Prediction of Permeability from the Skeleton of 3-D Pore Structure
Authors: Liang Z.R. , Philippi P.C. , Fernandes C.P. , Magnani F.S. 
Published: December 2007

Abstract
The main purpose of the present work is to determine the 3-D pore structure network by using image analysis techniques and predict the permeability of the porous rock. In this work, these techniques are applied to 3-D pore structure reconstructed by the truncated Gaussian method using Fourier transform from the thin section image of a Berea sandstone. The skeleton of a 3-D pore structure provides a way of visualizing the graph of the pore network. It is extracted using a thinning algorithm, which preserves connectivity, i.e., this network and original pore structure have the same topology. It gives both visual and quantitative information about the connectivity of the pore space. the coordination number for every node and local hydraulic radius. Once the network of pore structure is obtained, the macroscopic transport properties of the rock such as permeability can be calculated. The predicted permeability for Berea sandstone rock is in good agreement with the experimental value and empirical correlations.

Introduction
The prediction of equilibrium and transport properties of porous media is a long-standing problem of great theoretical and practical interest, particularly in petroleum reservoir engineering. The permeability is the most important physical property of a porous medium in the same way as the porosity is its most important geometrical property. Past theoretical attempts to derive macroscopic transport coefficients from the microstructure of porous media entailed a simplified representation of the pore space, often as a bundle of capillary tubes. These models have been widely applied because of their convenience and familiarity to the engineers. But they do have some limitations. For example, they are not well suited for describing effect of the pore space inter-connectivity and long range correlation in the system. Network models have been advanced to describe phenomena at the microscopic level and have been extended in the last few years to describe various phenomena at the macroscopic level. These models are mostly based on a network representation of the porous media in which larger pores (pore bodies) are connected by narrower pores (pore throats). Network models represent the most important and widely used class of geometric models for porous media. They are not only used in theoretical calculations but also in the form of micromodels in experimental observations. A network is a graph consisting of a set of nodes or sites connected by a set of links or bonds. The nodes of the network could for example represent the centers of pore bodies. The links represent connections between them. The nodes can be chosen deterministically as for the sites of a regular lattice or randomly as in the realization of a Poisson or other stochastic point process. Similarly the links connecting different nodes may be chosen according to some deterministic or random procedure. Finally the nodes are dressed with convex sets such as spheres representing pore bodies, and the bonds are dressed with tubes providing a connecting path between the pore bodies. The original idea of network of a pore space is rather old, but it was only in the early 80s that systematic and rigorous procedures were developed to map, in principle, any disordered rock onto an equivalent random network of bonds and sites. Once this mapping is complete one can study a given phenomena in porous media in great details. Dullien reviewed the details of various pore-scale processes, including detailed descriptions of many aspects of network models. The most important features of pore network geometry and topology that affect fluid distribution and flow in reservoir rocks are the pore throat and pore body size distributions, the pore body-to-pore throat size aspect ratio and the pore body coordination number. These data have been tentatively assumed in the previous works. The extension of these techniques to real porous media has been complicated by the difficulty in describing the complex 3-D pore structure of real porous rocks. Information about the pore structure of reservoir rocks is often obtained from mercury intrusion and sorption isotherm.