Fig. 12: Relationship between the initial extraction rate,In C1 and temperature, for oil extraction fromIrvingia gabonensis kernel at 2.5 mm particles size, using hyperbolic model.
For the pseudo second order model, Fig. 13 shows the relationship that exists between extraction capacity, Cs and temperature at particles size of 2.5 mm and the plot lead to Eq. (30).
\(C_{s}\ =0.33T\ -59.84\) (30)
By the combination of equations (13), (28), and (30), the equation that describes the development of Ct versus time and temperature model for pseudo second-order model can be written as Equation (31).
\(C_{t}\ =\ \frac{t}{k_{0}\text{\ exp}\left(\frac{2942}{T}\right)\ +\ \left(\frac{t}{0.33T\ -59.84}\right)}\)(31)
This equation shows the model for the evaluation of oil yield during solvent extraction of oil from Irvingia gabonensis kernel, for different temperature at any given time, using pseudo second-order model. This equation simply explains that the longer the time of extraction and the higher the extraction temperature are, the higher would be the concentration \(C_{t}.\)
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Fig. 13: Relationship between the saturated extraction capacity, \(\mathbf{C}_{\mathbf{s}}\), and temperature, for the extraction of oil from Irvingia gabonensis kernel at 2.5 mm particles size, using pseudo second order model.
Similarly, Fig. 14 shows the relationship between the constant related to maximum extraction yield C2 (min-1) and temperature at 2.5 mm particle size. The plot gives rise to equation (32).
\(C_{2}\ =0.001T\ -0.284\) (32)
The combination of equations (3), (29) and (32), the equation that describes the development of y̅ versus time and temperature model for hyperbolic model can be written as Equation (33).
\(\overset{\overline{}}{y}\ =\ \frac{k_{0}\text{\ exp}\left(\frac{2913}{T}\right)t}{1\ +\ \left(0.001T^{2}\ -0.284T\right)}\)(33)
Similarly, this equation shows the model for the evaluation of oil yield during solvent extraction of oil from Irvingia gabonensis kernel, for different temperature at any given time, using hyperbolic model.
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Fig. 14: Relationship between the constant related to maximum extraction yield, \(\mathbf{C}_{\mathbf{2}}\), and temperature, for the extraction of oil from Irvingia gabonensis kernel at 2.5 mm particles size, using Hyperbolic model.
The models represented by equations (31) and (33) for pseudo second-order and hyperbolic models, respectively, were compared with the experimental data. Fig. 15 shows the comparison between the experimental and the models calculated IGK oil yield at different particle sizes and time, for temperature of 55 °C. From the plots (Fig. 15 and Table 1), good fit between the experimental and the calculated models’ data was obtained for both pseudo second-order and hyperbolic models. This is an indication of the validity of the relationships.
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