Study of transport properties of low permeable sedimentary clay formations is of growing interest in exploration of non-conventional resources, and for long term radioactive waste repositories where these formations play the role of a natural shield which prevents the spreading of radioactive materials in the environment. Recent advances in imaging techniques allow to obtain 3D volume of compacted clay sample with pixel size of order of few nano-meters which enables us to explore transport properties of these media by means of numerical simulation. In our study, the Lattice Boltzmann Model (LBM) is applied to simulate fluid flow inside the 3D image of a compacted illite sample to explore its transport properties. The impact of different image segmentation methods applied to treat the raw data on the numerical results is addressed. Because of the nano-metric pore size, various physical phenomena may influence fluid flow. In this study, we consider the influence of gas slippage effect (the Klinkenberg effect) on the permeability. The numerically obtained results are compared with experimental data obtained for a reconstructed compacted illite sample. If the original geometry is not strongly modified by the applied image segmentation method, the numerically calculated Klinkenberg factor follows well existing trends and provides predictions close to the experimental values.