Although the application of lipase in the production of biodiesel from vegetable oils has been thoroughly addressed in the literature, most of the studies were purely parametric. On the other hand, significant number of kinetic studies is found in the literature on the esterification of free fatty acids rather than the transesterification of vegetable oil. The industrial interest, however, is on the production of biodiesel from the triacylglyceride (oil), not the free fatty acids. The main difference between esterification of free fatty acids and transesterification of triglycerides (oils) is that in the first O-H bonds are broken, whereas in the second ester bonds are the ones that are broken. In addition, the by-product of esterification is water, whereas it is glycerol in transesterification. An attempt to model vegetable oil transesterification was done (Al-Zuhair, 2005), assuming that the reaction took place in two consecutive steps. In the first step, triglycerides are hydrolyzed to produce free fatty acids and in the second step, the free fatty acids produced in the first step are esterified to produce fatty acids methyl esters. This study combined the enzymatic kinetics models of hydrolysis of oils (Al-Zuhair et al., 2003) and esterification of FFA (Janssen et al, 1999; Krishna and Karanth, 2001). However, it was later shown that it was more accurate to assume that transesterification takes place by direct alcoholysis of the triglycerides (Al-Zuhair et al., 2007). In order to understand the reaction behavior and to propose suitable mechanismic steps, experimental determination of the separate effects of oil and methanol concentrations on the rate of enzymatic transesterification were determined. The proposed mechanism of alcoholysis of oils was based on the enzymatic hydrolysis mechanism (Bailey and Ollis, 1986) and presented by a Ping-Pong Bi Bi mechanism shown in Fig. 6.3. To account for the inhibition by alcohol, competitive inhibition was assumed when an alcohol molecule reacts with the enzyme directly to produce a dead-end enzyme-alcohol complex (E. A). And to account for the inhibition by the substrate, competitive inhibition was also assumed when a substrate molecule reacts with the acylated enzyme to produce another dead-end complex, namely, acylated enzyme-substrate complex (E-Ac. S). Based on this mechanism and assumptions, the reaction rate presented in Eq. [6.4] was derived:

where и is the initial reaction rate, V „ is the maximum reaction rate, K„ and K.

max s

are the dissociation constants for the substrate (S) and the alcohol (A), respectively, and KIS and KIA are the inhibition constants for the substrate and the alcohol, respectively. Numerical values of the parameters found in Eq. [6.4] are shown in Table 6.2 for lipases from different sources.

Equation [6.4] describes the initial reaction rate in the absence of any product inhibition, which is similar to the one proposed by Krishna and Karanth (2001) for the esterification of short-chain fatty acids with alcohol. On the other hand, Janssen et al. (1999) derived an equation to be used when the water, taken as one of the products, was assumed to inhibit the reaction. This modification was applicable when free fatty acids were considered as the substrate. However, when the substrate was the triglyceride, the product water is replaced with monoglyceride, diglyceride or glycerol. And unlike water which is usually present in the reaction medium at time zero, these products are not. Therefore, the product inhibition was neglected, especially when considering the initial rate of reaction.

6.6 Future trends