A Novel Kinetic Model of Enzymatic Biodiesel Production in a Recirculating Fixed Bed Reactor

Entrapped lipase derived from Candida rugosa can be used as an alternative for commercial heterogeneous catalysts in the biodiesel synthesis process. The inclination towards a recirculating reactor with lipase-containing beds stems from its capability to simultaneously improve both yield and reproducibility in the biodiesel synthesis process. To industrialize biodiesel production with entrapped lipase in a recirculating reactor, optimization is essential, and this can be estimated using a kinetics model. In this context, a kinetics model based on the Ping-Pong Bi-Bi mechanism was developed for enzyme transesterification. Following this, experiments on biodiesel synthesis were carried out in a fixed-bed reactor with a recirculated substrate, and a biodiesel concentration of 2177.231 mol/m³ was achieved from 917.804 mol/m³ triglyceride. In this study, 3 models, namely Model 1, 2, and 3, were developed based on the Ping-Pong Bi-Bi mechanism, and each has assumptions that determine its complexity. To validate these models, two sets of secondary data were taken and fitted into the respective model. The sum relative error is used to express the differences between model and experimental data. Model 1, predicting each component in transesterification, exhibited the highest error of 1.64, while Model 3, assuming excess alcohol and incorporating a pseudo-steady-state for di- and monoglyceride, yielded the lowest error. Despite these variations, every model demonstrated good agreement in following each component profile accurately, providing a more precise description of the reaction elements.

Biodiesel; Candida rugosa lipase; Enzyme kinetic; Modelling; Recirculating fixed-bed reactor; Transesterification

Homogeneous catalysts are commonly used in biodiesel production due to their relatively simpler production methodology. However, alternative approaches such as non-catalytic processes, including high-pressure methodology, acid-catalyzed esterification, and heterogeneous catalyst transesterification has been explored (Kalita et al., 2022; Feng et al., 2010; Demirbas, 2008). Among these methodologies, heterogeneous catalyst transesterification is an important advancement to mitigate the well-recognized limitations associated with homogeneous catalysts and non-catalytic routes (Monika, Banga, and Pathak, 2023; Wancura et al., 2021; Kareem et al., 2020). The development of heterogeneous catalysts holds the potential for low-cost and stable catalysts (Aisyah et al., 2023).

Recent advances in heterogeneous catalyst studies present the opportunity to cost-effectively incorporate enzymes as catalysts (Kalita et al., 2022; Ng et al., 2022; Budžaki et al., 2018). Lipase, particularly sourced from Candida rugosa, stands out as a recognized and effective biocatalyst for transesterification, playing a crucial role in the evolution of biodiesel production. The notable activity and ready availability of Candida rugosa lipase (CRL) further emphasize its efficacy in the transesterification process (Iuliano et al., 2020; Yücel, Terzio?lu, and Özçimen, 2012). The use of recirculating fixed-bed reactors is preferred over other types due to their enhanced efficiency (Ani et al., 2018; Ren et al., 2012). These reactors not only reduce size requirements but also enable the reuse of heterogeneous catalysts compared to batch processes (Aliyah et al., 2016). Despite these advantages, addressing challenges related to reaction rates, catalyst cost, and enzyme inhibition is imperative for enhancing the use of immobilized enzymes in biodiesel production (Hermansyah et al., 2023; Hidayatullah et al., 2018). To overcome these challenges, the application of kinetic models becomes crucial in identifying correlations among operational parameters (Hidayatullah et al., 2021).

Various kinetics models have been developed to illustrate the initial rate of ester production by incorporating stepwise transesterification. These models are designed to predict reactant, by-product, and product concentrations concerning both time and substrate concentration (Rahma and Hidayat, 2023; Ezzati, Ranjbar, and Soltanabadi, 2021; Calabrò et al., 2010; Pessoa, Magalhães, and Falcão, 2009; Xu, Du, and Liu, 2005). While biodiesel synthesis often involves transesterification reactions, many models simplify the process by assuming a single substrate, typically triglyceride concentration (Fedosov et al., 2013; Al-Zuhair, Ling, and Jun, 2007; Al-Zuhair, 2005). Although this simplification aids in determining substrate consumption and product formation rates, it tends to overlook by-product formation. Some models use empirical equations for kinetics, lacking practicality in handling varying substrate concentrations. Intermediate products are important to be put into kinetics to fully elucidate the synthesis pathways (Muharam and Soedarsono, 2020). To address this, there is a need for a model showing stepwise biodiesel production from triglycerides, emphasizing formation sequences including enzymes.

In this study, CRL was immobilized within calcium alginate beads to serve as a biocatalyst in the reactor. A novel mathematical model was developed to predict both the reaction yield and the intermediates generated during transesterification. To illustrate changes in concentration relative to residence time, enzymatic kinetics was integrated with plug flow mass balance. The proposed kinetics model is closely in line with experimental data, capable of representing each transesterification element (alcohol, biodiesel, triglyceride, diglyceride, monoglyceride, and glycerol), and representing enzymatic transesterification pathway following the Ping-Pong Bi-Bi mechanism. Subsequently, 3 models with different assumptions and complexity were proposed. Model 1 includes all triglyceride derivatives in the reaction and considers alcohol as the limiting reactant. Model 2 is the simplified version of model 1 by assuming pseudo-steady state for diglyceride and monoglyceride concentration. Model 3 assume excess alcohol, resulting in complete reactions and therefore assumes diglyceride and monoglyceride concentration to be zero. 

