A procedure of estimating the absolute rock permeability directly from a microscopic 3D rock image has been developed. Both computer-tomography and computer- generated images of reconstructed reservoir rock samples can be used as input. A physics-based depositional model serves to reconstruct natural sedimentary rock, and generate 3D images of the pore space at an arbitrary resolution. This model provides a detailed microstructure of the rock, and makes it possible to calculate the steady state velocity field in the single-phase fluid flow. In particular, using our model, one can analyze unconsolidated rocks whose micro-tomographic images cannot be obtained. The lattice-Boltzmann method is used to simulate viscous fluid flow in the pore space of natural and computer-generated sandstone samples. Therefore, the permeability is calculated directly from the sample images without converting them into a pore network or solving Stokes' equation of creeping flow. We have studied the effect of compaction and various styles of cementation on the microstructure and permeability of reservoir rock. The calculated permeability is compared with the Kozeny-Carman formula and experimental data.