ORIGINAL PAPER

Kinetics of enzymatic trans-esterification of glyceridesfor biodiesel production

Vincenza Calabro • Emanuele Ricca •

Maria Gabriela De Paola • Stefano Curcio •

Gabriele Iorio

Received: 23 March 2009 / Accepted: 21 October 2009 / Published online: 10 November 2009

� Springer-Verlag 2009

Abstract In this paper, the reaction of enzymatic trans-

esterification of glycerides with ethanol in a reaction

medium containing hexane at a temperature of 37 �C has

been studied. The enzyme was Lipase from Mucor miehei,

immobilized on ionic exchange resin, aimed at achieving

high catalytic specific surface and recovering, regenerating

and reusing the biocatalyst. A kinetic analysis has been

carried out to identify the reaction path; the rate equation

and kinetic parameters have been also calculated. The

kinetic model has been validated by comparison between

predicted and experimental results. Mass transport resis-

tances estimation was undertaken in order to verify that the

kinetics found was intrinsic. Model potentialities in terms

of reactors design and optimization are also shown.

Keywords Biodiesel � Lipase � Kinetics �Oil trans-esterification � Enzyme

List of symbols

CSTBR Continuous stirred tank bio-reactor

D Diolein (in reaction mechanism)

dp Catalyst particle diameter

[e] Enzyme concentration (g/l)

E Enzyme (in reaction mechanism)

E0 Activate complex (in reaction mechanism)

E–Et Enzyme–ethanol complex (in reaction

mechanism)

E–D Enzyme–diolein complex (in reaction

mechanism)

E–M Enzyme–monolein complex (in reaction

mechanism)

E–P Enzyme–product complex (in reaction

mechanism)

E–T Enzyme–triolein complex (in reaction

mechanism)

EO Ethyloleate (in reaction mechanism)

[EO] Ethyloleate molar concentration (mol/l)

D[EO] Ethyloleate production (mol/l)

Et Ethanol (in reaction mechanism)

[Et] Ethanol molar concentration (mol/l)

G Glycerol (in reaction mechanism)

[G] Glycerol molar concentration (mol/l)

Ki Kinetic parameters (various dimension)

ks Mass transport coefficient (m/s)

M Monolein (in reaction mechanism)

me Mass of enzyme (g)

mso Mass of simulating oil (g)

MW Molecular weight [Da]

P Products in terms of total sum of glycerol,

monolein and diolein (M ? D ? G) (in reaction

mechanism)

[P] Concentration of products in terms of total sum

of glycerol, monolein and diolein (M ? D ? G)

(mol/l)

Sh Sherwood number

T Triolein (in reaction mechanism)

[t] Triolein mass concentration (g/l)

[T] Triolein molar concentration (mol/l)

t Time (h)

tD Diffusion time (h)

tv Reaction time (h)

U Units of enzyme (Unit)

[U] Concentration of enzyme in terms of Unit

(Unit/l)

V. Calabro � E. Ricca (&) � M. G. De Paola � S. Curcio �G. Iorio

Department of Engineering Modelling, University of Calabria,

via P. Bucci Cubo 45/A, Arcavacata di Rende (CS), Italy

e-mail: ericca@unical.it

123

Bioprocess Biosyst Eng (2010) 33:701–710

DOI 10.1007/s00449-009-0392-z

v Reaction rate (mol/l h)

VH Hexane volume (ml) or (l)

VSO Simulating oil volume (ml) or (l)

Subscript

0 Referring to initial conditions

Greek symbols

a, b Kinetic parameters

d, e Functions of Et0d0, d1, e0, e1, e2 Parameters

s CSTBR mean residence time (h)

Introduction

Vegetable oils and fats can be used not only for food

industry transformation, but also for applications in energy

field. Three techniques have been proposed to render

vegetable oils feasible for diesel engines: pyrolysis [1],

micro-emulsification [2], trans-esterification [3]: the latter

is the best technique able to give a product very similar to

‘‘petro-diesel’’ [4, 5].

