Effective permeability of porous media in subsurface environments (or packed beds in reactors, for instance) is subject to potentially large uncertainties due to heterogeneity of natural systems. We present a lattice Boltzmann method (LBM) to study the flow of single-phase non-Newtonian fluids by using a power law effective viscosity in different bidimensional porous media; arbitrarily and randomly generated. Macroscale-equivalent local effective permeability distributions and permeability bands at core scale are predicted. Our final goal is to propose a method for constructing core predictions from data obtained in thin samples of porous media, especially for non-Newtonian fluids (contaminated aquifers, petrochemicals and oil, for instance) whenever experiments are costly or just not available. (C) 2009 Elsevier Ltd. All rights reserved.