A significant portion of oil remains in a reservoir after primary and secondary recovery. An understanding of the mechanisms and flow paths of fluids in permeable rock is important if greater recovery is to be realized from the reservoirs. The permeability of the reservoir rocks is not predictable from first principles. In this paper, a simple model that approximates a porous medium as a network of interconnected pores has been developed. This paper relates the use of the model to characterize fluid flow through a complex porous medium. The model consists of a regular matrix of pores that are connected by different-sized connections between the pores or, more precisely, ostioles. Because the pores are assumed to be considerably larger in size than the ostioles, all flow resistance lies in the ostioles. Hagen-Poiseuille's equation was used to give the relation between ostiole size and conductivity. Several different ostiole size distributions were studied in conjunction with Monte-Carlo simulation which assigned a size to each ostiole. The model has been used to evaluate the complexity of flow paths and the effect of mono-sized particle movement in the porous media. The particles plug the ostioles and reduce the permeability. This permeability reduction has been determined as a function of the number and size of the particles. In addition, a percolation threshold for complete flow blockage in the porous media was determined. A series of permeability reduction curves was calculated for different particle sizes for the ostiole size distributions. The shape of the permeability reduction curves provided information about the intrinsic ostiole size distribution. An experimental procedure has been proposed for determination of ostiole size distributions based on the reduction of flow rate with mono-sized particles.