A mathematical model for cellulase production by Trichoderma reesei RUT-C30 grown in a cellulose medium with lactose as fed batch in an airlift reactor is proposed. To describe adequately the mass transfer between the air bubbles and the broth, it uses computational fluid dynamics (CFD) including multiphase Eulerian–Eulerian formulation, with a detailed description of the bubble size distribution through the use of the population balance model (PBM) and the class method (CM). The kinetics of the biomass growth is further coupled to the fluid flow conditions using partial differential equations for all the species involved, providing detailed information of important reactor conditions such as the distribution of oxygen, cellulose, and the shear stress within the reactor over the entire period of fermentation. Predicted results agree well with the available overall measurements for a typical fed-batch operation and detailed profiles of the predicted concentration fields are discussed from an engineering viewpoint. Biotechnol. Bioeng. 2012; 109:2025–2038. © 2012 Wiley Periodicals, Inc.