Effect of Ultrasound Technique for Production of Biodiesel Using Enzyme as Catalyst: A Mathematical Study

As fossil fuels decline on a global scale, there is a rising interest in developing a cost-effective process for producing biodiesel from renewable sources, like Jatropha curcas plant. Enzymatic transesterification of Jatropha oil with alcohol is an effective technique to produce biodiesel. Due to mass transfer limitation between Jatropha oil and alcohol, the reaction is very slow. To overcome this we have used ultrasound frequency for excessive production of biodiesel. This article examines the impact of ultrasound frequency on the enzymatic transesterification of Jatropha oil through a mathematical model. Optimal control theory through Pontryagin Minimum Principle is employed on ultrasound to optimize frequency and improve cost-effectiveness of the system. The model’s validity is confirmed through simulated results and comparison with experimental data from the literature.