A previously presented mathematical model based on a tanks-in-series model with back flow for an airlift bioreactor is extended by considering the variations of the oxygen in the gas phase and the hydrostatic pressure along the bioreactor. C The kinetic model used considers the effect of two substrates (glucose and dissolved oxygen) on the growth rate. A set of first order differential equations for the material balances of the micro-organism, glucose, product, dissolved oxygen, and oxygen in the gas phase around the hypothetical well mixed stages in the riser and the downcomer were solved simultaneously using Athena software package. The model has been validated with experimental data of gluconic acid fermentation in two different scales of internal loop airlift bioreactor, 10.5 dm(3) and 35 dm(3). The scale up effects on the performance, kinetic parameters and model predictions of gluconic acid fermentation in airlift bioreactors were studied. The model is simple enough to be used in design and scale up studies and it can be adapted to other airlift system configurations and fermentation systems other than gluconic acid fermentation. (C) 2004 Elsevier Ltd. All rights reserved.