Biodiesel is a mixture of alkyl esters of fatty acids from

biological source. It can be obtained by means of inorganic

or enzymatic catalytic trans-esterification of glycerides of

fatty acids of vegetal oils with short chain alcohols.

Trans-esterification can reduce viscosity, because linear

esters without glycerol are less viscous then ramified chain

of tri-glycerides [6].

To increase the reaction rate a catalyst is normally used.

Trans-esterification can advance with a mechanism of acid,

basic or enzymatic catalysis with the use of lipase. The

latter mechanism has been only recently taken into

account, to overcome the inconveniences of acid catalysis

[4, 7, 8] (the kinetics is too slow) and basic catalysis (faster

but displaying some drawbacks: substrate loss due to the

conversion in soap products, high viscosity, gel formation

and difficulty to separate the glycerol that can be entrapped

in the soap products, [3, 9–12]).

Enzymatic trans-esterification is the most expensive but

it offers some advantages, as:

– the presence of free fatty acids in the reaction mixture

does not give the production of saponification products;

– a higher yield and a better glycerol recovery can be

obtained.

Studies carried out recently have demonstrated that

ethanol, less than methanol used at present, favors high

conversion for all the used solvents: it has been also

demonstrated that the lipase is better performing with

longer chain alcohols [13–16].

Some studies [17–21] carried out with methanol showed

the possibility of introducing alcohol step by step, to avoid

alcohol inhibition: this method requires preliminary kinetic

and dynamic studies for a systematic application.

In the open Literature different kinetic studies have been

reported for lipase-catalyzed reaction in different condi-

tions: lipase from Rhizomucor miehei and Thermomyces

lanuginose on sunflower oil [22, 23], lipase from Mucor

miehei on palm oil [24] and lipase from Pseudomonas

cepacia on simulating waste cooking oil [25].

In this work Lipozyme� MM IM, a commercial lipase

from Mucor Miehei immobilised on a macroporous ion

exchange resin, has been then used for the experiments

finalised to the definition of the reaction mechanism during

trans-esterification of triolein with ethanol. Hexane was

used as solvent; other solvents are suitable (such as tert-

butanol, for example [26]), but hexane was preferred for its

very low boiling point (68.7 �C), implying an extreme ease

of separation from products.

A detailed kinetic study has been carried out taking into

account the inhibitory effect of ethanol. Mass transport

resistances estimation was undertaken in order to verify

that the kinetics found was intrinsic. Prior to the kinetic

study, recovery and reuse tests were run in order to pre-

liminarily evaluate the biocatalyst operational stability in

some of the reaction conditions chosen for kinetic tests.

Materials and methods

Reactants

Simulating oil with 60% of pure triolein has been used for

the kinetic analysis. The absence of free fatty acids is

certified by the supplier (Sigma-Aldrich, code nr. 92862

and lot nr. 423741/1). Moreover, in order to identify

components that could influence the reaction, in this work

the simulating oil used as substrate was tested according to

the analytical procedure shown hereafter, and di- and

mono-glycerides were not present in 60% pure triolein. For

this reason it is assumed that the remaining 40% of the

mixture does not influence the reaction.

Ethanol ([99.8%) from Fluka has been used as the

secondary substrate and hexane ([95%) from Fluka as

solvent, as suggested in the Literature [16]. HPLC grade

acetone and acetonitrile were supplied from Fluka too.

Biocatalyst

The catalyst was Lipozyme� MM IM (Novozymes,

Denmark), a lipase from Mucor miehei immobilised on a

macroporous particulate ion exchange resin. The diameter

of supporting particles ranged between 0.3 and 1.0 mm and

the wet bulk density is 0.42 g/ml. The enzyme is highly 1.3

specific, with a MW of 32 KDa and activity of 37 U/g.

702 Bioprocess Biosyst Eng (2010) 33:701–710

123

Experimental methodology

All the experimental reactions have been carried out at

37 �C and neutral pH.

