Kinetic Studies of Biodiesel Production from Jatropha curcas Oil

The world is confronted with the twin crisis of fossil fuel depletion and environmental degradation caused by fossil fuel usage. Biodiesel produced from renewable feedstocks such as Jatropha seed oil or animal fats by transesterification offers a solution. Although biodiesel has been produced from various vegetable oils such as Jatropha seed oil, the reaction kinetics studies are very few in literature, hence the need for this study. Jatropha curcas seed oil was extracted and analyzed to determine its free fatty acid and fatty acid composition. The oil was transesterified with methanol at a molar ratio of methanol to oil 8:1, using 1% sodium hydroxide catalyst, at different temperatures ranging from 32C to 65C, at atmospheric pressure. The order of the reactions with respect to the triglyceride's disappearance in the forward reaction at the chosen temperatures was found to be pseudo-first-order and found to be first-order for the reaction at 32C. The rate constants of the three consecutive reaction steps at 65C, namely, triglyceride to diglyceride, diglyceride to monoglyceride, and monoglyceride to glycerol, were found to be 0.422 min 0.117 min and 0.037min respectively. Their corresponding activation energies in J/mol were 22.165, 3.136, and 19.770, respectively.

. Biodiesel is typically produced by the transesterification reaction, which is a chemical reaction between a raw renewable oil consisting mainly of triglycerides molecules such as Jatropha seed oil and an alcohol such as methanol or ethanol in the presence of a catalyst such as sodium hydroxide, potassium hydroxide, calcium oxide or zeolite to chemically break the triglyceride molecule in the oil into fatty acid methyl or ethyl esters (biodiesel) with glycerol as a by-product (Ambat et al., 2018;. Biodiesel, unlike petrol diesel, is biodegradable and non-toxic (Sadaf et al., 2018) and produces about 60% less net life cycle carbon dioxide emissions, as it is itself produced from atmospheric carbon dioxide through photosynthesis in plants ( Živković et al., 2018;Mohammed and Jabbar, 2016).
Several studies have been conducted on biodiesel production Jatropha curcas oil catalyzed by various homogeneous and heterogeneous catalysts. (Sudsakorn et al., 2017) investigated biodiesel production from Jatropha Curcas oil using strontium doped CaO/MgO catalyst. The study revealed that methyl ester content of 99.6% was obtained at 65°C for two hours and the methanol-to-oil molar ratio of 9:1 with the catalyst amount of 5 wt%. (Kamel et al., 2018) investigated the optimization and mechanism of Jatropha curcas Linnaeus seed oil for biodiesel production. The study revealed that the optimum operating conditions of the Jatropha curcas oil transesterification process were ascertained as 60 min reaction time, 6:1 methanol to oil molar ratio, 1 wt.% catalyst loading, 400 rpm, and 60°C with a biodiesel production yields of 94 and 96% with calcined jatropha cake and KOH activated jatropha cake catalysts. Kinetic modeling of biodiesel production using non-edible Madhuca Indica oil has been reported by (Muthukumaran et al. 2017). The study's kinetic analysis revealed that the apparent activation energy and pre-exponential factor for transesterification of mahua oil were calculated as 22.306 kJ/mol and 60.51 min 1 , respectively. Biodiesel research has mainly focused on the development of cheap, non-edible oils to serve as raw materials. The kinetics of some of these oils must be developed due to differences in the oils' composition. Therefore, this study aimed to investigate the reaction kinetics of biodiesel production from transesterification of ester derived from local Jatropha seed oil.

MATERIALS AND METHOD
The materials used in this study include Jatropha seed oil extracted from fresh Jatropha seeds extracted using a crude hydraulic press, methanol of high grade (HPLC grade), and sodium hydroxide purchased from Sigma Aldrich, Germany. Hot plate with a magnetic stirrer, temperature regulation system, an improvised reactor (500ml beaker), a mercury thermometer, cotton wool, and Gas Chromatography-Mass Spectrophotometer (GC MS) were all employed during the kinetic studies.
An equivalent molar ratio of methanol to oil (8:1) was weighed and placed in two beakers labeled A and B. Beaker A containing the oil was heated to 100 o C to remove any moisture present in the oil. Prior to the reaction, the oil's free fatty acid was tested and found to be approximately 0.8%, hence suitable for transesterification to occur. One percent sodium hydroxide by weight of oil was dissolved in beaker B containing the methanol. The heated oil was allowed to cool to about 30 o C. The oil was transesterified with the sodium methoxide solution by adding the solution slowly to the oil to avoid clogging while stirring on the hot plate at 450 rpm. The temperature of the hot plate was set as required. The reaction mixture's aliquots were withdrawn at 15 minutes intervals of time for Gas chromatographic analysis to determine the percentage of fatty acid methyl ester (FAME) formed. The reaction was carried out at temperatures ranges from 32 -65 o C under atmospheric pressure. The maximum reaction time for each temperature was 120 min.

