Detailed measurements of multiphase flows that prevail in bioreactors tell us that different transport mechanisms are dominating on different observation scales. The consequence in terms of reactor modeling is that the processes on different scales can be treated independently. A three-dimensional, dynamical model is presented that can be used to describe bubble column bioreactors on the reactor scale. It is based on the Navier-Stokes equation system. On the next smaller scale, the dynamics of the gas phase is described in a Lagrangian way, by tracking many bubble clusters or bubbles simultaneously on their way through the reactor. The model is capable of describing bubble columns of different size and can thus be used for scale-up. Its performance is demonstrated with a production-scale beer fermenter.