Experiments have been carried out using a well mixed

batch reactor of 125 ml. The reaction mixture was prepared

in order to guarantee good mixing conditions in the fol-

lowing way: mixing simulating oil and Lipozyme, then

adding hexane, heating and stirring for 30 min; when the

temperature had reached 37 �C ethanol was added to start

the reaction. The reason for adding hexane to the reacting

mixture is to reduce the duration of the transient of mixing

by ethanol which, according to the present loading proce-

dure, has been added as the last substrate in order to avoid

enzyme deactivation.

Reaction samples of 200 ll were collected, more fre-

quently during first phase, less in the end taking care to not

have any catalyst in the sample. They were centrifuged to

separate possible small residuals or fragments of catalyst for

5 min at 5,400 rpm and then the supernatant was collected in

vials for analysis. The total amount of samples collected was

in any case lower than 5% of the total volume.

The feed mass ratios enzyme/triolein [e0/T0] adopted

were 1:8, 1:20, 1:30 and the reactants molar ratios ethanol/

triolein [Et0/T0] were 2:1, 2.5:1, 3:1.

Enzyme recovery and reuse

In order to verify the possibility of recovering and reusing

the enzyme after the reaction, it has been recovered by

filtration, washed three times with acetone, then dried at

room temperature and reused for the new reaction, as

suggested in the literature [27]. More cycles of reaction

have been carried out with high yields.

Residual activities were estimated as the ratio of initial

reaction rate at any cycle (initial slope of the trends) to the

initial reaction rate of the first use (time zero).

Analytical methods

Concentrations of reactants glycerides and product ethyl-

oleate have been measured with a quantitative analysis

carried out by means of a high pressure liquid chroma-

tography, HPLC (JASCO) under the following conditions:

RI detector, eluent phase acetone/acetonitrile 70/30 v/v,

flow rate 1 ml/min, internal normalization as integration

method. Prior to analysis the catalyst has been removed by

centrifugation and hexane by evaporation. Ethanol con-

centrations were not measured, but obtained by means of

the stoichiometric ratio 1:1 with ethyl-oleate.

The column was Alltech Adsorbosphere HS (C18)

5 lm, length of 250 mm and inlet diameter 4.6 mm, inte-

grated with a pre-column Alltech of 7.5 9 4.6 mm.

Experimental results

Analysis of the effect of [e0]/[T0] ratio

Experiments have been carried out at fixed ethanol/triolein

feed molar ratio [Et0]/[T0] = 2:1 (less than the stoichi-

ometric one), with a simulating oil/hexane volumetric ratio

VSO0=VH0

¼ 1:1.

Ethanol has been charged as limiting reactant, to avoid

any possible effect of enzyme inhibition.

The enzyme loading in the feed was equal to 34.4, 13.3,

7.52 g/l, corresponding to enzyme/triolein fed mass ratio

[e0]/[T0] of 1:8, 1:20, 1:30.

Results reported in Fig. 1a as concentration of product

(ethyloleate) and substrate (triolein) permit to calculate the

reaction yield in terms of moles of ethyloleate produced per

moles of fed ethanol (D[EO]/[Et0]) and in terms of moles

of ethyloleate produced per unit of active enzyme

(D[EO]/U0).

In Table 1 the results are reported and it is shown that an

intermediate amount of enzyme seems more effective, with

a low reduction of D[EO]/[Et0].

0

0,1

0,2

0,3

0,4

0,5

0,6

0 6 12 18 24 30time, (h)

Co

nce

ntr

atio

n, (

mo

les/

l)

[eo]/[to] = 1:8 [eo]/[to] = 1:20 [eo]/[to] = 1:30Ethyl Oleate Ethyl Oleate Ethyl OleateTriolein Triolein Triolein

0

0.1

0.2

0.3

50 10 15 20 25 30time, (h)

Co

nce

ntr

atio

n, (

mo

les/

l)

[eo]/[to] = 1:8 [eo]/[to] = 1:20 [eo]/[to] = 1:30Ethyl Oleate Ethyl Oleate Ethyl OleateTriolein Triolein Triolein

(a)

(b)