RESULTS AND DISCUSSION
The results of the biodiesel components obtained from the gas chromatographic analysis are shown in Table 1. The kinetic rate determination for Triglycerides (TG), Diglycerides (DG), and Monoglycerides (MG) are shown in Tables 2, 3, and 4, respectively. Concentration of triglyceride at time zero (CA0) =2.40mol/l.

Reaction Kinetics Model Derivation
The biodiesel or transesterification reaction is of the form represented in Eq. (1) where A = TG, B = alcohol (ROH), C = Glyceride and D = methyl esters (ME) Therefore, Eq. (1) becomes TG + ROH Glyceride + ME (2) Where the Glyceride could be either DG, MG or GL.
Eq. (2) is an equilibrium reaction that occurs in three consecutive steps forming intermediates. Stoichiometrically, 3 moles of alcohol are required to react with 1 mole of TG to 3 moles or esters and 1 mole of glycerol. Therefore, we have TG + ROH DG + ME DG + ROH MG + ME (4) MG + ROH GL + ME Overall reaction is therefore TG + 3 ROH GL + 3 ME From Eq. (3) TG + ROH DG + ME (7) and MG + ME DG + ROH (10) from Eq. (5) MG + ROH GL + ME (11) and GL + ME MG + ROH The overall order proposed for the forward reactions in Equations (7), (9) and (11) have been reported to be a second order for transesterification of waste cooking oil (Krishnan and Dass, 2012). There are conflicting reports from different authors on different vegetable oils (Turner, 2005). Sometimes same vegetable oil but different reaction conditions may also have different report (Wang et al., 2020). This would be proven by the data obtained from the experiment in this study. The way the reactions above were initiated and terminated are as follows. Formation of alkoxide from methanol and sodium hydroxide.
Alcohol catalyst alkoxides water The alkoxide ion attacks the glycerides molecules to form methyl esters and glycerol, as shown from Eq. (14) to (19). Transesterification DG --+ ROH ⇄ DG + RO DG + RO --⇄ MG --+ ME MG --+ ROH → MG + RO -- MG + RO --→ GL --+ ME In a saponification reaction, an almost inevitable side reaction associated with transesterification when using a homogeneous catalyst such as sodium hydroxide (NaOH) can take place. The following reaction represented in Eq. (20) to (23)  transesterification of high free fatty acid vegetable oil (e.g., Jatropha seed oil) with sodium hydroxide catalyst would result in a lot of soap formation with little or no biodiesel formation. Hence it is recommended that if sodium hydroxide catalyst must be used in Jatropha seed oil transesterification, the free fatty acid of the oil must be lower than 3% or 1%, and the oil must be dried or free from moisture. In the present study, the free fatty acid of Jatropha seed oil used was 0.8%, and the oil was preheated at a temperature of over 100 o C for about 5 -10 minutes to eliminate moisture. The molar ratio of methanol to the oil used was 8:1. The reactions were carried out at 32 o C, 40 o C, 60 o C, and 65 o C. At each reaction temperature, aliquots of the reaction mixture were withdrawn at every 15 minutes of time for 75 minutes. The reactions above are assumed to be elementary thus obeying, the law of mass action (Turner 2005, Freedman et al., 1986) 3.1.1 Assumptions of the kinetic model i.
The concentration of free fatty acid of the oil used was negligible. ii.
All the reactions and intermediates formed proceed at the same rate, with the same mechanism. iii.
Saponification reaction is negligible. v.
The concentration of alcohol is constant due to the high molar ratio of alcohol to triglyceride; hence reaction rate depends solely on the disappearance of the triglycerides. vi.
All reactions go to completion. vii.
The reactions are elementary and thus obey the law of mass action. viii.
The reverse reactions are negligible due to the high molar ratio of methanol to triglycerides used, causing equilibrium to shift to the right (Le Chartelier's Principles).

