Enzymatic biodiesel production kinetics under previously optimized conditions were investigated. Waste frying oil (WFO) was used as the raw material, Novozym 435 as catalyst, methanol as acyl acceptor and tert-butanol as co-solvent. To investigate pure transesterification kinetics improving product properties, 3 Å molecular sieves were incorporated into the reaction to provide an anhydrous medium avoiding the side reactions of hydrolysis and esterification. The effects of either WFO or methanol on the reaction rate were analyzed separately. The reaction was described by a Ping Pong mechanism and competitive inhibition by methanol. The results obtained in the kinetics study were applied in the operation of a semi-continuous reactor for biodiesel production. The operational conditions of each reaction cycle were: methanol-to-oil ratio 8/1 (mol/mol), 15% (wt) Novozym 435, 0.75% (v/v) of tert-butanol, 44.5°C, 200 rpm and 4 h of reaction time. The enzymes were successively reused by remaining in the reactor during all the cycles. Under these conditions, biodiesel production yields higher than 80% over 7 reaction cycles were observed. Both the kinetics study and the reactor operation showed that Novozym 435 was not inhibited at high methanol concentrations and that the kinetics of the proposed enzymatic process could be comparable to the conventional chemical process.
Kinetic studies of fatty acid alkyl ester (FAAE) production using different lipases have been reported in the literature. The early studies on this topic focused on free fatty acid (FFA) esterification for FAAE production. Krishna and Karanth  investigated the lipase-catalyzed esterification kinetics of FFA using the immobilized lipase Lipozyme IM-20 from Rhizomucor miehei. The reaction mechanism was described by a Ping Pong Bi Bi model including competitive inhibition by the two substrates (isoamyl alcohol and butyric acid). Similarly, Al-Zuhair et al.  studied butyric acid esterification catalyzed by a lipase from Mucor miehei using methanol as acyl acceptor. The results fitted to a Ping Pong mechanism model, including methanol competitive inhibition.
Although interesting results have been reported regarding FAAE production by esterification, industrial interest is focused mainly on the production of FAAE from triacylglycerides (TG), and not particularly from FFA . Therefore, recent kinetic studies using lipases have focused on FAAE production from TG, such as synthetic waste frying oil  and crude palm oil . According to Talukder et al. , FAAE production from TG can be carried out by lipases through two consecutive reactions of hydrolysis and esterification. In these successive reactions, TG are first hydrolyzed to produce FFA and subsequently FFA are esterified to produce FAAE. Alternatively, Al Zuhair et al.  reported that FAAE production could occur by a direct transesterification of TG. Similarly, Cheirsilp et al.  established that the concept of hydrolysis and transesterification occurring simultaneously is more appropriate than the model of two consecutive reactions of hydrolysis and esterification.
According to the previous analyses, kinetic studies showing the performance of lipase catalyzed processes for FAAE production have been already reported. However, the quality of the final product was not considered. In this context, Azócar et al.  showed that when Candida antarctica lipase immobilized on acrylic resin (Novozym 435) was used in an anhydrous organic medium, fatty acid methyl ester (FAME) production occurred mainly by the transesterification pathway, avoiding hydrolysis and esterification reactions . When FAME is mainly produced by hydrolysis and esterification, the final product is always characterized by a high acid value due to FFA produced during hydrolysis reaction . In contrast, if FAME is mainly produced by transesterification reaction in anhydrous medium, the acid value of the produced biodiesel is near to that established by the different international biodiesel standards and additionally, and it is possible to decrease the content of intermediary products, such as mono- and diglyceride . Therefore, it is of interest to study transesterification reaction kinetics by using an anhydrous medium to produce biodiesel in a lipase-catalyzed process. In addition, an anhydrous medium would allow us to investigate pure transesterification kinetics for FAAE production using lipase as the catalyst.
On the other hand, several efforts have been made in both enzyme reutilization and enzyme activity enhancement. In this sense, the use of the moderate polar co-solvent tert-butanol improves the miscibility between the alcohol and vegetable oil, increasing the mass transfer, and with the added benefit of promoting a high lipase activity and enzyme reuse ,  and . However, in previous kinetic studies, non-polar co-solvents such as n-hexane ,  and  and n-hexadecane  have been predominately used. In addition, using polar co-solvents was not effective to achieve high lipase activities . Regarding raw materials, transesterification kinetics using alternative feedstock, such as waste frying oil (WFO) , have been investigated only by Al-Zuhair et al. . Therefore, there is a need to use both appropriate co-solvents and alternative raw materials in kinetic studies of FAAE production using lipases.
