Bioprocess Biosyst Eng (2010) 33:701–710 DOI 10.1007/s00449-009-0392-z
ORIGINAL PAPER
Kinetics of enzymatic trans-esterification of glycerides for 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 Ó Springer-Verlag 2009
Abstract In this paper, the reaction of enzymatic transesterification 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 resistances 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)
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:
[email protected]
E–M E–P E–T EO [EO] D[EO] Et [Et] G [G] Ki ks M me mso MW P
[P]
Sh T [t] [T] t tD tv U [U]
Enzyme–monolein complex (in reaction mechanism) Enzyme–product complex (in reaction mechanism) Enzyme–triolein complex (in reaction mechanism) Ethyloleate (in reaction mechanism) Ethyloleate molar concentration (mol/l) Ethyloleate production (mol/l) Ethanol (in reaction mechanism) Ethanol molar concentration (mol/l) Glycerol (in reaction mechanism) Glycerol molar concentration (mol/l) Kinetic parameters (various dimension) Mass transport coefficient (m/s) Monolein (in reaction mechanism) Mass of enzyme (g) Mass of simulating oil (g) Molecular weight [Da] Products in terms of total sum of glycerol, monolein and diolein (M ? D ? G) (in reaction mechanism) Concentration of products in terms of total sum of glycerol, monolein and diolein (M ? D ? G) (mol/l) Sherwood number Triolein (in reaction mechanism) Triolein mass concentration (g/l) Triolein molar concentration (mol/l) Time (h) Diffusion time (h) Reaction time (h) Units of enzyme (Unit) Concentration of enzyme in terms of Unit (Unit/l)
123
702
Bioprocess Biosyst Eng (2010) 33:701–710
v VH VSO
Reaction rate (mol/l h) Hexane volume (ml) or (l) Simulating oil volume (ml) or (l)
Subscript 0 Referring to initial conditions Greek symbols a, b d, e d0, d1, e0, e1, e2 s
Kinetic parameters Functions of Et0 Parameters 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
123
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 conditions: 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 LipozymeÒ 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 tertbutanol, 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 preliminarily 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 LipozymeÒ 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.
Bioprocess Biosyst Eng (2010) 33:701–710
703
Experimental methodology
Experimental results
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 following 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 procedure, has been added as the last substrate in order to avoid enzyme deactivation. Reaction samples of 200 ll were collected, more frequently 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.
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 stoichiometric 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].
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 ethyloleate have been measured with a quantitative analysis carried out by means of a high pressure liquid chromatography, 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 concentrations 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, integrated with a pre-column Alltech of 7.5 9 4.6 mm.
(a)
0,5 0,4 0,3 0,2 0,1 0 0
6
12
18
24
30
time, (h) [eo]/[to] = 1:8 Ethyl Oleate Triolein
[eo]/[to] = 1:20 Ethyl Oleate Triolein
[eo]/[to] = 1:30 Ethyl Oleate Triolein
0.3
Concentration, (moles/l)
Enzyme recovery and reuse
Concentration, (moles/l)
0,6
(b) 0.2
0.1
0 0
5
10
15
20
25
30
time, (h) [eo]/[to] = 1:8 Ethyl Oleate Triolein
[eo]/[to] = 1:20 Ethyl Oleate Triolein
[eo]/[to] = 1:30 Ethyl Oleate Triolein
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
123
704
Bioprocess Biosyst Eng (2010) 33:701–710
(a)
Table 1 Yield of ethyloleate at different enzyme amount D[EO]/[Et0] (%)
D[EO]/U0 (mmoles/l U)
1:8
91
5
1:20
78
11
1:30
16
4
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 concentrations 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
123
Concentration of Ethyl Oleate, [EO], (moles/l)
[e0]/[T0] (-)
0.1
(b)
0.05
[Eto]/[To] = 2 [Eto]/[To] = 2,6 [Eto]/[To] = 3,1
0 0.2 time, (h)
0
0.4
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
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 availability. 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 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
Bioprocess Biosyst Eng (2010) 33:701–710
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
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 reaction, but appreciable differences in the results of reuse tests. Enzyme decay is more significant after the first recovery. 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 regiospecificity, consequently glycerol production is strongly limited.
