Multi-Objective Optimization of the Digestion Tank of an Industrial Phosphoric Acid Manufacturing Process

This paper deals with multi-objective optimization of the digestion tank of an industrial phosphoric acid manufacturing process. The objective is to determine the optimal set (i.e. Pareto front) of decision variables that maximize the productivity and minimize the chemical losses. The optimization problem is a nonlinear problem involving two conflicting criteria (i.e. phosphate losses and gypsum production) along with equality and inequality constraints. The equality constraints consist of mass and energy balances, electro-neutrality equations, and thermodynamic equilibrium relations, whereas the inequality constraints are mainly given by the excess of sulfuric acid and the upper limit of the operating temperature to improve the performances of the filtration process downstream. The decision variables are defined by the distribution ratios of sulfuric acid over the sections of the tank, and the cooling heat to be removed in order to control the operating temperature within the tank. The Pitzer thermodynamic model was used to predict the two conflicting criteria and the formulated problem is solved by means of epsilon-constraint method. Compared to the real industrial experiments, the resulting optimal values of decision variables show that their implementation would significantly improve the performances of the manufacturing units.