The aim of this work was to study FAME production kinetics mainly through the transesterification pathway in an anhydrous medium. The reaction was catalyzed by Novozym 435, with WFO as raw material, methanol as the acyl acceptor and tert-butanol as the co-solvent. In addition, a semi-continuous reactor for FAME production was operated under the optimal conditions established in kinetic trials.
Materials and methods
WFO collected from restaurants was filtered and characterized prior to its use as feedstock (Table 1). Density was measured at 20°C using a manual densimeter. Kinematic viscosity was measured at 40°C using a capillary viscosimeter. The acid value was determined by titration with KOH using phenolphthalein as indicator. The peroxide value was determined by titration with Na2S2O3, and iodine by the Wijs method . Candida antarctica lipase immobilized on acrylic resin (Novozym 435) donated by Novo Industries (Denmark) was used as the catalyst. Molecular sieves (3 Å) used to generate the anhydrous medium and tert-butanol used as the co-solvent were from Sigma–Aldrich. Methyl heptadecanoate was used as an internal standard and was chromatographically pure. All other chemicals were of analytical grade.
Property Value Density at 20°C (kg/m3) 926 Kinematic viscosity at 40°C (cSt) 47.9 Acid value (mg KOH/g) 4.6 Free fatty acid (%) 2.3 Iodine value (g I2/100 g aceite) 89 Peroxide index (mEq/kg) 10.5
Samples were filtered before the analysis.
where υ is the initial reaction rate (mol L−1 min−1), Vmax is the maximum reaction rate (mol L−1 min−1), KM is the dissociation constant for methanol (M) (mol L−1), and [M] is methanol concentration (mol L−1).
The obtained values were then optimized using Excel solver to find the minimum objective function (Eq. (2)) that compares the measured reaction rate with that predicted by the proposed kinetic equation. The inhibition constant for methanol KIM was first assumed according to previous reports  to be subsequently optimized by Excel solver.
where OF is the objective function, υ pred the predicted rate of reaction and υ exp the experimental rate of reaction.
According to the results obtained in the determination of the kinetic constants, a Ping Pong model with competitive inhibition by methanol with respect to the WFO was shown to best describe the reaction according to the following equation:
where υ is the initial reaction rate (mol L−1 min−1), Vmax is the maximum reaction rate (mol L−1 min−1), KW and KM are the dissociation constants for WFO (W) and methanol (M), respectively (mol L−1), [W] is WFO concentration (mol L−1), [M] is methanol concentration (mol L−1) and KIM is the inhibition constant for methanol (mol L−1).
Reactor for FAME production by transesterification
A semi-continuous reactor was designed for FAME production mainly by transesterification reaction (Fig. 1). The reactor vessel was glass with 0.5 L reaction volume. A glass heating jacket with hot water controlled by thermostat was used for temperature control and a magnetic stirrer for stirring. A packed column filled with 20 g of 3 Å molecular sieves was connected to the reactor to continuously remove the water from the reaction. The reaction mixture was continuously recirculated through the column to produce and maintain anhydrous conditions. To complete the set-up, a glass settler was connected to the reactor to separate the products after the transesterification reaction.
The reaction samples were centrifuged for 10 min at 4000 rpm. The upper layer was extracted and subsequently treated at 85°C for 30 min to eliminate the residual solvents, tert-butanol and methanol. FAME yield was determined by quantification of FAME content in the treated sample, carried out using a Clarus 600 chromatograph coupled with a Clarus 500T mass spectrometer from Perkin Elmer (GC-MS). An Elite-5ms capillary column with length 30 m, thickness 0.1 μm and internal diameter 0.25 mm was used. Sample vials were prepared by adding 3 μg of sample to 100 μL methyl heptadecanoate as an internal standard (initial concentration of 1300 mg L−1). The following temperature program was used: 50°C for 1 min and then increasing temperature at a rate of 1.1°C/min up to 187°C. The split vent flow rate was 50, both the injector and detector temperatures were 250°C and He was used as the carrier gas.
