The reduction in permeability of sediments due to blockages caused by the trapping of suspended particles is a common concern for the extraction processes of oil or natural gas. In this study, the effect of trapped fine particles in sand sediments is studied numerically using a three-dimensional lattice Boltzmann method. The geometrical properties of larger, immobile, sand grains are digitally extracted by the spherical harmonics series expansions of CT scans of real sand grains. The migrating fine particles are assumed to be spherical in shape with their volumes following a log-normal distribution. These fine particles, together with larger frame sands, are positioned, without overlapping, within a microscopic, cubic, domain with periodic boundaries. The remaining empty volume is filled with water and imposing a pressure gradient simulates the flow of fluid through the sediment. As a result of fine particles becoming trapped by the frame sand, the initial porosity of which is 0.589, the absolute permeability of the system is reduced by approximately 60-90 %, corresponding to fine particle saturations of 0.15-0.29, respectively. The permeability change due to the trapping of fine particles is also modelled theoretically using not only volume saturations but also specific surface areas of both the frame sands and the fine particles with a coefficient of proportionality.