In this thesis the basic properties of the lattice- Boltzmann method (LBM) are introduced. Also, a particle model used in combination with LBM is presented, and the combined model is then applied to ink propagation in samples of paper. Simulation geometries were acquired with two different methods, namely confocal microscopy and X-ray tomography. The effect of simulation parameters and paper properties on ink propagation was considered. Promising results were acquired with both image acquiring techniques, but for a better consistency between simulations and experiments the methods should be combined so as to get images that include the full thickness of the sample together with the ink distribution. Adjustment of simulation parameters in confocal microscopy geometries showed that diffusion coefficient was the main parameter that explained the form of the ink distribution curves. This suggests an intuitively expected result: ink tends to move with the major flow channels unless diffusion is strong enough to separate enough of ink particles from the flow. Simulations done in samples of varying sizing gave incoherent results. One simulation series was in agreement with experimental results, while another was not. Possible explanations to this dilemma includes effects of paper heterogeneity on the results, differencies in paper properties in macroscopically different parts of the paper, and chemical effects not taken into consideration in the model. We can conclude however that simulations with the methods applied here qualitatively capture the main features of the settling in paper. In part this conclusion is based in the fact that the experimentally observed division into two separate components in the distribution of attached ink pigments was also realised in the simulations.