705
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 simplified, 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 reactions are expressed with their kinetic constant. In the scheme the inhibition is reported as a reversible step, giving a different 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:
d½T dt d½T K1 ½T½Et K2 ½P½EO ¼ ½e0 dt K3 ½T] þ K4 ½Et] þ K5 ½T][Et] þ K6 ½P] þ K7 ½EO] þ K8 ½P][EO] þ K9 ½T][P] þ K10 ½Et][EO] þ K11 ½Et2 þ K12 ½Et½P
vT ¼
ð1Þ
123
706
Bioprocess Biosyst Eng (2010) 33:701–710
Fig. 4 Scheme of the transesterification of glycerides
T E-T
Et
D E
E-D
E’
E’-Et EO
E-M
G
Fig. 5 Scheme of reaction with the Ping-Pong mechanism hypothesis
E
Et E-T
E’
E
E’-Et
P (M + D + G)
EO
Fig. 6 Scheme of reaction when triolein reaction is the limiting step E-Et
k5 [Et] k-5 E k4
k-1
E’-Et
E-T
k-2 [P]
k-3
½EO ¼ 2:25 ð½T ½T0 Þ
ð3Þ
½P ¼ ½T0 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. triolein 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 simplified as: d½T a ½T ½Et b ½P ½EO ¼ vT ¼ ½e0 dt ½T2 þd ½T þ e
k1 [T] k-4 [EO]
ð2Þ
E
M
T
½Et ¼ 2:25 ð½T ½T0 Þ þ ½Et0
ð5Þ
where a and b are kinetic constant that have to be estimated; d and e are functions of initial ethanol concentration [Et0]:
k2
k3 [Et] E’
Fig. 7 Mechanism of reaction, King-Altman model
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 approximate the concentration of products and ethanol as function of triolein actual concentration [T] and substrates initial concentrations [T0] and [Et0]:
123
Fig. 8 Empirical correlation for the determination of the stoichiometric coefficient between ethyloleate production and triolein consumption
Bioprocess Biosyst Eng (2010) 33:701–710
707
ð6Þ
Kinetic Model Validation
0,7
[e0] = 13.3 g/l
The values of d½T 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—CurveÒ 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.
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
VSOo/VHo = 1:1
0,4 0,3 0,2 0,1 0 0
6
12
18
24
time, (h) Ethanol
Ethyl Oleate
Mono- + Di-Glycerides + Glycerol
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 0,7
Concentration, (moles/l)
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 predicted and experimental data can be seen with respect to ethyl-oleate and ethanol concentrations; they will be discussed 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 experimental points. The agreement is particularly good in the
[Et0]/[T0] = 2:1
0,5
Triolein
Model validation
[e0]/[t0] = 1:20
0,6 Concentration, (moles/l)
d ¼ d1 ½Et0 þ d0 e ¼ e22 ½Et0 2 þe1 ½Et0 þ e0
0,6 0,5 [e0] = 34.4 g/l
0,4
[e0]/[t0] = 1:8
[Et0]/[T0] = 2:1
VSOo/VHo = 1:1
0,3 0,2 0,1 0 0
6
12
18
24
time, (h) Triolein
Ethanol
Ethyl Oleate
Mono- + Di-Glycerides + Glycerol
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
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 quadratic dependence on ethanol concentration in the kineitc model (see Eq. 6) and the importance of considering
123
708
Bioprocess Biosyst Eng (2010) 33:701–710
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
0,6
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:
0,4
tD ¼
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
1
Concentration, (moles/l)
[e0] = 13.8 g/l
[e0]/[t0] = 1:20
[Et0]/[T0] = 3:1
VSOo/VHo = 1:1
0,8
0,2 0 0
12
24
36
48
60
72
time, (h) Triolein
Ethanol
Ethyl Oleate
Mono- + Di-glycerides + Glycerol
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
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 experimental 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 reaction 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 equations in the literature [23, 24] and, unfortunately, this did
123
dp ¼ 180 s ¼ 0:05 h ks
ð7Þ
where the mean particle diameter is 600 lm [32]. The characteristic time of the reaction has been calculated 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, jvT0 j 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 ¼
T0 ¼ 0:9 h ¼ 3200 s vT0
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).
Bioprocess Biosyst Eng (2010) 33:701–710
709
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.