Fig. 1 a Time course of ethyloleate and triolein concentration as

function of enzyme initial amount. [Et0]/[T0] = 2:1, VSO0=VH0

¼ 1 :1: b Zoom of initial points

Bioprocess Biosyst Eng (2010) 33:701–710 703

123

The reaction yield evaluated as the moles of ethyloleate

produced per mole of ethanol (limiting reactant) is related to

enzyme loading in a fashion which is slower than linear, with

ethyloleate production at [e0]/[T0] = 1:30 being much

lower than for [e0]/[T0] = 1:20 and 1:8 (Table 1). A similar

trend can be observed in Fig. 1b where initial velocity data

can be derived from initial slopes of concentration against

time. At high enzyme loading (1:8 and 1:20) the reaction rate

is proportional to enzyme loading, but this is not true for low

loadings. The explanation to this observation is that when

small quantities of enzyme are loaded the effects of alcohol

inhibition (further discussed throughout the text) are more

relevant and they reveal themselves by inactivating the small

amount of enzyme present within the reacting mixture.

When higher loadings are adopted the amount of inhibition

remains the same, since other conditions such as substrates

concentration are unchanged, but the amount of enzyme

supposed to support this effect is higher and the observable

effect of inhibition is consequently lower.

Kinetics seems faster with a higher [e0]/[T0] feed mass

ratio: a ratio of 1:8 permits to achieve in 3 h the maximum

amount of ethyloleate, 0.6 mol/l, whereas after 6 h with a

ratio of 1:20 only 0.45 mol/l of ethyloleate have been

produced; however, the performance per unit of catalyst is

maximal when [e0]/[T0] = 1:20 is adopted.

Analysis of the effect of [Et0]/[T0]

The experiments have been carried out at fixed amount of

enzyme and triolein equivalent to [e0]/[T0] = 1:20 and

with a simulated oil/hexane ratio VSO0=VH0

¼ 1:1.

In Fig. 2a the results in terms of ethyloleate concentra-

tions are reported for different ethanol concentrations.

If the tendencies are considered at the end of the reaction,

at a first sight, it seems that the reaction runs better when a

higher amount of ethanol is used. This is in agreement with

the fact that ethanol is a substrate whose concentration could

positively influence the reaction progress, but it is known

from the literature that substrate inhibition can occur at

certain alcohol concentrations [20]. The indication about the

presence of inhibition cannot be derived from data at high

conversion, because in that situation ethanol (the limiting

substrate) has been consumed and of course the conversion

of the experiment at high ethanol loading can rise over the

others at low ethanol concentrations. The inhibition effect

must be searched for at the initial stages of the reaction when

the observed effect does not depend on the substrate avail-

ability. A look at the initial points in Fig. 2a shows that there

are not significant differences among the three tendencies

and indeed, if the points are zoomed (Fig. 2b), it becomes

clear that the reaction rate at high ethanol concentration is

the lowest among the three sets of data. This is a proof of

ethanol inhibition.

In Table 2 reaction yield in these conditions are

summarized.

Enzyme recovery and reuse

In Fig. 3 the time course of the triolein and ethyloleate

concentration are reported for the experiments carried out

Table 1 Yield of ethyloleate at different enzyme amount

[e0]/[T0] (-) D[EO]/[Et0] (%) D[EO]/U0 (mmoles/l U)

1:8 91 5

1:20 78 11

1:30 16 4

0

0.05

0.1

0.40.20time, (h)C

on

cen

trat

ion

of

Eth

yl O

leat

e, [E

O],

(mo

les/

l)

[Eto]/[To] = 2

[Eto]/[To] = 2,6

[Eto]/[To] = 3,1

(a)

(b)

Fig. 2 a Time course of ethyloleate and triolein concentration as

function of ethanol/triolein feed molar ratio, [Et0]/[T0]. [e0]/

[T0] = 1:20 and VSO0=VH0

¼ 1 : 1: b Zoom of initial points

Table 2 Yield of ethyloleate at different ethanol/triolein molar feed

ratio

[Et0]/[T0] (-) D[EO]/[Et0] (%) D[EO]/[T0] (%)

2.0 78 1.5

2.6 71 1.7

3.1 83 2.6

704 Bioprocess Biosyst Eng (2010) 33:701–710

123

under the following operating conditions: [Et0]/[T0] = 2:1,

VSO0=VH0

¼ 1 : 1, [e0] = 34.4 g/l and me0/mso0 = 0.08.

