Kinetic analysis for the esterification of high free fatty acid feedstocks with a structural identifiability approach

Esterification is the first step in the biodiesel production process from low cost feedstock, which is typically characterized by its high content (>5%) of free fatty acids (FFAs). Although multiple attempts have been made to describe the kinetics of the esterification process for this feedstock, there is no consensus regarding which model is the most suitable. In this paper, two models were evaluated as candidates to describe the esterification of grease trap wastes, a synthetic mixture of tallow fat and canola oil, and oleic acid, which all have a high degree of acidity. The first model considers a pseudo-first order reaction, whereas the second model considers the reversibility of the reaction. All parameters involved in these models are structurally identifiable and are estimated with the Levenberg–Marquardt method. A statistical analysis based on Akaike's weights show that the reversible model provides the best fit for all experimental runs compared to the first order model. This result was obtained from variations in catalyst loading and moisture content. Practical applications: The design and implementation of monitoring algorithms or robust control laws for a process carried out in a continuous stirred tank reactor (CSTR) require the knowledge of its dynamical mathematical model that contains a kinetic term. In the particular case of the esterification reactions for feedstock with high content of FFAs developed in the presence of homogeneous acid catalyst, there exists a discrepancy on the mathematical structure of such kinetic term. In this study we perform some batch experiments, considering industrial reagent grade alcohols, to deduce which model (among the two simplest kinetic models) better describes the esterification of oleic acid, grease trap wastes and a mixture of tallow fat and canola oil. Then, the results obtained from this basic research could be applied if monitoring-regulation tasks are required for the esterification of the feedstock considered herein when such esterification be carried out in a CSTR under industrial conditions. Low cost feedstock has been esterified under variations in catalyst loading and initial moisture content. Two kinetic models were used to fit experimental data and a structural identifiability analysis has been conducted for each parameter contained in these models. According with Akaike's weights, the kinetic model that considers the reversibility of the esterification reaction provides the best fit for all experimental runs.