We present a model for the description of dark IV curves in midinfrared quantum well infrared photodetectors at low temperatures, in a regime where dark current is dominated by interwell tunneling. The model separates the IV curve into a low-field and a high-field region allowing us to identify the effects ascribed to miniband transport and carrier localization, respectively. At low fields the system is thought as a superlattice and described by means of a high-density correction of the Esaki-Tsu model. This approach allows us to simulate current saturation phenomena that occur at low temperatures at intermediate fields. On the other hand, high-field transport effects are described in the localized Wannier-Stark basis in order to account for tunneling and field-assisted thermionic emission effects. We then compare simulations with our measurements of the IV curves of mid-IR quantum well infrared photodetectors finding good quantitative agreement between theory and experiment.