Lattice Boltzmann algorithm is an increasingly popular method of modeling fluid flow in complex media because of its ability to simulate the Navier-Stokes equation in a parallel mode and to handle complicated geometry. In this paper, a lattice Boltzmann method is used to simulate 3D fluid flow in correlated porous media. The fluid pressure at the inlet and the outlet of the flow domain is specified by spatial extrapolation of particle populations. The effect of porosity and spatial correlation on the permeability of 3D porous media is studied. The hydraulic radius of an exponentially correlated porous medium can be estimated from its porosity and correlation length. Carman-Kozeny equation is used to estimate the permeability with the Kozeny constant expressed as a function of the correlation length. A predictive model for the permeability of a porous structure has been developed from this analysis. A general porous media can be modeled as a superposition of several exponentially correlated porous media and its permeability can be estimated from this model by using a linear combination of the correlation lengths of the superimposing media.