Integral Transforms Analysis of Three-Dimensional Mass Transfer in the Transesterification Process in Microreactors

Hybrid Approach in Microscale Transport Phenomena: Application to Biodiesel Synthesis in Micro-reactors

“…The findings presented are part of an ongoing collaborative research aiming to improve the design of the microreactors recently demonstrated for biodiesel synthesis [66], targeting residence times of around one minute or less. For this purpose, the hybrid approach has been employed throughout the development and design of this microfluidic system [67][68][69][70][71], then validated through experimental tests employing high speed and thermal imaging infrared cameras [72]. Advanced additive micro-manufacturing platforms were also used to propose a more economical fabrication of multiple microreactors to assemble a modular prototype [72].…”

“…Thus, the computational simulation is an important tool that helps to understand the physical-chemical phenomenon and, consequently, to determine the suitable conditions that maximize the conversion of triglycerides during the biodiesel synthesis. The mathematical model is obtained through a steady-state mass balance that considers diffusive-convectivereactive effects to describe the transesterification route for biodiesel synthesis in a microreactor of rectangular section [67][68][69][70][71][72], as represented in Figure 3. The dimensionless mass transfer equations for the species concentrations, considering second order consecutive elementary and reversible reactions preferably in the triglyceride phase, under isothermal conditions and with constant physical properties, can be written as:…”

“…where Fs are the dimensionless concentrations and the kinetic expressions for each species, Gs, are given by [69]:…”

“…while the velocity profiles for the vegetable oil and the alcohol, assumed fully developed and in laminar stratified regime, are given by [69]:…”

“…Equations ( 1) constitute a nonlinear system of three-dimensional partial differential equations, coupled through the kinetic expressions for each species, which has been solved by the Generalized Integral Transform Technique (GITT) [69][70]. First of all, in order to homogenize the boundary condition of the alcohol species in the Y direction and ensure improved convergence behavior, a simple filter is proposed as:…”