**Author details**

= - ( ) <sup>M</sup> 2 3

> = ( ) <sup>G</sup> 3

= ++ ( ) <sup>E</sup> 123

dC W

.r r

r

rrr

The differential equations system was integrated using the Euler Method. The optimization

Figure 7 shows the concentration of fatty acid methyl ester (FAME) *versus* time (h) on the transesterification of WCO with methanol. The solid line represents the model fitted to the data points. It was observed that the kinetic model fits experimental concentration data quite well. The model parameters, k1, k2 and k3, have got the value of 0.00979, 0.01348 and 0.01956

.mol-1.h-1.gcat-1, respectively. It was observed that k1<k2<k3, which can be explained due to the molecular size of monoglycerides, diglycerides and triglycerides and due to the textural characteristics of PW-NH2-SBA-15. The size of monoglycerides is smaller than that of digly‐ cerides and triglycerides. Consequently, it is expected that, near the active sites of catalyst, the amount of monoglycerides is higher than the amount of diglycerides and triglycerides. As the reaction rate is dependent on reactant concentration, a high concentration of monoglycerides

0 20 40 60 80

Time (h)

Biodiesel production from WCO with methanol was carried out over tungstophosphoric acid immobilized on SBA-15 by grafting technique, at 60°C. After PW immobilization, the mor‐

dt V (7)

dt V (8)

dt V (9)

dC W

dC W

was carried out by the *SOLVER* routine in a *Microsoft Excel* spreadsheet.

dm6

leads to high reaction rates.

296 Biofuels - Status and Perspective

**5. Conclusions**

phology of the support remained.

0

0,1

0,2

[FAME] (mol.dm-3)

**Figure 7.** Concentration of FAME (mol.dm-3) versus time (h).

0,3

M. Caiado, A. Tropecêlo and J.E. Castanheiro\*

\*Address all correspondence to: jefc@uevora.pt

CQE, Departamento de Química, Universidade de Évora, Évora, Portugal
