| A hybrid model for a flotation column is presented which combines a first-principles model with artificial neural networks. The first-principles model is derived by making material balances on both phosphate and silica particles in the slurry phase. Neural networks are used to relate the model parameters with operating variables such as particle size, superficial air velocity, frother concentration, collector and extender concentration, and pH. One-level and two-level hybrid modeling structures are compared and it is shown that the two-level structure offers significant advantages over the other. Finally, a sequential run-to run optimization algorithm is developed which combines the hybrid model with an optimization technique. The algorithm guides the changes in the manipulated variables after each experiment to determine the optimal column conditions. Designed experiments were performed in a lab scale column to generate data for the initial training of the neural networks. |
