Optimal Control of Batch Production of Biodiesel Fuel under Uncertainty

2014-02-24T00:00:00Z (GMT) by Pahola T. Benavides Gallego
The continuing depletion of fossil fuel reserves and the increasing environmental concerns have encouraged engineers and scientists to look for cleaner alternatives, such as renewable fuels that can reduce the negative impact of conventional fuels. Therefore, biodiesel has become one of the best candidates for the replacement of petroleum-based diesel due to its similarities in properties and performance. One of the pathways to produce biodiesel is the transesterification reaction of triglycerides from vegetable oils and short-chain alcohols (e.g. ethanol or methanol). Two operating modes can be used for production of biodiesel: continuous and batch. In the first part of this research, a comparison between these two processes was studied based on their performance operation and economics. It was found that batch processes can be an attractive option over continuous processes. However, modeling and controlling batch processes is complex due to their dynamic nature and become more challenging while incorporating uncertainties in process parameters. In biodiesel production, one of the most influential uncertainties is the feed composition because the percentage and type of triglycerides vary considerably, therefore, variability in the initial concentration of triglycerides was considered in this work. These uncertainties lead into dynamic uncertainties which can be represented using stochastic differential equations in terms of stochastic processes. In this research, batch production of biodiesel was improved through dynamic optimization also known as optimal control under deterministic and stochastic conditions. This strategy consists of finding a control policy (e.g. reactor temperature) that change with time in order to maximize or minimize a performance index, namely, concentration, reaction time, and profit. Due to the time dependent nature of these processes, optimal designs and control problems involve differential and algebraic equations that can be difficult to solve. In this research, a new methodology that involves the application of NLP techniques, maximum principle as well Ito processes, Ito calculus and the stochastic maximum principle (i.e. stochastic optimal control) was presented for the solution of the proposed problems.