Fig. 13 Optimization of a CSTBR where transesterification takes place. Simulation carried out with [T0] = 0.3 moles/l, [e0] = 34 g/l
From the mass balance on the substrate triolein it is possible to evaluate the characteristic mean residence time s: s¼
V ½T ½T0 ¼ F 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 benefits 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 transesterification 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
References 1. Billaud F, Dominguez V, Broutin P, Buston C (1995) Production of hydrocarbons by pyrolysis of methyl esters from rapeseed oil. J Am Oil Chem Soc 72:1149–1154 2. Ziejewski M, Kaufman KR, Schwab AW, Pryde EH (1984) Diesel engine evaluation of a nonionic sunflower oil-aqueous ethanol microemulsion. J Am Oil Chem Soc 61:1620–1626 3. Fukuda H, Kondo A, Noda H (2001) Biodiesel fuel production by trans-esterification of oils. J Biosci Bioeng 92:405–416 4. Ma F, Hanna MA (1999) Biodiesel production: a review. Bioresource Technol 70:1–15 5. Schwab AW, Bagby MO, Freedman B (1987) Preparation and properties of diesel fuels from vegetable oils. Fuel 66:1372–1378 6. Clark SJ, Wangner L, Schrock MD, Piennaar PG (1984) Methyl and ethyl soybean esters as renewable fuels for diesels engines. J Am Oil Chem Soc 61:1632–1638 7. Freedman B, Pryde EH, Mounts TL (1984) Variables affecting the yields of fatty esters from trans-esterified vegetable oils. J Am Oil Chem Soc 61:1638–1643 8. Srivastava A, Prasad R (2000) Triglycerides-based diesel fuels. Renew Sus Energ Rev 4:111–133 9. Formo MW (1954) Ester reactions of fatty materials. J Am Oil Chem Soc 31:548–559 10. Wright HJ, Segur JB, Clark HV, Coburn SK, Langdon EE, DuPuis RN (1944) A report on ester interchange. Oil Soap 21:145–148 11. Eckey EW (1956) Esterification and interesterification. J Am Oil Chem Soc 33:575–579 12. Freedman B, Butterfield RO, Pryde EH (1986) Transesterification kinetics of soybean oil. J Am Oil Chem Soc 63:1375–1380 13. Mittelbach M (1990) Lipase catalyzed alcoholysis of sunflower oil. J Am Oil Chem Soc 67:168–170 14. Abigor R, Uadia P, Foglia T, Haas M, Jones K, Okpefa E, Obibuzor J, Bafor M (2000) Lipase-catalyzed production of biodiesel fuel from some Nigerian lauric oils. Biochem Soc Trans 28:979–981 15. Shimada Y, Sugihara A, Nakano H, Kuramoto T, Nagao T, Gemba M, Tominaga Y (1997) Purification of docosahexanoic acid by selective esterification of fatty acids from tuna oil with Rhizopus delemar lipase. J Am Oil Chem Soc 74:97–101 16. Nelson LA, Foglia A, Marmer WN (1996) Lipase-catalyzed production of biodiesel. J Am Oil Chem Soc 73:1191–1195 17. Shimada Y, Watanabe Y, Samukawa T, Sugihara A, Noda H, Fukuda H, Tominaga Y (2000) Conversion of vegetable oil to biodiesel using immobilized Candida antarctica lipase. J Am Oil Chem Soc 77:355–360 18. Shimada Y, Watanabe Y, Sugihara A, Tominaga Y (2002) Enzymatic alcoholysis for biodiesel fuel production and application of reaction to oil processing. J Mol Catal B Enz 17:133–142
123
710 19. Samukawa T, Kaieda M, Matsumoto T, Ban K, Kondo A, Shimada Y, Noda H, Fukuda H (2000) Pretreatment of immobilized Candida antarctica lipase for biodiesel fuel production from plant oil. Biosci Bioeng 90:180–183 20. Kaieda M, Samukawa T, Kondo A, Fukuda H (2001) Effect of methanol and water contents on production of biodiesel fuel from plant oil catalyzed by various lipases in a solvent-free system. J Biosci Bioeng 91:12–15 21. Kaieda M, Samukawa T, Matsumoto T, Ban K, Kondo A, Shimada Y, Noda H, Nomoto F, Ohtsuka K, Izumoto E, Fukuda H (1999) Biodiesel fuel production from plant oil catalyzed by Rhizopus oryzae lipase in a water-containing system without an organic solvent. J Biosci Bioeng 88:627–631 22. Dossat V, Combes D, Marty A (2002) Lipase-catalysed transesterification of high oleic sunflower oil. Enzyme Microb Technol 30:90–94 23. Al-Zuhair S (2005) Production of biodiesel by lipase-catalyzed transesterification of vegetable oils: a kinetic study. Biotechnol Prog 21:1442–1448 24. Al-Zuhair S, Ling FW, Jun LS (2007) Proposed kinetic mechanism of the production of biodiesel from palm oil using lipase. Process Biochem 42:951–960
123
Bioprocess Biosyst Eng (2010) 33:701–710 25. Al-Zuhair S, Dowaidar A, Kamal H (2009) Dynamic modeling of biodiesel production from simulated waste cooking oil using immobilized lipase. Biochem Eng J 44:256–262 26. Jeong GT, Park DH (2008) Lipase-catalyzed transesterification of rapeseed oil for biodiesel production with tert-butanol. Appl Biochem Biotechnol 148:131–139 27. Soumanou MM, Bornscheuer UT (2003) Improvement in lipasecatalyzed synthesis of fatty acid methyl esters from sunflower oil. Enz Microb Technol 33:97–103 28. Du W, Xu Y (2005) Study on acyl migration in immobilized Lipozyme TL catalyzed transesterification of soybean oil for biodiesel production. J Mol Cat B 37:68–71 29. Levenspiel O (1999) Chemical reaction engineering, 3rd edn. Wiley, New York, p 63 30. Cheirsilp B, H-Kittikun A, Limkatanyu S (2008) Impact of transesterification mechanisms on the kinetic modeling of biodiesel production by immobilized lipase. Biochem Eng J 42:261–269 31. Bird RB, Stewart WE, Lightfoot EN (1960) Transport phenomena. Wiley, New York 32. Berben PH, Groen C, Christensen MW, Holm HC (2001) Interesterification with immobilized enzymes. SCI Lecture Paper Series, p 121
