Fig. 8: Relationship between the absolute temperature and the
pseudo second-order initial extraction rate h for the extraction of oil
from Irvingia gabonensis kernel at particles size of 0.5mm.
Obviously, the initial extraction rate, C1, increased
with temperature, so did the constant that is related to maximum
extraction yield, C2. Similarly, the initial extraction
rate, h, extraction capacity, Cs, and the second-order
rate constant, k, all increased with temperature. These findings were in
line with the findings of Rakotondramasy et al. [42] for the
solid–liquid extraction of protopine from Fumariaofficinalis L.
It is important to note that when the temperature was kept at 308K, for
a particle size of 0.5 mm, the initial extraction rate
C1 for hyperbolic model was 6.21
min-1. This value was slightly higher than
5.15gL-1 min-1 obtained for the
initial extraction rate in pseudo second-order model. On the other hand,
the constant related to maximum extraction yield C2, for
hyperbolic model, at the same constant temperature of 308 K and 0.5 mm
particle size was 0.085 min-1, while the second-order
rate constant, k was 0.0011 Lg-1min-1. However, the extraction capacity,
Cs, at the same temperature and particle size was
68.97gL-1. This value was very close to pseudo
second-order model calculated oil yield, Ct, 68.52 wt.
%. This is an indication of the fitting of the second-order model for
the extraction of oil from IGK.
Activation energy determination
The linearized Arrhenius equation [Equation (14)], was used to
determine the relationship between k and T, the k0 and
Ea. This was done by plotting In k versus 1000/T
for pseudo second-order kinetic model (Fig. 9). The plot shows that the
rate constant increases with the increases in temperature. However, a
modified form of Arrhenius equation [Equation (25)] was used to
determine the relationship between C2 and T, the
k0 and Ea for hyperbolic kinetic model.
Like the pseudo second-order model, this was carried out by plotting In
C2 against 1000/T (Fig. 10).
\(\text{In\ }C_{2}\ =In\ k_{0}\ +\ \left(-\ \frac{E_{a}}{R}\ \bullet\ \frac{1}{T}\right)\)(25)
Using Equations 14 and 25, activation energies were calculated from the
slopes and the values of temperature independent factors calculated from
the intercept for the pseudo second-order (Fig. 9) and hyperbolic (Fig.
10) models, respectively. The relationships for the activation energy of
extractions at 328K and 2.5 mm particle size, modeled using pseudo
second-order and hyperbolic models, are given by Equations (26) and
(27), respectively.
\(k\ =\ k_{0}\text{\ exp\ }\left(\frac{-11900}{8.314\ \times 328}\right)\)(26)
\(C_{2}\ =\ k_{0}\text{\ exp}\left(\frac{-18790}{8.314\ \times 328}\right)\)(27)
Their respective R2 values for pseudo second-order and
hyperbolic models were 0.9582 and 0.9453.
In both models, the activation energies were positive, which is an
indication that the extraction of oil from IGK is an endothermic
process. In the case of pseudo second-order models, the activation
energies for average particles size of 0.5, 1.0, 1.5, 2.0 and 2.5 mm
were 5.49, 5.57, 5.79, 6.11, and 11.90 kJ/mol, respectively. Similarly,
for hyperbolic model, the activation energies at these average particle
sizes were 7.03, 11.03, 12.52, 16.63 and 18.79 kJ/mol, respectively.
These results show that irrespective of the kinetic model used, the rate
constants were dependent on the temperature, and they increased with
increase in temperature. Also, the rate constants for the models were
more temperature sensitive for larger particles size than for the
smaller ones. This is manifested in the higher values of the activation
energies obtained for larger average particles sizes. This observation
is in close agreement to that obtained by Bucic-Kojic et al. [43]
for the extraction of polyphenols from grape seeds. Thus, the influence
of temperature on the extraction rate constant was more pronounce in
larger particles size, than in the smaller ones. Finally, it could be
seen that the activation energy values obtained for hyperbolic model at
different particles size diameters, were higher than those obtained for
pseudo second-order model. This could be attributed to the higher values
of the rate constant obtained for hyperbolic model, compared to those
obtained for pseudo second-order model [18].
[CHART]