Dynamic optimization of a batch transesterification process for biodiesel production

With the advancement of studies in the field of renewable fuels, biodiesel production has received a lot of attention over the years. Biodiesel production is based on transesterification reaction between a vegetable oil containing triglycerides and a shorter chain alcohol e.g. methanol. A batch transesterification process needs tighter control on reaction temperature for achieving higher triglyceride conversion. Here, open loop control called optimal control has been employed on the transesterification kinetic model of a batch process. A multi-objective optimization problem is formulated with two objectives namely, maximization of methyl ester concentration at batch end time and minimization of final batch time. An e-constraint approach is adopted for solving the multi-objective optimization problem. Orthogonal collocation on finite elements scheme is employed to generate the optimal temperature trajectory. Under the framework of collocation method, state and control profiles have been discretized using piecewise linear Lagrange's polynomials and the control problem has got transformed into an NLP problem. fmincon solver is utilized in solving the NLP in MATLAB®. Maximum methyl ester concentration at final batch time and the minimum batch end time have been determined to be 0.8315 mol/l and 67.4 min, respectively. Optimal results have been found with two finite elements and five interior collocation points.