Indirect Measurement of Variables in a Heterogeneous Reaction for Biodiesel Production

Abstract

This research focuses on the development of a state observer for performing indirect measurements of the main variables involved in the soybean oil transesterification reaction with a guishe biochar-based heterogeneous catalyst; the studied reaction takes place in a batch reactor. The mathematical model required for the observer design includes the triglycerides’ conversion rate, and the reaction temperature. Since these variables are represented by nonlinear differential equations, the model is linearized around an operation point; after that, the pole placement and linear quadratic regulator (LQR) methods are considered for calculating the observer gain vector L(x). Then, the estimation of the conversion rate and the reaction temperature provided by the observer are used to indirectly measure other variables such as esters, alcohol, and byproducts. The observer performance is evaluated with three error indexes considering initial condition variations up to 30%. With both methods, a fast convergence (less than 3 h in the worst case) of the observer is remarked.