They were chosen in order to have a relatively fast reac-

tion, but appreciable differences in the results of reuse

tests.

Enzyme decay is more significant after the first recov-

ery. In particular, the residual activity, in terms of value of

the initial reaction rate at any cycle (initial slope of the

trends), was always higher than 75%. Differences can also

be observed on the final conversion values; in this respect

one can deduct that reuses damage the enzyme even from

the point of view of completing the reaction progress, i.e.

not only kinetics are slower in the first stages, but the final

ethyl-oleate concentration obtainable after every reuse is

lower and lower.

Kinetic analysis and discussion

Experimental data have been elaborated to evaluate the

kinetic rate as a function of triolein concentration.

The reaction pattern can be predicted as a sequence of

three reactions in series, with the production of one mole of

ester by each step and the production of glycerol only at the

third step, when monoglycerides are converted (Fig. 4).

But the lipase that has been used shows a 1–3 regio-

specificity, consequently glycerol production is strongly

limited.

The King-Altman kinetics method has been followed:

the method is based on singling out geometrical rules that

permit to evaluate the concentrations of enzyme in all its

complexes (E, ES, EP, etc.).

When the related expressions are introduced in the

elementary kinetic equation that represents the reaction

path, it is possible to obtain the kinetic model.

A Ping-Pong mechanism ethanol inhibition has been

hypothesized to describe the kinetics of the reaction, as

schematised in Fig. 5.

Lipase attacks triolein giving the activated complex E–T

that transforms into the enzyme-substrate complex E0,consisting of the enzyme connected to the oleic chain with

the release of diolein, D.

Diolein will form the activated complex E–D that

releases monolein, M, and again the complex E0.Monolein and enzyme give the complex E–M, releasing

E0 and glycerol G. The complex E0 during these phases

reacts with ethanol, referred to as Et, giving the complex

E0–Et that releases the product ethyloleate, referred to as

EO, and enzyme E again.

The proposed mechanism has been revised and simpli-

fied, considering triolein and ethanol as reactants, and

ethyloleate, glycerol and the other glycerides (monolein

and diolein) as products. These glycerides are found, in

fact, in the reactant mixture at the end of the reaction.

The mechanism might be described as Ping-Pong Bi–Bi.

Assuming that triolein conversion will be the dominant

step, as a consequence of the higher triolein concentration

in the reacting mixture, the scheme of reaction patterns

becomes the one showed in Fig. 6, where glycerides and

glycerol are reported as product P.

The method of King-Altman has been then introduced:

following the scheme reported in Fig. 7, where all the

enzyme complexes are reported and the elementary reac-

tions are expressed with their kinetic constant. In the scheme

the inhibition is reported as a reversible step, giving a dif-

ferent pattern from the one assumed by Ping-Pong-bi_bi

mechanism. Pseudo-steady state is also assumed.

By considering all the kinetic rates for the elementary

reaction reported in Fig. 7, it is possible to formulate the

kinetic rate equation, as disappearance of triolein T, as

follows:

Fig. 3 Time course of triolein and ethyloleate during the n-cycle of

recovery and reuse of lipase. [Et0]/[T0] = 2:1, VSO0=VH0

¼ 1 : 1;me0/mso0 = 0.08

vT ¼ �d½T�dt

� d½T�dt¼ K1½T�½Et� � K2½P�½EO�

K3½T]þ K4½Et]þ K5½T][Et]þ K6½P]þ K7½EO]þ K8½P][EO]þ K9½T][P]þ K10½Et][EO]þ K11½Et�2 þ K12½Et�½P�� e0½ �

ð1Þ

Bioprocess Biosyst Eng (2010) 33:701–710 705

123

where [T], triolein concentration [mol/l]; [Et], ethanol

concentration [mol/l]; [P], glycerol, monolein and diolein

products concentration [mol/l]; [EO], ethyloleate product

concentration [mol/l]; [e0], enzyme concentration [g/l]; Ki,

constant to be calculated.

