This work concerns a fundamental understanding of how heterogeneities induced by flow barriers and connate water affect the displacement efficiency of polymer floods, which has rarely been studied in the available literature. Here, a series of water/polymer injection experiments to heavy oil performed on five-spot glass micromodels containing randomly distributed shale structures is presented. It has been found that macroscopic efficiency of polymer flooding majorly depends on flow barriers distribution/configuration; shale content and geometrical characteristics; presence of connate water and wettability of medium. Microscopic pictures revealed that the main parts of connate water were trapped in some pores/throats near and especially behind the shale streaks; also, presence of connate water causes a reduction of sweep efficiency due to premature breakthrough of displacing fluid in an oil-wet media. In absence of connate water, polymer solution could linger and stick to the pore walls to delay the time for a polymer to channel to the production site. Results of this work disclose requirements for a detailed geologic study of barrier size and distribution for successful design of EOR processes in heterogeneous reservoirs.