The growth of red marine alga Porphyridium sp. cultivated in an internal loop airlift (ALR) photobioreactor was simulated. The model proposed integrates a dynamic formulation of the kinetics of photosynthesis, photoinhibition, and the fluid dynamics of the ALR, including shear stress effects on the kinetics of growth. The kinetic parameters obtained previously for a system under defined light/dark cycles were used, and satisfactory agreement was found. The maintenance term was modified to take into account the detrimental effects of shear stress in the bioreactor on the rate of growth. A hybrid method for approximate solution of the equations is proposed. The conditions of gas flow rate and illuminance required for positive growth were found. This is the first mathematical model that predicts the effect of gas flow rate, column height, column diameter, and cross-sectional areas on the productivity of a photosynthetic process in an airlift bioreactor. Extrapolations done using the model indicate the possibility of predicting the optimal diameter for an assembly of ALR photobioreactors. (C) 2004 Elsevier Ltd. All rights reserved.