clements and GKnothe Biodiesel Production Technology Subcontractor ReportNational Reanewable Energy Laboratory 2004

[15] H J Wright J B Segur H V Clark S K Coburn E ELangdon and R N DuPuis ldquoA report on ester interchangerdquoOilamp Soap vol 21 no 5 pp 145ndash148 1944

[16] H Fukuda A Kondo and H Noda ldquoBiodiesel fuel productionby transesterification of oilsrdquo Journal of Bioscience and Bioengi-neering vol 92 no 5 pp 405ndash416 2001

[17] L Friesenhagen and H Lepper ldquoProcess for the productionof fatty acid esters of short-chain aliphatic alcohols from fatsandor oils containing free fatty acidsrdquoUS Patent 4608202 1986

[18] P Felizardo J MacHado D Vergueiro M J N Correia J PGomes and J M Bordado ldquoStudy on the glycerolysis reactionof high free fatty acid oils for use as biodiesel feedstockrdquo FuelProcessing Technology vol 92 no 6 pp 1225ndash1229 2011

[19] A Tafesh and S Basheer ldquoPretreatment methods in biodieselproduction processesrdquo in Pretreatment Techniques for Biofuelsand Biorefineries Z Fang Ed Green Energy and Technologypp 417ndash434 Springer Berlin Germany 2013

[20] D Kusdiana and S Saka ldquoEffects of water on biodiesel fuelproduction by supercritical methanol treatmentrdquo BioresourceTechnology vol 91 no 3 pp 289ndash295 2004

[21] K Komers F Skopal R Stloukal and J Machek ldquoKinetics andmechanism of the KOHmdashcatalyzed methanolysis of rapeseedoil for biodiesel productionrdquo European Journal of Lipid Scienceand Technology vol 104 pp 728ndash737 2002

[22] A K CokerModeling of Chemical Kinetics and Reactor DesignGulf Publishing Houston Tex USA 2001

[23] C D Holland and R G Anthony Fundamentals of ChemicalReaction Engineering Prentice-Hall 1979

[24] J K Rodrıguez-Guerrero M F Rubens and P T V RosaldquoProduction of biodiesel from castor oil using sub and super-critical ethanol effect of sodium hydroxide on the ethyl esterproductionrdquoThe Journal of Supercritical Fluids vol 83 pp 124ndash132 2013

[25] G Vicente M Martınez and J Aracil ldquoOptimisation ofintegrated biodiesel production Part I A study of the biodieselpurity and yieldrdquoBioresource Technology vol 98 no 9 pp 1724ndash1733 2007

[26] A Srivastava and R Prasad ldquoTriglycerides-based diesel fuelsrdquoRenewable and Sustainable Energy Reviews vol 4 no 2 pp 111ndash133 2000

[27] B Klofutar J Golob B Likozar C Klofutar E Zagar andI Poljansek ldquoThe transesterification of rapeseed and wastesunflower oils mass-transfer and kinetics in a laboratory batchreactor and in an industrial-scale reactorseparator setuprdquoBioresource Technology vol 101 no 10 pp 3333ndash3344 2010

[28] S D Crymble ldquoOptimization and Reaction Kinetics of the Pro-duction of Biodiesel from Castor Oil via Sodium Methoxide-Catalyzed Methanolysisrdquo Dave C Swalm School of ChemicalEngineering Mississippi State University Miss USA 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Chemical Engineering 13

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgment

Thework was carried out with the financial support from theMinistry of Education Malaysia

References

[1] A Demirbas ldquoBiodiesel from triglycerides via transesterifica-tionrdquo in Biodiesel pp 121ndash140 Springer London UK 2008

[2] D Darnoko and M Cheryan ldquoKinetics of palm oil transesteri-fication in a batch reactorrdquo JAOCS Journal of the American OilChemistsrsquo Society vol 77 no 12 pp 1263ndash1267 2000

[3] T Leevijit WWisutmethangoon G Prateepehaikul C Tongu-rai and M Allen ldquoA second order kinetics of palm oil transes-terification in a batch reactorrdquo in Proceedings of the Joint Inter-national Conference on Sustainable Energy and Environment pp277ndash281 2004

[4] S Jain andM P Sharma ldquoKinetics of acid base catalyzed trans-esterification of Jatropha curcas oilrdquo Bioresource Technology vol101 no 20 pp 7701ndash7706 2010

[5] H Noureddini and D Zhu ldquoKinetics of transesterification ofsoybean oilrdquo Journal of the American Oil Chemistsrsquo Society vol74 no 11 pp 1457ndash1463 1997

[6] D Kusdiana and S Saka ldquoKinetics of transesterification in rape-seed oil to biodiesel fuel as treated in supercritical methanolrdquoFuel vol 80 no 5 pp 693ndash698 2001

