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In this work, phonon transport in two-dimensional (2D) porous silicon structures with aligned pores is investigated by Monte Carlo simulations considering the frequency-dependent phonon mean free paths (MFPs). A boundary condition based on the periodic heat flux with constant virtual wall temperature is developed for the studied periodic structures. Such periodic boundary conditions enable the simulation of the lattice thermal conductivities with a minimum computational domain. For the 2D case, it is found that phonon size effects caused by the periodically arranged pores can be remarkable even when the pore size and spacing are much larger than the averaged phonon MFPs. Our results show the importance of considering the frequency dependence of phonon MFPs in the analysis of micro- and nanostructured materials.