Although the unconventional gas has accounted for 40% of the recoverable resource of natural gas, its production contributed only 14% of nature gas supply in 2010. This share of unconventional gas in nature gas provision is expected to rise to 21% and 32% in 2020 and 2035, respectively [1]. To predict the gas permeability through ultra-tight porous media, gas rarefaction effect which enhances permeability should be taken into account. In this work, gas flows through samples of porous media are directly simulated by solving the BGK kinetic equation [2] using Discrete Velocity Method (DVM) and lattice Boltzmann method (LBM) for a wide range of the Knudsen number. While the LBM cannot capture rarefaction effect, the results indicate that the resolution of the velocity grid has little influence on the DVM results for complex geometry, even in the free molecular flow regime