Results and discussion
Effect of methanol concentration on initial reaction rate
The effect of methanol concentration on FAME yield was investigated (Fig. 2). The experiments were carried out at a methanol-to-oil molar ratio in the range of 0.6/1–15/1. According to Fig. 2, two main concentration zones could be distinguished. In the lower area, FAME yields of less than 60% were obtained at methanol-to-oil molar ratios lower than the stoichiometric ratio (
Effect of WFO concentration and initial reaction rate
A non-inhibitory, non-limiting concentration of methanol was used in these assays to evaluate the sole effect of WFO concentration on FAME yield. Experiments were carried out at a methanol-to-oil molar ratio between 3/0.375 and 3/1. FAME yields obtained with different WFO concentrations were expressed as FAME concentration. The data of the product concentration versus the initial reaction time (20 min) were plotted for each WFO concentration. The initial reaction time was established considering a slope with R > 0.9, similar to the methanol kinetics methodology. The change in the initial reaction rate with different initial concentrations of WFO is shown in Fig. 4; there was no WFO inhibition in the range of the initial concentrations investigated. Similar results of competitive inhibition by alcohol, without inhibition by substrate were reported by Al Zuhair et al. . However, in another investigation by the same authors, WFO inhibition during the transesterification reaction was reported . Moreover, inhibition caused by FFA has been also found .
Kinetic parameters obtained were compared with references showing significant differences (Table 2). Krishna and Karanth  used butyric acid and isoamyl alcohol with Lipozyme IM-20 as the catalyst in an n-hexane system. In this study, it was found that substrate inhibition occurred, probably because butyric acid, being a short-chain polar acid, concentrates in the microaqueous layer and causes a pH drop in the enzyme microenvironment leading to enzyme inactivation. In the present study it was possible that long chain FFA present at the beginning of the reaction (Table 1) did not produce inhibition because the water was removed during the reaction by the molecular sieves. Despite these differences, there are some similarities with other reported investigations. In the study carried out in , the experimental conditions were similar to the current work, and no substrate inhibition was observed. This result could be related to the use of tert-butanol as co-solvent in both cases. In addition, the results shown in Table 2 are in agreement with the higher inhibitory effect of methanol compared to WFO. In this sense, Al-Zuhair et al.  only found substrate inhibition at methanol-to-oil molar ratios higher than 1/4.
The results obtained for the kinetic constants, KW and KM, indicate a higher affinity for WFO compared to methanol. The high KM value indicates the strong methanol concentration dependence of transesterification, where high methanol concentrations are required to increase transesterification reaction rate catalyzed by Novozym 435, avoiding substrate limitation. However, high methanol concentrations are also responsible for lipase inhibition. Therefore the use of tert-butanol as a co-solvent can avoid these problems. Although the different orders of magnitude observed in the kinetic constants showed in Table 2, a similar tendency of KM values being higher than KW values can be observed.
Several transesterification and esterification kinetic studies catalyzed by lipases using short chain alcohols have reported alcohol inhibition only, which can be described by the Ping Pong mechanism with inhibition by methanol.
According to Figure 7 and Figure 8, the Ping Pong kinetic model adequately predicted reaction performance, indicating that all simplifications assumed when carried out to use the Michaelis-Menten kinetics were suitable for kinetic constant determination. At higher methanol concentrations, the model predicted a moderate reduction in initial reaction rate. The reason for the high enzyme activity at high methanol concentrations could be related to the use of the co-solvent in the reaction. The possibility of using high methanol dosages when an enzymatic catalyst is used in biodiesel production could promote a more competitive industrial process. This is because high stoichiometric molar ratios of methanol to oil can shift the equilibrium to product formation, diminishing reaction time and therefore making a process feasible for scaling. Figure 7 shows the positive effect of increasing initial WFO concentration in the initial reaction rate.
Start up of a semi-continuous bioreactor for biodiesel production
The results described were used to establish the operational conditions of a semi-continuous bioreactor for enzymatic FAME production (Fig. 1). Novozym 435 was used as catalyst, methanol as acyl acceptor, WFO as raw material, tert-butanol as co-solvent and molecular sieves were used to extract water during the reaction (anhydrous medium). Methanol and WFO concentrations were established according to the results obtained in the kinetic study (methanol-to-oil molar ratio of 8/1). The operation of the reactor was carried out over 30 h, maintaining the same enzymes inside the reactor during successive cycles at 44.5°C, 200 rpm and 4 h of reaction time. New doses of alcohol and WFO, as well as molecular sieves of 3 Å were added in each reaction cycle.
The results during the start-up did not show any significant enzymatic activity loss during the successive reaction cycles of 4 h each one, with FAME production yields higher than 80% (Fig. 9). The different starting times of each reaction show that consecutive reactions were carried out, that is, the first from 0 to 4 h, the second from 4 to 8 h and so on.
- 11110282, PIA Project DI12-7001 from Universidad de La Frontera.