The objective of this research study is to be able to scale-up and optimize aerobic fermentation processes via computer simulations. As an example the production of penicillin by P. chrysogenum is studied. In vivo kinetics of the cell can be understood by conducting stimulus response and scale down experiments. These experiments provide dynamic information that can be used to estimate parameters of enzyme kinetic models. The transport phenomena inside the bioreactor can by understood by solving hydrodynamic model using computational fluid dynamics (CFD). Thus, with information from intracellular and extracellular environments, an integrated model is solved using CFD. In these simulations, the multiphase flow and transport phenomena taking place inside the bioreactor are simulated, and integrated with the microbial reaction kinetics. The micro-organisms inside the reactor are followed along their trajectories, where they experience a changing environment. The dynamic response of the cells to this environment dictates the productivity and selectivity of the cells. By simulating both the flow in the reactor and the response of the cells, the entire process inside the bioreactor can be assessed and scaled-up and optimization can be done without the need of costly experiments, both in time and financial resources.