The analysis of experimental data permits to approxi-

mate the concentration of products and ethanol as function

of triolein actual concentration [T] and substrates initial

concentrations [T0] and [Et0]:

½Et� ¼ 2:25 � ½T� � T0½ �ð Þ þ Et0½ � ð2Þ½EO� ¼ �2:25 � ½T� � T0½ �ð Þ ð3Þ½P� ¼ T0½ � � ½T� ð4Þ

based on stoichiometry and semi-empirical correlations.

In particular, it must be noted that a highly 1, 3 specific

lipase as the one here adopted would lead to an ethyloleate/

reacted triolein ratio of 2 in Eq. 3. However, some authors

report an acylic migration which is responsible for the

mutation of 1–2 diglyceride into 1–3 diglyceride; the latter

can react until glycerol formation [28]. This could be the

reason for a coefficient not equal to 2, but a value ranging

between 2 and 3 depending on the extent of the acyl

migration. In order to understand what value should be

adopted, all the experimental data of ethyl-oleate vs. trio-

lein were graphed (Fig. 8) and a good agreement was found

with a coefficient of 2.25, which is the one in Eqs. 2 and 3,

based on semi-empirical correlation. What can be assumed

at this stage is that the acrylic migration is responsible for

the added value of 0.25.

With this assumption the kinetic rate vT might be sim-

plified as:

vT ¼ �d½T�dt¼ a � T½ � � Et½ � � b � P½ � � EO½ �

T½ �2þd � T½ � þ e� e0½ � ð5Þ

where

a and b are kinetic constant that have to be estimated;

d and e are functions of initial ethanol concentration

[Et0]:

Fig. 4 Scheme of the trans-

esterification of glycerides

D

ME-D

E-M

E-T

G

E’ E’-EtEE

EO

T

Et

Fig. 5 Scheme of reaction with the Ping-Pong mechanism hypothesis

E-T

P(M + D + G)

E’ E’-Et E E

EO

T Et

Fig. 6 Scheme of reaction when triolein reaction is the limiting step

E

E’-Et

E’

E-Et

k-1

k4

E-T

k2

k-2 [P]k-3

k-4 [EO]

k1 [T]

k3 [Et]

k5 [Et]k-5

Fig. 7 Mechanism of reaction, King-Altman model

Fig. 8 Empirical correlation for the determination of the stoichiom-

etric coefficient between ethyloleate production and triolein

consumption

706 Bioprocess Biosyst Eng (2010) 33:701–710

123

d ¼ d1 � Et0½ � þ d0 � e ¼ e 22 � Et0½ � 2þe1 � Et0½ � þ e0 ð6Þ

The values ofd½T�dt

were found according to the procedure

suggested by Levenspiel [29].

Fitting of experimental data

Non linear fitting Pearson VII strong method coupled to the

Table—Curve� software has been used to estimate the

kinetic parameters.

The values of di and ei are resumed in Table 3, whereas

kinetic constants a and b are reported in Table 4.

Model validation

Model validation has been obtained by comparison with

experimental data used for the fitting and data not used for

the fitting.

In Figs. 9, 10, 11 and 12 the validation is presented, for

different operating conditions in terms of feed mass ratio

enzyme/triolein or feed molar ratio ethanol/triolein. It can

be observed that the difference between model results and

experimental trends of triolein concentration is always

nearly undetectable, while some differences between pre-

dicted and experimental data can be seen with respect to

ethyl-oleate and ethanol concentrations; they will be dis-

cussed as they occur in any of the following figures. It is

necessary to remind here that ethanol concentrations are

obtained from a mass balance starting from measured

values of ethyl-oleate concentrations and that the model

was implemented on triolein data only; the theoretical

curves relative to ethyl-oleate are predictions and for this

reason the validity of the model will be assessed on the

basis of their capability to predict the experimental values.

