A new model for phosphate column flotation is presented which for the first time relates the effects of operating variables such as frother concentration on column performance. This is a hybrid model that combines a first-principles model with artificial neural networks. The first-principles model is obtained from material balances on both phosphate particles and gangue (undesired material containing mostly silica). First-order rates of net attachment are assumed for both. Artificial neural networks relate the attachment rate constants to the operating variables. Experiments were conducted in a 6-in.-dia. (152-mm-dia.) laboratory column to provide data for neural network training and model validation. The model successfully predicts the effects of frother concentration, particle size, air flow rate and bubble diameter on grade and recovery.