2.1. Materials

        In this study, cooking palm oil was used as a triglyceride substrate, and was produced by PT. Salim Ivomas Pratama, Tbk. (Jakarta, Indonesia). The lyophilized CRL Type VII, bovine serum albumin (BSA), and all additional reagents were purchased from Merck & Co (Rahway, NJ, USA).

2.2. Reactor configuration and design

       The reactor was configured to recirculate the substate mixture with dimensions of 15 cm in length and 1.1 cm in inner diameter. Immobilized enzymes were positioned within the reactor and secured using wire mesh. To maintain a consistent temperature of 37°C, the reactor jacket was enveloped with heated water from a water bath. This setup was linked to both a peristaltic pump and a water pump. The peristaltic pump introduced the mixed substrate into the reactor while the water pump circulated heated water to ensure the reactor temperature stability.

2.3. Enzyme Immobilization

    The first step of the immobilization includes the production of sodium alginate solution. Subsequently, lipase solution was introduced to a sodium alginate solution to generate a 20 ml mixture containing 1.5% sodium alginate and 100 mg of lipase. Using a syringe, the enzyme mixture was extruded into a 2% CaCl₂ solution. The resultant beads were left suspended in the CaCl₂ solution for 1 hour. Then, the beads were transferred to a fresh 2% CaCl₂ solution and maintained at 4°C for 24 hours.

2.4. Biodiesel Synthesis and Quantification

2.5. Model mechanism and assumptions

    Biodiesel synthesis was carried out in 3 sequential elementary reaction stages. The transesterification follows Ping-Pong Bi-Bi mechanism that involves the formation of diglyceride and monoglyceride, and each reaction is reversible (Bornadel et al., 2013; Gog et al., 2012; Fjerbaek, Christensen and Norddahl., 2009). This process was carried out involving T, A, D, B, M, and G, denoting triglyceride, alcohol, diglyceride, biodiesel, monoglyceride, and glycerol respectively. Assuming there was no water-induced hydrolysis process, the only reaction in the system is transesterification.

  The mechanism of the Ping-Pong Bi-Bi transesterification was constructed using these assumptions. The mechanism itself was modified according to the method proposed by Hermansyah et al. (2006). Figure 2 shows the mechanism alongside the reaction constants. The mechanism and kinetics described are designed specifically for the process of transesterification. 

Figure 2 Mechanism of Ping-Pong Bi-Bi transesterification.

2.6. Mathematical Model Derivation

2.7. Model Validation

The compatibility between secondary and estimation data from the developed kinetics model is shown by fitting it with transesterification data from other studies. There are 3 data sets used for model fitting, namely experimental data from this study, data from Shibasaki-Kitakawa et al. (2007), and data from Vicente (2006). Table 1 shows the experimental data and it was used to perform fittings with Models 2 and 3. Triglyceride and alcohol concentration in Table 1 were calculated from FAME concentration based on stoichiometric equilibrium. The data in Table S1 was obtained from Shibasaki-Kitakawa et al. (2007) and will be used for fitting with Model 3. The data shown in Table S2 was obtained from Vicente (2006) and will be used for fitting with Model 1. The fitting quality will be assessed using the relative error sum in Equation 38.

        Using the Microsoft Excel software, differential equations were simulated through 4^th-order Runge-Kutta numerical calculations, and the Solver program within Excel was used for data fitting. The alignment between experimental data and fitting results showcases the model's accuracy in estimating experimental data. Each model iteratively adjusts its kinetics parameters to minimize the sum of relative errors, aiming to achieve a value close to 0.

3.1. Modelling result

        In Figures 3-4, Model 3 presents concentration profiles with the assumption of excess alcohol. The data fitting from Table 1 and S1 to Model 3 is shown in Figure 3a and 3b, respectively. While Model 3 is capable of estimating the formation of both biodiesel and triglycerides, it tends to overestimate the concentration of biodiesel. According to molar balance principles, it is expected that additional products arise from the transformation of triglycerides. Assuming only transesterification occurs, diglycerides and monoglycerides are expected as secondary products. However, due to Model 3 assumption of the absence of intermediate product formation, it simulates a thorough conversion of diglycerides and monoglycerides into biodiesel and glycerol.

        It is crucial to take into account alcohol concentration, especially when making incremental additions, as alcohol plays the role of a limiting reactant. Model 2 incorporates alcohol concentration into its equations and assumes a pseudo-steady state for intermediates (D and M) to simplify the model. The visual representation of the fitting results obtained from the data in Table 1 can be observed in Figure 3c. Model 2 can replicate the concentration profiles of each component by assuming a pseudo-steady state for diglycerides and monoglycerides. The fitting results of Model 2 do not significantly differ from those of Model 3. This shows that Model 2 is capable of simulating the data while considering limited concentrations of methanol.

