A numerical method system to estimate the permeability of sand sediments, at a microscopic scale, was developed. Initially, 3D geometrical representations of the sand grains are reconstructed from a series of 2D X-ray CT scans of real sand grains. 2D cross-sectional slices of the grain outlines are combined together to produce 3D objects via spherical harmonics series expansions. Then, the reconstructed sand grains are packed randomly inside a cubic, microscopic, domain by a combination of a growth method and a simulated annealing method to achieve a predefined porosity. Finally, a single-phase water flow within the domain was simulated numerically, using the lattice Boltzmann method. The calculated permeability of these systems compares well with the values provided by conventional theoretical models. One of the contributions of this study is to show that it is possible to predict the permeability of sand sediments of variable porosities, using sand grains from CT images with changing size distributions and orientations.