Mathematical Modeling of the Transesterification Reaction by Finite Elements: Optimization of Kinetic Parameters Using the Simplex Sequential Method

The use of biodiesel as fuel has been presented as a viable alternative in the search for renewable energies. It can be produced from the transesterification reaction of vegetable oils with methanol in the presence of sodium or potassium hydroxide as catalysts. In the present research, the transesterification reaction of soybean oil was modeled considering the three steps of the direct and reverse reactions following a second order general kinetics by the finite element method using the COMSOL Multiphysics (R) software. The values of rate constants were determined using the simplex optimization method coupled with the desirability functions. The optimized rate constants for the forward reactions were 0.250 x 10(-6) (k(1f)), 1.137 x 10(-6) (k(2f)) and 3.134 x 10(-6) (k(3f)); and for the reverse reactions were 0.202 x 10(-6) (k(1r)), 0.884 x 10(-6) (k(2r)) and 0.219 x 10(-6) (k(3r)) all in m(3) mol(-1) s(-1). The kinetic model proposed for the reaction can be simulated by the finite element method (FEM) under realistic conditions.