Castor seeds were collected from wild castor plants growing on moist marginal soil near Iluju in Ogbomosho, Oyo State, Nigeria. Ripe castor fruits were hand-cleaned and sun-dried for 4 - 5 days until the capsules burst open, revealing the seeds inside. The seed pods were then removed, and the shells and beans (cotyledons) were separated using tray-winnowing. Before extraction, the beans were ground into a paste with a mortar and pestle [23][24].

The cocoa pods, obtained from a farm at Ilorin, Kwara State, Nigeria were sun-dried for 5 d before being reduced to ashes (Figure 1(a)) by placing crucibles containing the dried pods in a muffle furnace set to 600˚C for 35 min according to [24][25] (Figure 1(b)). The ash was then sieved to achieve an average particle size of 0.8 mm and then analyzed by atomic absorption spectroscopy to determine the metal composition for use as a transesterification catalyst [24][25].

(a) (b)

Figure 1. CPH before (a) and after (b) sun-drying and calcination.

2.3.1. Oil Extraction

For the purpose of extraction, castor seed paste (40 g) was wrapped in a clean muslin cloth and placed in the thimble, which was inserted at the center of the extractor. About 50 mL of hexane was weighed and poured into a round-bottom flask. The round bottom flask and a condenser were attached to the extractor to form the soxhlet extractor. The solvent in the extractor was then heated until it boiled and vaporized through the vertical tube into the condenser at the top. The liquid condensate is dropped into the cotton wool thimble at the center, containing the solid sample that retains the extract. The extract seeped through the thimble into the flask via the siphon. After extracting for 3 h, the sample was dried at 60˚C (to remove residual solvent) and weighed to determine the yield of oil extracted using Equation (1) [24].

where y 1 and y 2 are the weights of castor beans before and after extraction, respectively.

2.3.2. Typical Experimental Run in Biodiesel Production

A small-scale laboratory glass reactor placed on a hot plate with a magnetic stirrer was used for the trans-esterification reaction. The Biodiesel sample was prepared using castor oil (Figure 2). Catalyst loading ranging from 3% to 6% weight (relative to oil) was used in the trans-esterification processes, with a methanol-to-oil ratio of 6:1 to 10:1. The reaction time and temperature ranged from 1 h to 4 h and 45˚C to 60˚C. A separating funnel separated the fatty acid methyl esters from the glycerol.

The yield of the biodiesel produced was then calculated using Equation (2).

Definitive screen designs were used to study the main effects and the interactions

Figure 2. Biodiesel product.

between the experimental variables. The modeling of the trans-esterification process was also investigated using the four variables, which in turn produced 13 experimental runs for the optimization studies. The model equation produced was validated, and its level of significance was investigated using the R-squared and analysis of variance (ANOVA). Table 1 shows the experimental variables used in the design process.

Table 1. Experimental Variables and Levels Used for the Biodiesel Synthesis.

The kinetic study of the reaction at optimal conditions by the variation of the effect of the reaction time and temperature was investigated. The study was based on the following assumptions: the occurrence of a single-step transesterification reaction and that, since methanol was in excess, no reversible reaction occurred. Hence,

For transesterification reaction

k = Over all equilibrium constant, k′ = Equilibrium constant, [MtOH] is the concentration of Methanol.

Knowing that

From Equation (4). we have

where,

From Equation (6), the values for “k” at four different temperatures of 45˚C, 50˚C, 55˚C, and 60˚C, was determined by plotting − ln ( 1 − X c a s t o r   o i l ) against t, after which Equation (7).

Arrhenius equation was used to determine the activation energy by plotting ln k against 1 T .

Hence, the slope and the intercept were used to determine the activation energy E a and the frequency factor k o

After washing the deposited FAMEs on the active site of the used catalyst, the catalyst was dried at 40˚C until constant weight was achieved. This procedure was then repeated after each cycle. The catalyst was reused four times.

Table 2 presents the actual and predicted values. Equation 8 shows the resulting equation from the definitive screen design, a response surface methodology. The analysis of variance (ANOVA) results in an F-value of 354.40, which implies that the model terms are significant. In this case, A, B, C, D, AB, AC, AD, BC, BD, CD, and A² are the significant quadratic coefficients of the model.

where the Yield of biodiesel ( Y C C P H ), A is the temperature (˚C), B is the reaction time (h), C is the methanol/oil ratio, and D is the catalyst loading (wt%) was an effective factor considered. Also, based on the model, the methanol/oil ratio has the highest effect on the biodiesel yield due to the high positive coefficient. This was also confirmed by the ANOVA, which indicates the order of significance of the independent variables and denotes that methanol/oil is the most important variable affecting the biodiesel yield. In addition, a low lack of fittest of 4 was noted

