Nuclear Magnetic Resonance (NMR) is an increasingly popular well-logging tool in petroleum industry because it is the only tool that attempts to estimate formation permeability. In this paper, spatially correlated porous media are generated. Permeabilities of these media are computed by the lattice Boltzmann method. NMR relaxation responses are simulated by a random walk technique and formation factors are computed by solving a Laplacian equation. The testing of commonly used NMR permeability correlations shows that three conditions should be met for the validity of these correlations. The surface relaxivity should not vary significantly. The formation factor should depend only on porosity. And the characteristic pore body radius should be proportional to the characteristic throat radius. The correlations are improved by including surface relaxivity and formation factor.