Determination of the Rates and Order of the Reactions
From Eq. (7) to (12), the rates of the reactions according to LMA are obtain as follows: r TG = dC TG dt = K 1 C TG C ROH + K 2 C DG C ME (24) r DG = dC DG dt = K 1 C TG C ROH = K 2 C DG C ME − K 3 C DG C ROH + K 4 C MA C ME (25) r MG = dC MG dt = K 1 C DG C ROH = K 4 C MG C ME − K 5 C MA C ROH + K 6 C G C ME (26) r ME = dC ME dt = K 1 C TG C ROH − K 2 C DG C ME − K 3 C DG C ROH − K 4 C MG C ME + K 5 C MA C ROH + K 6 C G C ME (28) Where CTG, CDG, CME, CGL, CROH, and CME are mole concentrations of TG, DG, MG, G, ROH, and ME, respectively in the reaction mixture. Eq. (24) to (29)  Then for a first-order reaction in a batch reactor, where -dC A dt (rate of disappearance of reactant A), K is the rate constant, and CA is the concentration of reactant A at any given time, t. - The value of K in Eq. (35) can be determined by plotting versus t as shown in Fig. (1).
The fittings of the kinetic data obtained at 32 o C into Eq. (35) gave a straight line which is an indication that the transesterification reaction is a first-order reaction with a rate constant of 0.112min -1 . However, the kinetic data obtained at reaction temperatures of 40 o C, 60 o C, and 65 o C could not fit into the first-order reaction mechanism. Hence, they were subsequently tested in a second-order reaction represented in Eq. (36).
From Eq. (36), a plot of 1/CA versus time would give a straight line to indicate a second-order reaction. The second-order reaction mechanism did not fit for reactions at 40 o C, 60 o C, and 65 o C; hence an n th order determination was considered. A plot of CA versus time and dCA/dt versus ln CA was used to determine the values of K as in Table 5. The order of the triglyceride disappearance was found to be pseudo-first-order. A plot of In K versus 1/T for the three consecutive reaction steps shows that the TG disappearance involves high activation energy. In contrast, the energy of conversion of MG to GL involves very low activation energy. In fact, the third step, which is the MG conversion to GL and ester, is the rate-determining step. From Fig. 1 it can be seen that the reaction is typical of first-order at 32 o C. (Wang et al., 2020) reported that the triglyceride disappearance in the forward reaction appears to be pseudo-firstorder or second-order depending upon conditions used. (Khrishnan and Dass, 2012) reported a second-order mechanism for the transesterification of waste cooking oil. (Al-Zuhair, 2007), in his work on kinetics of lipase catalysed methanolysis of palm oil did not follow second order kinetics as indicated by (Freedman et al., 1986). (Noureddini and Zhu, 1997) found that the rate of reaction is temperature-dependent. (Turner's, 2005) reported on modeling and simulation of reaction kinetics for biodiesel production shows that there are conflicting findings as to the order of reaction and estimates of reaction rate constants vary widely in biodiesel reaction kinetics. However, a first-order reaction kinetics obtained for the reaction at 32 o C in this study is in agreement with Hymore and Audu's report on the kinetics of alcoholysis of rubber seed oil. This report also agrees with Mittelbach's report, which says that the rate of reaction is temperature-dependent. This is true and in agreement with what is obtained in this study. As soon the reaction temperature was raised from room temperature of 32 o C to 40 o C and above, the rate of reaction changed. The reaction order could no longer fit into the first-order reaction mechanism nor the second-order mechanism. An n th order mechanism was proposed for reactions at 40 o C, 60 o C and 65 o C. Pseudo first-order kinetics was obtained. These results agree with the report of (Freedman et al., 1986) mechanism; hence a further attempt was made to fit the data into second-order reaction expression. The fittings of the data into second-order reaction expressions are represented in Fig. 3. and 65 o C are pseudo-first-order. The DG disappearances are also pseudo-first-order. These results are in agreement with the report of (Freedman et al., 1986).

Determination of the Activation Energy of Reactions
To determine the activation energies of the reactions, we use the Arrhenius law. The Arrhenius law is stated in Eq. (41) below. In k = -Ea/RT + In A (41) Where K is the reaction rate constant R is gas constant given as 0.082 liter atm.mol -1 deg -1 in this case T is temperature of reaction A is frequency or pre-exponential factor and Ea = activation energy of reaction. A plot of In K versus 1/T yield a straight line whose slope equals -Ea/R. Therefore the activation energy in joules/mol is obtained as: Activation energy (Ea) = -slope x gas constant The graph intercept = In A. Further testing of the kinetic models revealed that the reaction order of the TG disappearing to DG are pseudo-first-order. Only the reaction at 60 o C may be approximated to the second order. All the DG disappearing to MG, are all pseudo-first-order reactions. As for the MG disappearing to esters and glycerol, the orders are also pseudo-first-order except for the reactions at 32 o C and 60 o C, which are 3 rd order and 4 th order, respectively. These results agree with those obtained by (Freedman et al., 1986) in the kinetics of soybean oil transesterification with methanol. According to Freedman, all the forward reactions were pseudo-first-order. cooking oil transesterification with methanol .since different oils have different molecular weight and composition, it is possible that reaction order and the activation energy of the reaction may not exactly be the same. The values of activation energy obtained in this study for DG agrees with (Krishnan and Dass, 2012). A common observation from Freedman work and that of Krishnan and Dass is that of the MG transformation's activation energy to ester being the lowest of the three. This shows that the MG transformation to GL and ester is the rate-determining step.
A summary of all the rate constants in weight percent per minute at different temperatures for the glycerides transformation are shown in Table 6. Table 6 .Summary of rate constants at different temperatures.

CONCLUSIONS
The kinetics of biodiesel production from Jatropha curcas seed oil by transesterification reaction has been investigated. The disappearance of the triglycerides molecules in the forward reaction was found to follow a first-order reaction mechanism at 32 o C with a rate constant of 0.112 min -1 and R 2 of 0.914 for the kinetic prediction. The activation energy of the TG disappearance is 22.165 kJ/mol, which indicates that the reaction at the beginning is temperature-sensitive, but as the reaction proceeds, the second step of diglyceride breaking down to monoglyceride and then to esters and glycerol are temperature-insensitive as both have low activation energies. Considering the very low activation energy of the monoglyceride disappearance to methyl esters and glycerol, little or no energy of activation is required at this step due to its very low value.