Figure 3 Fitting of a) data from this study using Model 3, b) data from Shibasaki-Kitakawa et al. (2007) using Model 3, and c) data from this study using Model 2

        Figure 4 shows the data fitting from Table S2 into Model 1, which considers the concentration profiles of A, D, and M. The Model examines the formation of D and M as intermediates, recognizing their potential impact on biodiesel yield. Diglycerides and monoglycerides can form due to the transesterification reaction occurring in three elementary steps(Kadi et al., 2019). When enzymes catalyze the formation of biodiesel, one of the three fatty acid chains on triglycerides is detached, resulting in the formation of diglycerides. Monoglycerides are generated when one of the two fatty acids in a diglyceride reacts to form biodiesel, leaving a single fatty acid chain on the glycerol molecule.

        Model 1 shows a strong agreement with the data. After reaching the peak, both D and M decrease and reach very low concentrations. The reduction in the concentration of D and M is attributed to a gradual reaction with a consumption rate higher than the formation rate. The negligible amount of D and M at the higher reaction time has been observed in most reports (Chen et al., 2020; Tran, Chen and Chang, 2016; Haigh et al., 2014). Model 1 can replicate this phenomenon while also simulating biodiesel formation. The model overestimates biodiesel and underestimates alcohol concentration. However, the prediction of triglyceride concentration yields accurate results. Despite triglycerides being completely consumed, the data shows a lower concentration of biodiesel than in the simulation. A few possibilities might explain this, including the potential formation of other side products such as inactive enzyme-fatty acid complexes or even the adsorption of triglycerides onto the enzyme's support matrix.

Figure 4 Fitting to Model 1 using data from Vicente et al. (2006)

        Table 2 presents a comparison of kinetics parameters, showing the highest reaction constant derived from an experiment conducted by Vicente et al. (2006). The experiment used 1 wt% catalyst (based on oil) for transesterification. According to the investigation, the reactant was 240 g of B. carinata oil (± 800 mol/m³), and for simplicity, it was assumed to be equivalent to 300 mL (assuming a density of 800 g/L). This led to the calculation of the concentration of catalyst used, which is 8 kg/m³. Shibasaki-Kitakawa et al. (2007) synthesized biodiesel using 2 g of PA306s resin and 10g of reactants consisting of oil and 10 - 20 molar equivalents of methanol (based on oil). Assuming this 10g was equal to 20 ml of reactant, the concentration of the catalyst is estimated to be 100 kg/m³. Although the kinetics constant for each catalyst might appear low, the overall reaction rate can be substantial with the assistance of a significant quantity of catalysts.

Table 2 Comparison of kinetics parameter

        In the context of the stepwise transesterification reaction, K₁ signifies the inclination to yield diglycerides. K₂ represents the tendency to generate monoglycerides from diglycerides, and K₃ shows the propensity to release glycerol from monoglycerides. These constants show forward reactions. In Models 2 and 1, where diglycerides and monoglycerides are assumed to react rapidly, K₂ and K₃ are excluded. Conversely, K₄, K₅, and K₆ denote hindrances to biodiesel formation. K₄-K₆ are associated with k₂, k₄, and k₆, reflecting the rate constants of diglyceride, monoglyceride, and glycerol release. K₄ represents the dissociation of triglyceride, leading to the enzyme complex producing biodiesel from the fatty acid of triglyceride. The same meaning also applies to K₅ and K₆, with the only difference in the source of fatty acid (such as diglyceride for K₅, and monoglyceride for K₆).

        In Model 3, a total of 6 parameters need to be estimated, while Models 1 and 2 require 4. The resulting parameter data shows that ion exchange resin exhibits the highest K₁ reaction rate. Model 2, assuming a controlled alcohol reaction, shows significant changes in the constant K₆ when compared to Model 1. The experiment carried out by Vicente et al. (2006) had the highest value of kinetics constants compared to other studies. 

    In conclusion, 3 mechanistic models based on the Ping-Pong Bi-Bi mechanism were developed to predict how each part of triglyceride transesterification behaves. Each model could provide a better understanding of how both the reactants and products change over time. Model key parameter helps to explain how operational conditions affect the transesterification process. Data fitting of this experiment data into Model 3 resulted in 4.13×10^-2, which shows good alignment. However, Model 1 had a high sum relative error, due to many substrates and product concentrations that the model need to adjust, therefore the sum relative error calculates all the misalignments, producing the highest sum of error. This model could become a go-to reference for understanding transesterification kinetics and further studies on the inhibition of substrate and product are needed to improve the model.

    The study was supported by supported by the Ministry of Education, Culture, Research, and Technology of Indonesia through the Penelitian Dasar Unggulan Perguruan Tinggi (PDUPT) scheme, with grant numbers 021/E5/PG.02.00.PL/2023 and NKB-905/UN2.RST/HKP.05.00/2023 in the year 2023.

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