In this work, we investigated whether a series of nanopores connected by channels can be used to separate polymer mixtures by molecular size. We conducted multiscale coarse-grained simulations of semiflexible polymers driven through such a device. Polymers were modelled as chains of beads near the nanoporesand as single particles in the bulk of the channels. Since polymers rarely escape back into the bulk of the channels after coming sufficiently close to the nanopores, the more computationally expensive simulations near the pores were decoupled from those in the bulk. The distribution of polymer positions after many translocations was deduced mathematically from simulations across a single nanopore-channel pair, under the reasonable assumption of identical and independent dynamics in each channel and each nanopore. Our results reveal rich polymer dynamics in the the nanopore-channel device, and suggest that it can indeed produce polymer separation. As expected, the mean time to translocate across a single nanopore increases with chain length. Conversely, the mean time to cross the channels from one nanopore to the next decreases with chain length, as smaller chains explore more of the channel volume between translocations. As such, the time between translocations is a function of the length and width of the channels. Depending on the channel dimensions, polymers are sorted by increasing length, decreasing length, or non-monotonically by length such that polymers of an intermediate size emerge first. [J. Chem. Phys. 149, 174903 (2018); https://doi.org/10.1063/1.5037449]