Recent developments in organic solar cells show interesting power conversion efficiencies. However, with the use of organic semiconductors and bulk heterojunction cells, many new concepts have to be introduced to understand their characteristics. Only few models investigate these new concepts, and most of them are one-dimensional only. In this work, we present a two-dimensional model based on solving the drift-diffusion equations. The model describes the generation of excitons in the donor phase of the active layer and their diffusion towards an interface between the two separate acceptor and donor domains. Then, when the exciton reaches the interface, it forms a charge transfer state which can split into free charges due to the internal potential. Finally, these free charges are transported toward the electrodes within their respective domains (electrons in acceptor domain, holes in donor domain) before being extracted. In this model, we can follow the distribution of each species and link it to the physical processes taken into account. Using the finite element method to solve the equations of the model, we simulate the effect of the bulk heterojunction morphology on photocurrent curves. We concentrate on the morphology parameters such as the mean acceptor/donor domain sizes and the roughness of,the interface between the donor and acceptor domains. Results are discussed in relation with experimental observations.