For a broad range of applications the most important transport property of porous media is permeability. Here we calculate the permeability and porosity of ordered sphere packs, simple, body-centered and face-centered cubic, as simple diagenetic processes reduces their pore spaces. For diagenesis we use simple geometrical models including compaction by plastic deformation, compaction by pressure solution, consolidation of cementation, consolidation by surface precipitation and temporary consolidation by capillary action until porosity becomes isolated. For flow simulations at selected porosity levels we use the lattice-Boltzmann method with a 15-speed and 19-speed models on three dimensional lattices. For validation purposes, the lattice-Boltzmann method is compared against an explicit finite-difference method for incompressible flow in simpler geometries. Simulating slow creeping flow through three-dimensional channels of different polygonal cross sections and three-dimensional porous structures of intermediate complexity checked the accuracy of the lattice-Boltzmann scheme used. We explore pore space microstructure transitions and universal character of the permeability-porosity relationships obtained.