Here, r1 and r1;r2 and r2 are the rate constants for the
reversible formation of complex C1, acylated enzyme and
by product glycerol respectively in the first step of biodiesel
formation. r3 and r3;r4 and r4 are the rate constants for
the reversible formation of complex C2 and biodiesel formation
respectively in the final step. For the inhibition reaction,
r5 and r5 are the rate constants for the reversible formation
of dead-end complex C3.
(A3) As without stirring, the rate of transesterification reaction is
very slow and incomplete due to mass transfer resistance
[26,47], so the effect of stirring is included in the reaction
kinetics in a logistic fashion as earlier model by the two
expressions, ksxB 1 xB
Bmax and ksxC3 1 xC3
C3max , where C3max
is the maximum concentration of dead-end complex.
We denote the concentration of TG; E; AcE; C1; C2; C3; AL; BD and
GL as xT ; xE; xAcE; xC1; xC2; xC3; xA; xB and xG respectively. Now from the
above assumptions with the above reaction mechanism followed
by law of mass action we can formulate the set of differential equations
given below:
dxE