This paper considers the theoretical operation of a novel wall-mounted oscillating water column wave energy device designed to be resonant over a broad range of frequencies. A curved duct with a submerged opening in a vertical wall is partitioned into a number of separate narrow channels of uniform width using thin annular baffles. Each channel connects the submerged opening to its own internal free surface whose rise and fall drives the air enclosed above through a Wells-type turbine through which energy is harvested. The different channel lengths within the duct encourages, when subjected to forcing from incident waves, resonance across a range of frequencies. The two-dimensional problem described in this work is analysed using classical linearised water wave theory and the geometric complexity of the partitioned duct is simplified by homogenisation. This allows the solution to the water wave problem to be reduced to a scalar integral equation whose solution is approximated using a standard numerical method. It is shown that it is possible, even with the most basic choice of turbine power take-off strategies, to achieve efficiencies close to 100% across much of the range of frequencies defined by the resonance associated with the longest and shortest channels of the device. Viscous damping within the channels is shown to have a negligible effect for practical configurations.