Estimation of kinetic coefficients in micro-reactors for biodiesel synthesis: Bayesian inference with reduced mass transfer model

Abstract

High yields in the production of biodiesel at very short residence times can be obtained by means of micro-reactors technology. The theoretical study of the reaction mechanisms involved in biodiesel synthesis in micro-reactors is crucial in achieving adequate design conditions towards maximizing biodiesel production. Such a physico-chemical phenomenon involves complex liquid–liquid flow and mass transfer processes, besides the transesterification reaction, and the determination of the kinetic coefficients is essential in using the mathematical models for the design of the micro-reactors. In this work, a nonlinear coupled mathematical model of first-order ordinary differential equations has been developed, using the Coupled Integral Equations Approach (CIEA) for model reduction, starting from a diffusive-convective-reactive three-dimensional mathematical model that describes the local species concentrations involved in the biodiesel synthesis. The ODEs system is numerically solved using the NDSolve routine of the Mathematica platform. The Markov Chain Monte Carlo method (MCMC) is employed in solving the inverse problem to estimate the kinetic coefficients, using synthetic experimental data with low conversion rates, which maximize the presence of intermediate species and increase the sensitivity of the problem to the desired parameters. The results presented indicate that the CIEA in combination with the MCMC statistical inference yield an efficient and robust combination for the direct - inverse analysis of such reactive mass transfer problems.