An Eulerian-Eulerian-Lagrangian hybrid model for the simulation of emulsions in stirred tank reactors (STR) is presented. Emulsions are widely used in chemical processes. Understanding the drop size distribution (DSD) is important for emulsions as it affects heat and mass transfer. Droplet breakup and droplet coalescence processes are the main phenomena, which affect DSD. In the present thesis, we mainly focus on the effect of the fluid dynamics (e.g. turbulent dissipation rate) on breakup and coalescence processes, which subsequently determine DSD. First, we developed a correlation for the local Sauter mean diameter based on local fluid parameters like the local shear rate. The experiment was executed in a Taylor-Couette flow device as it shows a well-defined flow pattern compared to STR. Second, we introduced a novel breakup model based on the developed correlation. This method was coupled with an Eulerian-Eulerian-Lagrangian approach to compute the liquid-liquid DSD in STR. Furthermore, coalescence models were included besides the breakup model separately, either implicitly or explicitly. We applied these models on several experimental cases from the literature. In general the simulated results were in a good agreement with the experimental data. In addition, we investigated the common scale-up rules in the STRs numerically by using the Eulerian-Eulerian-Lagrangian model, where the computed results are in accordance with the data from literature.