Although thermal methods have been popular and successfully applied in heavy oil recovery, they are often found to be uneconomic or impractical. Therefore, alternative production protocols are being actively pursued and interesting options are water and polymer flooding. Such techniques have been successfully tested in recent laboratory investigations, where oil recovery was found to be much higher than expected. Moreover, in some of the core scale waterflood experiments reported using 2D slabs of Bentheimer sandstone, X-ray scans performed during the flooding sequence provided evidence of an interesting new phenomenon – post breakthrough, highly dendritic water fingers were seen to thicken and coalesce, forming braided water channels and improving sweep efficiency. However, despite encouraging results, these experimental studies show that the mechanisms governing water displacing extra heavy oil are still poorly understood. This means that the optimization of this process for eventual field applications is still somewhat problematic. Ideally, a combination of two-phase flow experiments and simulations should be put in place to help inform our understanding of the process. To this end, a new fully dynamic network model is described. It has been developed to investigate unsteady state drainage floods and has been applied here in the context of waterfloods of heavy oil in oil-wet media. It has subsequently been used to investigate finger thickening during water flooding of extra-heavy oils. The displacement physics has been implemented at the pore scale and, following a successful benchmarking exercise against numerous micromodel experiments, a range of slab-scale (30cm x 30cm) simulations has been carried out and compared with the corresponding experimental observations. They reveal that the model is able to replicate finger architectures similar to those observed in the experiments. Subsequently, for the first time to our knowledge, finger thickening following water breakthrough is reproduced and interpreted. The simulator is then used to investigate the effects of different system parameters on finger swelling behaviour. Finally, a sensitivity study is performed to better understand the effects of different system variables upon the sweep efficiency, the displacement front stability and unsteady-state relative permeability.