Comparison of orthogonal collocation, control vector parameterization and multiple shooting for optimization of acid recovery in batch electrodialysis

From the solid waste of palm oil, i.e. empty fruit bunch (EFB), sugar can be produced through the hydrolysis process by using hydrochloric acid (HCl). The acid must be separated from the sugar to yield pure sugar and to reduce the processing costs by recovering and recycling the hydrochloric acid. Electrodialysis (ED) which is a membrane separation characterized by an electrical field orthogonal to the membrane, is a feasible method for acid recovery. Since, it has the capability of separated ionic chemicals from nonionic chemicals in process or waste streams to achieve product purity. Optimum operating conditions are very important for the electrodialysis process to ensure maximum ED performances. The Nernst-Planck derived relationship is used to build the dynamic model which contains of set ordinary differential equations (ODE). The dynamic optimization problem is solved using a direct method, i.e. orthogonal collocation (OC), control vector parameterization (CVP) and multiple shooting (MS). The economic function which is intended to minimize energy consumption for achieving 99% of acid recovery is considered as objective function. The performances of those direct-based dynamic optimization techniques which are the accuracy and the efficiency in optimal computation are compared and analyzed. The accuracy in searching optimal solution is based on the minimum energy consumption and maximum acid recovery obtained. While, the efficiency of the dynamic optimization’s computation is evaluated by CPU time consumed. The optimization results shows that the control trajectories obtained from OC able to generate the lowest energy consumption with maximum acid recovery at the acceptable CPU time.