[7] M Diasakou A Louloudi and N Papayannakos ldquoKinetics ofthe non-catalytic transesterification of soybean oilrdquo Fuel vol 77no 12 pp 1297ndash1302 1998

[8] H Maeda S Hagiwara H Nabetani et al ldquoBiodiesel fuelsfrom palm oil via the non-catalytic transesterification in abubble column reactor at atmospheric pressure a kinetic studyrdquoRenewable Energy vol 33 no 7 pp 1629ndash1636 2008

[9] P C Narvaez S M Rincon and F J Sanchez ldquoKinetics of palmoil methanolysisrdquo Journal of the American Oil Chemistsrsquo Societyvol 84 pp 971ndash977 2007

[10] E Minami and S Saka ldquoKinetics of hydrolysis and methylesterification for biodiesel production in two-step supercriticalmethanol processrdquo Fuel vol 85 no 17-18 pp 2479ndash2483 2006

[11] B Freedman R O Butterfield and E H Pryde ldquoTransesteri-fication kinetics of soybean oil 1rdquo Journal of the American OilChemistsrsquo Society vol 63 no 10 pp 1375ndash1380 1986

[12] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

[13] J M Douglas Conceptual Design of Chemical ProcessesMcGraw Hill 1988

[14] J van Gerpen B Shanks R Pruszko D Clements and GKnothe Biodiesel Production Technology Subcontractor ReportNational Reanewable Energy Laboratory 2004

[15] H J Wright J B Segur H V Clark S K Coburn E ELangdon and R N DuPuis ldquoA report on ester interchangerdquoOilamp Soap vol 21 no 5 pp 145ndash148 1944

[16] H Fukuda A Kondo and H Noda ldquoBiodiesel fuel productionby transesterification of oilsrdquo Journal of Bioscience and Bioengi-neering vol 92 no 5 pp 405ndash416 2001

[17] L Friesenhagen and H Lepper ldquoProcess for the productionof fatty acid esters of short-chain aliphatic alcohols from fatsandor oils containing free fatty acidsrdquoUS Patent 4608202 1986

[18] P Felizardo J MacHado D Vergueiro M J N Correia J PGomes and J M Bordado ldquoStudy on the glycerolysis reactionof high free fatty acid oils for use as biodiesel feedstockrdquo FuelProcessing Technology vol 92 no 6 pp 1225ndash1229 2011

[19] A Tafesh and S Basheer ldquoPretreatment methods in biodieselproduction processesrdquo in Pretreatment Techniques for Biofuelsand Biorefineries Z Fang Ed Green Energy and Technologypp 417ndash434 Springer Berlin Germany 2013

[20] D Kusdiana and S Saka ldquoEffects of water on biodiesel fuelproduction by supercritical methanol treatmentrdquo BioresourceTechnology vol 91 no 3 pp 289ndash295 2004

[21] K Komers F Skopal R Stloukal and J Machek ldquoKinetics andmechanism of the KOHmdashcatalyzed methanolysis of rapeseedoil for biodiesel productionrdquo European Journal of Lipid Scienceand Technology vol 104 pp 728ndash737 2002

[22] A K CokerModeling of Chemical Kinetics and Reactor DesignGulf Publishing Houston Tex USA 2001

[23] C D Holland and R G Anthony Fundamentals of ChemicalReaction Engineering Prentice-Hall 1979

[24] J K Rodrıguez-Guerrero M F Rubens and P T V RosaldquoProduction of biodiesel from castor oil using sub and super-critical ethanol effect of sodium hydroxide on the ethyl esterproductionrdquoThe Journal of Supercritical Fluids vol 83 pp 124ndash132 2013

[25] G Vicente M Martınez and J Aracil ldquoOptimisation ofintegrated biodiesel production Part I A study of the biodieselpurity and yieldrdquoBioresource Technology vol 98 no 9 pp 1724ndash1733 2007

[26] A Srivastava and R Prasad ldquoTriglycerides-based diesel fuelsrdquoRenewable and Sustainable Energy Reviews vol 4 no 2 pp 111ndash133 2000

[27] B Klofutar J Golob B Likozar C Klofutar E Zagar andI Poljansek ldquoThe transesterification of rapeseed and wastesunflower oils mass-transfer and kinetics in a laboratory batchreactor and in an industrial-scale reactorseparator setuprdquoBioresource Technology vol 101 no 10 pp 3333ndash3344 2010

[28] S D Crymble ldquoOptimization and Reaction Kinetics of the Pro-duction of Biodiesel from Castor Oil via Sodium Methoxide-Catalyzed Methanolysisrdquo Dave C Swalm School of ChemicalEngineering Mississippi State University Miss USA 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of