The carrier recombination in organic solar cells is investigated by numerical modeling to understand the weak dependence of the open-circuit voltage on the workfunction of the electrodes. In Ohmic contact structures, photocarriers recombine predominantly with dark carriers diffused from the electrode into the semiconductor. Such dark carrier recombination becomes the main limit of power conversion efficiency and open-circuit voltage. For a given semiconductor decreasing the workfunction difference of the electrodes reduces simultaneously the dark carrier recombination and the flat band voltage. The balance between these two opposite factors gives a nearly constant open-circuit voltage. In an ideal bilayer structure there is no dark carrier recombination and the efficiency is demonstrated to be 60% higher than single layer blend.