Massive parallel lattice-Boltzmann method simulations of flow through highly polydispersed spherical particle packings formed using Monte-Carlo methods were performed. The computed fluid permeabilities were compared to experimental data obtained from blocks made of three natural ground calcium carbonate powders compressed at different levels. The agreement with experimental measurements is excellent considering the approximations made. A series of flow simulations was also performed for packings of spherical particles compressed at different levels with increasing polydispersity modeled with both log-normal and Weibull size distributions. The predicted permeabilities were found to follow reasonably well the Carman-Kozeny correlation although an increasing deviation towards lower predicted permeabilities with increasing polydispersity was observed. Finally, following a careful analysis of the inherent numerical errors, an expression relating the Kozeny "constant" to the size distribution and compression level was derived from the Simulation results, which led to a modified correlation. (C) 2008 Elsevier Ltd. All rights reserved.