Comprehensive Pore Structure Characterization Using 3D Computer Reconstruction and Stochastic Modeling
Authors: Ioannidis M.A. , Kwiecien M.J. , Chatzis I. , Macdonald I.F. , Dullien F.A.L. 
Published: December 2007

Abstract
Computer algorithms implementing 3D partitioning of a pore space into its constituent pores by detecting local constrictions (pore throats) in the void continuum are applied to serial section data and stochastically simulated porous media. For the case of a Berea sandstone sample, good agreement is found between the pore and throat size distributions and pore coordination number statistics of the real medium and those of its simulated counterpart. Comprehensive characterization of stochastic models corresponding to other porous media is also performed. The results are used to:explore the relationships between statistical properties (porosity, autocorrelation function) and salient geometrical and topological aspects of the microstructure, andpredict the absolute permeability, formation factor and resistivity index vs. saturation relationship using network models.
Comparison with experimental data suggests that stochastic simulation may serve as a basis for the prediction of petrophysical properties.

Introduction
Network models of the pore structure, first introduced by Fatt, have found widespread use in the simulation and interpretation of flow phenomena in porous media. Their power and versatility lies in the ability to explain macroscopic behavior by explicitly accounting for the relevant pore-level physics. It is necessary, however, that proper pore structure information be supplied as input to network models, if they are to serve effectively in the prediction of reservoir properties. Required input data consist of characteristic size distributions of pores and throats, as well as information concerning the degree of connectivity of the pore network (e.g., coordination number). Accurate determination of these parameters requires careful analysis of the pore space in 3D.
The task of objectively identifying pores and throats in a complex pore space continuum has come into focus in recent years. Various workers have concentrated on algorithm development for the analysis of the porous microstructure, with applications to 3D data obtained by serial sectioning of pore casts, magnetic resonance imaging, or synchrotron emission tomography. Alternatives to the acquisition of real 3D data have also been developed which are based on stochastic simulation methods. These methods promise to generate model pore structures representative of their complex real counterparts. If successful, they could not only drastically reduce the time and cost associated with tomographic studies, but also overcome many of their technical limitations (e.g. limited resolution). If combined with competent algorithms for pore structure characterization, stochastic simulation could then serve as a basis for the generation of geometrical and topological data required by network simulators of capillary and transport phenomena.
Statistical description of porous media in terms of the porosity and autocorrelation function is based on the assumption of statistical homogeneity. In this context, porosity and autocorrelation are statistical moments of a random phase function Z(r) taking the value of unity if a point r in space belongs to the void phase or the value of zero otherwise: (1)
(2)
Stochastic simulation utilizes measurements of porosity and autocorrelation from binary images of thin-sections to create statistically homogeneous 3D model porous media with the same properties. The statistical equivalence between 2D image and 3D model data has been validated, even with respect to higher order statistics. A direct comparison, however, of the 3D geometry and topology of a real porous medium to those of its simulated counterpart is lacking.
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