Table 2.Actual and predicted values for the trans-esterification using CPA.

according to the ANOVA Table 3. This indicates that the model represents the actual relationship of all the parameters, which are all within the selected range. In actual fact, the P-value of 0.0414 and F-value of 354.40 of the model are indications of the significance of the model. The regression model adequately predicts the biodiesel yield within the design space, as the R² of 0.9997 is in reasonable agreement with the adjusted R² of 0.9969. At this R²-value, the optimal condition that was achieved was 50˚C temperature, 2.5 reaction time, 10:1 methanol to oil ratio, and catalyst loading of 6 wt%. Also, the R² value correlates with the predicted and actual values, which is shown in Figure 3. This indicates that the model can be used to navigate within the design space.

Table 3.ANOVA for response surface reduced quadratic model.

As shown in Figure 4(a), at a catalyst loading of 3 wt %, and temperature ranges between 48 - 55˚C the biodiesel yield increases from 30 - 98%. Also, at the catalyst loading of 6 wt %, the biodiesel yield attains 97% when the temperature is at 47˚C, but as the temperature increases yield of biodiesel decreases to 35%. Figure 4(b) displays the time and temperature profile in relation to biodiesel yield. At the time 1 h, temperature increases from 51 - 60˚C, the biodiesel yield remains constant. Then, between temperatures 45 - 57˚C, the biodiesel yield increases 35 - 80%. However, at 4 h, between 54 - 60˚C, the biodiesel yield also remained constant, but the biodiesel also attained a yield of 80% at a temperature 47˚C and remained constant till the temperature decreased to 45˚C. Figure 4(c), a methanol to oil ratio of 5 w/w, as the temperature slightly increases between 45 - 60˚C, the biodiesel yield remains slightly constant. However, with a methanol to oil ratio of 10 w/w, the biodiesel yield attains 98% when the temperature is 45˚C, but as the temperature increases, the yield of biodiesel tends to decrease slightly. At a catalyst loading of 6 wt %, as the heating time increases from 1 - 4 h according to the illustration in Figure 4(d), the biodiesel yield also increases from 41 - 72%. Furthermore, at a catalyst weight of 3, biodiesel attains 90% when the time is 1 h, but as the time increases, the yield of biodiesel decreases slightly. Figure 4(e) shows that, with a catalyst loading of 3 wt %, the methanol to oil ratio increases from 5 - 8 wt/wt, the biodiesel yield also increases from 30 - 98%, and then remains constant between 9 - 10 wt/wt. Also a catalyst loading of 6 wt%, the biodiesel yield remains constant between 6 wt/wt and 7 wt/wt, but later increases as the methanol to oil ratio increases. As represented in Figure 4(f), at 4 h, the methanol to oil ratio increases from 5 - 10 wt/wt, and the biodiesel yield increases significantly from 39 - 99%. Nevertheless, at 1 h, the biodiesel yield first remains constant and later attains 98%, when the methanol to oil ratio is 9.8 wt/wt.

The kinetics studies of the reactions were carried out at optimal conditions. Figure 5 shows the conversion of biodiesel at different temperatures (45˚C, 50˚C, 55˚C, 60˚C) within the time limit of 1 - 4 h. These conversion values were employed to determine the rate constants for each temperature used, and the gradients 0.381, 0.138, 0.1019, and 0.132, each possessing an R-squared value of 0.987, 0.933, 0.934, and 0.970, as reported in Figure 6. The plots show that the reaction takes the path of a first-order reaction. In order to determine activation energy and the exponential factor, the Arrhenius equation was followed, and the obtained values are 69.48 kJ/mol and 421.257 s⁻¹, respectively, as shown in Figure 7. The value of the activation energy and exponential factor depends on the types of feedstocks, catalysts, and the oil used.

Figure 3. The graph of predicted and Actual value.

Figure 4. Response Surface Plot for the Design Variables and Biodiesel Yield.

Figure 5. The plot of biodiesel conversion against time.

Figure 6. The plot of − ln ( 1 − x ) against t .

In order to investigate the stability and reusability of the developed catalyst, the catalyst was examined under the optimum conditions of the reaction with a time of 2.5 h, a temperature of 50˚C, a methanol-to-oil ratio of 10:1, and a catalyst loading of 6 wt%. The results showed that the catalyst may be reused for four times. It could be result of the leaching or deposition of glycerol on the active site of the catalyst. The chart in Figure 8. shows the biodiesel yield after four cycle usage. The reduction in activity is attributed to these phenomena based on theoretical expectations and observed trends.

Figure 7. Arrhenius Plot of ln ( K ) against 1 / T ∗ 10 3 .

Figure 8. The reusability studies of the reaction.