Many heavy oil reservoirs contain discontinuous shales which act as barriers or baffles to flow. However, there is a lack of fundamental understanding about how the shale geometrical characteristics affect the reservoir performance, especially during polymer flooding of heavy oils. In this study, a series of polymer injection processes have been performed on five-spot glass micromodels with different shale geometrical characteristics that are initially saturated with the heavy oil. The available geological characteristics from one of the Iranian oilfields were considered for the construction of the flow patterns by using a controlled-laser technology. Oil recoveries as a function of pore volumes of injected fluid were determined from analysis of continuously recorded images during the experiments. We observed a clear bypassing of displacing fluid which results in premature breakthrough of injected fluid due to the shale streaks. Moreover, the results showed a decrease of oil recovery when shales' orientation, length, spacing, distance of the shale from production well, and density of shales increased. In contrast, an increase of shale discontinuity or distance of the shale streak from the injection well increased oil recovery. The obtained experimental data have also been used for developing and validating a numerical model where good matching performance has been observed between our experimental observations and simulation results. Finally, the role of connate water saturation during polymer flooding in systems containing flow barriers has been illustrated using pore level visualizations. The microscopic observations confirmed that besides the effect of shale streaks as heterogeneity in porous medium, when connate water is present, the trapped water demonstrates another source of disturbance and causes additional perturbations to the displacement interface leading to more irregular fingering patterns especially behind the shale streaks and also causes a reduction of ultimate oil recovery. This study reveals the application of glass micromodel experiments for studying the effects of barriers on oil recovery and flow patterns during EOR processes and also may provide a set of benchmark data for recovery of oil by immiscible polymer flood around discontinuous shales.