It is evident from Fig. 9 that the model is able to predict

reaction performance with a good agreement with experi-

mental points. The agreement is particularly good in the

first stages of the reaction until a reaction time of 8 h. As

far as the final concentrations values are concerned, the

model slightly overestimates ethyl-oleate production.

Figure 10 shows results in operating conditions identical

to those reported in Fig. 9 except for the enzyme loading

(1:8 vs. 1:20). In this regard it is worth to notice that again

the model can correctly predict initial tendencies (until a

conversion of around 50%), but underestimates the final

values of ethyl-oleate concentrations.

When comparing Fig. 11 with Fig. 9 (obtained in the

same conditions except for ethanol concentration), it is

really interesting to notice that the agreement between

predicted and experimental data is better at higher ethanol

concentrations, proving the importance of having a qua-

dratic dependence on ethanol concentration in the kineitc

model (see Eq. 6) and the importance of considering

Table 3 Values of kinetic parameters di and ei for the Eq. 6

d1 -1.85

d0 0.618

e2 2.84

e1 -3.34

e0 1.11

Table 4 Values of kinetic parameters and constant for the Eq. 6

Value Standard deviation

a 0.00387 0.000147

b 0.000162 0.0001

R2 0.984

Kinetic Model Validation

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0 6 12 18 24

time, (h)

Co

nce

ntr

atio

n, (

mo

les/

l)

Triolein Ethanol Ethyl Oleate Mono- + Di-Glycerides + Glycerol

[e0] = 13.3 g/l [e0]/[t0] = 1:20 [Et0]/[T0] = 2:1 VSOo/VHo = 1:1

Fig. 9 Comparison between experimental data and kinetic model

predictions. Initial feed reactants: Triolein [T0] = 0.30 mol/l, Ethanol

[Et0] = 0.60 mol/l. Dots: experimental values. Continuous line:

kinetic model predictions

Kinetic Model Validation

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0 6 12 18 24time, (h)

Co

nce

ntr

atio

n, (

mo

les/

l)

Triolein Ethanol Ethyl Oleate Mono- + Di-Glycerides + Glycerol

[e0] = 34.4 g/l [e0]/[t0] = 1:8 [Et0]/[T0] = 2:1 VSOo/VHo = 1:1

Fig. 10 Comparison between experimental data and kinetic model

predictions. Initial feed reactants: Triolein [T0] = 0.30 mol/l, Ethanol

[Et0] = 0.60 mol/l. Dots: experimental values. Continuous line:

kinetic model predictions

Bioprocess Biosyst Eng (2010) 33:701–710 707

123

inhibition effects at [Et0/T0] lower than the stoichiometric

one, as it was also pointed out by Cheirsilp et al. [30].

The comments reported for Fig. 11 are still valid for

Fig. 12 with an even better agreement between theoretical

and experimental data.

As a conclusion, a good agreement between the exper-

imental data and the model prediction is observed for the

products as well as for the substrate, at the beginning and at

the end of the reaction. As a consequence the proposed

model might be assumed valid for the prediction of reac-

tion performances.

The good prediction capability of the model can be

attributed to the presence of terms related to reaction

reversibility within the kinetic equation (Eqs. 1 and 5).

This term is not explicitly reported in other kinetic equa-

tions in the literature [23, 24] and, unfortunately, this did

not allow for a quantitative comparison of the values of the

kinetic parameters.

Due to superficial immobilization of the enzyme, mass

transport resistances are present during the reaction and the

kinetics found could be apparent. To prove that, instead,

the kinetics is intrinsic, mass transfer resistances have been

calculated on the basis of the operating conditions and the

properties of immobilised enzyme. A reaction time tv and a

diffusion time tD have been estimated and compared.

Mass transfer resistance and process rate

To estimate mass transfer resistances it must be taken into

account that lipase was immobilised on a support surface,

thus no internal immobilization or transport is expected.

As a consequence, mass transfer resistance are located

externally to the support.

The mass transport coefficient ks was estimated by

assuming the lowest value for Sherwood number (Sh), that

correspond to no motion of a single particle: Sh = 2 [31].

