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

Abstract

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 ® 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 × 10 −6 (k 1f), 1.137 × 10 −6 (k 2f) and 3.134 × 10 −6 (k 3f); and for the reverse reactions were 0.202 × 10 −6 (k 1r), 0.884 × 10 −6 (k 2r) and 0.219 × 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.

Simultaneous Transfer of Na+, K+, and Fe2+ Ions During Salting of Precooked Mushroom (Agaricus bisporus): Mathematical Modeling, Optimization, and Experimental Validation

“…Regarding the mathematical modeling, the percentage error values for Fe 2+ can be considered acceptable. Angilelli et al, 18 Galvan et al, 16 and Ferrari and Hubinger 28 reported percentage error values of up to 11.24, 16.96 and 25.00%, respectively.…”

“…The finite element method (FEM) is used to solve differential equations using a variational formulation or residual weight procedure, where a partial differential equation is transformed into a system of ordinary differential equations for a time dependent problem. 16 Several authors 17,18 have used finite element simulation coupled with optimization methods and desirability functions to determine mass transfer parameters.…”

Evaluation of the Oxidation Degradation Process of Biodiesel via 1H NMR Spectroscopy

“…Howell et al 30 investigated the steps of the castor oil degradation. Recently, the technique was applied to study the transesterification process of the biodiesel production, monitoring the reaction products as fatty acid methyl esters (FAME), triglycerides (TG), monoglycerides (MG) and diglycerides (DG), 31 but researches using the NMR to study biodiesel degradation are not common.…”