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Nanoporous and microporous materials made from aligned cylindrical pores play important roles in present technologies and will play even bigger roles in future technologies. The insight into the phonon thermal conductivity of these materials is important and relevant in many technologies and applications. Since the mean free path of phonons can be comparable to the pore size and interpore distance, diffusion-approximation based effective medium models cannot be used to predict the thermal conductivity of these materials. Strictly speaking, the Boltzmann transport equation (BTE) must be solved to capture the ballistic nature of thermal transport; however, solving BTE in such a complex network of pores is impractical. As an alternative, we propose an approximate ballistic-diffusive microscopic effective medium model for predicting the thermal conductivity of phonons in two-dimensional nanoporous and microporous materials made from aligned cylindrical pores. The model captures the size effects due to the pore diameter and the interpore distance and reduces to diffusion-approximation based models for macroporous materials. The results are in good agreement with experimental data.