By that value, the mass transfer coefficients ks has been

calculated as equal to 3.3 9 10-6 m/s which corresponds a

characteristic diffusive time tD equal to:

tD ¼dp

ks

¼ 180 s ¼ 0:05 h ð7Þ

where the mean particle diameter is 600 lm [32].

The characteristic time of the reaction has been calcu-

lated assuming the fastest conditions in terms of kinetic.

That happens when Lipozyme concentration, [e0], is equal

to 34 g/l, which corresponds a specific initial kinetic rate,

jvT0j

of 0.338 mol/l h (equivalent to 9.4 9 10-5 mol/l s) and at

initial triolein concentration [T0] of 0.3 mol/l.

The kinetic time has been calculated as

tv ¼T0

vT0

¼ 0:9 h ¼ 3200 s ð8Þ

By comparison between tD and tv, reaction results much

slower than transport (tv/tD = 20) even though the most

conservative conditions were assumed for calculations. As a

consequence, the reaction can be considered the limiting

step over the entire process and the kinetic model found is

intrinsic. This is a relevant result because it allows designers

to use the model in the calculations of any kind of reactor,

with kinetics separated from mass transport effects.

Bioreactors optimization

A macroscopic mathematical model has been formulated in

order to evaluate the operating conditions in a continuous

stirred tank bioreactor (CSTBR).

Fig. 11 Comparison between experimental data and kinetic model

predictions. Initial feed reactants: Triolein [T0] = 0.30 mol/l, Ethanol

[Et0] = 0.77 mol/l. Dots: experimental values. Continuous line:

kinetic model predictions

Kinetic Model Validation

0

0,2

0,4

0,6

0,8

1

0 12 24 36 48 60 72

time, (h)

Co

nce

ntr

atio

n, (

mo

les/

l)

Triolein Ethanol Ethyl Oleate Mono- + Di-glycerides + Glycerol

[e0] = 13.8 g/l [e0]/[t0] = 1:20 [Et0]/[T0] = 3:1 VSOo/VHo = 1:1

Fig. 12 Comparison between experimental data and kinetic model

predictions. Initial feed reactants: Triolein [T0] = 0.30 mol/l, Ethanol

[Et0] = 0.93 mol/l. Dots: experimental values. Continuous line:

kinetic model predictions

708 Bioprocess Biosyst Eng (2010) 33:701–710

123

From the mass balance on the substrate triolein it is

possible to evaluate the characteristic mean residence

time s:

s ¼ V

F¼ T½ � � T0½ �

vT

ð9Þ

The kinetic rate vT has been obtained from Eq. 5 and a

value of [T0] = 0.3 mol/l has been used.

CSTBR performances are reported in Fig. 13 in terms of

triolein concentration versus ethanol initial concentration at

different s values.

All curves display an optimum when [Et0] ranges

between 0.7 and 0.8 mol/l at any s; this corresponds to

ethanol/triolein feed molar ratios of 2.3–2.7. This is a result

of ethanol role in the reaction mechanism: ethanol is a

reactant and, as such, augmenting its concentration

enhances the reaction rate, but it is an inhibitor too and,

when certain values of ethanol concentration within the

feed are reached, its inhibitory effect overcomes the ben-

efits of a high concentration.

Conclusions

The trans-esterification carried out with triolein at 60% has

been studied.

The immobilized enzyme can be used for the trans-

esterification in a certain number of reuse tests, partially

maintaining the initial stability. This must be considered an

important point because it is no use to know the reaction

kinetics relative to one use of the enzyme without having

an estimation of the operational stability, i.e. the capability

of retaining the that activity.

Kinetic mechanism and model have been proposed and

validated. They provide designers with a reliable tool for

reactor sizing and optimization. In particular the kinetic

equation found has been proven to be intrinsic, and this is

crucial in reactors performance modeling where kinetics

and mass transport term within the mass balance can be

taken into account separately, with a great enhancement in

terms of flexibility and predictive capability of models.

Another aspect of process design strongly empowered

by the results presented in this work is optimization of

operating conditions. An example on the optimization of a

continuous stirred bioreactor has been presented and it is

clear how the model can be a tool for decision making in an

optimization context.

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