Different approaches for the dynamic model for the production of biodiesel

[Display omitted] •Nonlinear model with variant parameters of the transesterification reaction.•Takagi–Sugeno model with material and energy balance for the transesterification reaction.•Simulation of a nonlinear mathematical model for the production of biodiesel. The industrial production of biodiesel requires mathematical models that adjust to real conditions. The present study is a proposal for the design and validation of a mathematical model for the oil transesterification reaction, representing a promising alternative that contributes to making the biodiesel production process more efficient. This proposal centers on the presentation of analytical models capable of simulating the real batch reactor scenarios in which the transesterification process is carried out. The objective of this study was to design a dynamic model for the batch reactor system, using reaction kinetics and the heat and mass balance, as well as demonstrating the different approaches, such as Takagi–Sugeno modeling and the linear approach. Furthermore, the physical and kinetic parameters were considered a time variant variable. The Takagi–Sugeno (TS) model is presented as a convex combination of linear models through the nonlinearities represented below, a combination which enables the testing of both the simplicity versus complexity of the nonlinear systems and their functionality, via the application of an estimator. The linearization of the nonlinear model was undertaken as a simple representation of the system. The different models were simulated and the results compared with those reported in the literature in order to confirm their applicability. Finally, an experimental validation is presented in order to demonstrate the utility of the models which could be used in processes for optimizing control in the production of biodiesel.