The demand for petroleum is expected to increase in the coming decades, while the production of petroleum from subsurface reservoirs is becoming increasingly complex. To meet the demand petroleum reservoirs should be operated more efficiently. Physics-based petroleum reservoir models that describe the flow in subsurface porous media can play an important role here. In this thesis possibilities are investigated to determine on one hand models with a complexity that is suitable for model-based operation (i.e. the relevant dynamic processes can be adequately described), and on the other hand models that only contain parameters that can be validated by measurements (in this thesis the pressure and phase-rate measurements in the wells). The most relevant dynamics of the model are determined by the controllability and observability properties. These indicate that reservoir models behave as models of much lower order than the currently used models, and that reduced-order reservoir models should focus for fixed well positions on correctly modeling the fluid front(s). In the second part identifiability and structural identifiability have been quantified and used to determine which (physical) model parameters can be reliably estimated from measurement data. From the analysis it was concluded that the parameters of reservoir models are not identifiable from production measurements and that they are largely based on qualitative geological information. Pressure measurements only contain information about grid block permeabilities in an area close to the wells in which is measured, and phase-rate measurements contain after water breakthrough only information about grid block permeabilities in the area between the injection and production wells. This supports the need to use information of other measurement types, such that better model-based decisions can be taken to make the operation of petroleum reservoirs more efficient.