The efficiency of many technological processes such as filtration and catalysis and the durability of many materials such as concrete are highly dependent on the underlying transport properties of the relevant microstructure. Understanding the relationships between microstructure (or specifically pore structure) and transport is therefore critical for designing improved materials and systems. Computational materials science has advanced to the point where transport properties such as fluid permeability and electrical conductivity can be computed on quite large three-dimensional systems, containing as many as 2563 nodes [1]. With the ever increasing processing speeds and memory capacities of computers, much larger systems will be tractable in the very near future. Now that these computational techniques have been developed, the bottleneck in elucidating microstructure- property relationships may be in obtaining adequate representations of the real three-dimensional microstructure of the porous media of interest.
Experimentally, three-dimensional images may be built up from a set of serial sections [2], but without the development of an automated system, this is a tedious and time-consuming task. X-ray microtomography offers one possibility for rapidly obtaining a three-dimensional image of a microstructure and resolution limits have improved to be on the order of several microns which may be adequate for many porous materials [3,4]. Alternately, computer models may be used to generate three-dimensional microstructures of interest either by somewhat empirical rules as has been done for rocks [5] or by simulation of the underlying physical processes as has been done for cement paste [6]. While each of these models has proven extremely useful for a specific class of materials, their applicability to porous media in general is limited. The ``ideal'' technique for creating three-dimensional porous media for computational analysis would be applicable to most porous media and would be based on a set of consistent procedures (or rules).
In light of this, an attractive approach to this problem is to reconstruct a representative three-dimensional porous medium from a two-dimensional view of the system, such as that provided by a single micrograph illustrating the pore system. Based on the work of Joshi [7], Quiblier has developed a computational technique for creating a three-dimensional microstructure using autocorrelation analysis of a two-dimensional image [8]. Adler et al. [9] have utilized this technique to reconstruct Fontainebleau sandstones and have computed permeabilities [9] and conductivities [10] to compare to experimental measurements. Agreement was fair, but the transport properties (conductivity and permeability) of the reconstructed porous media were consistently lower than those of the real samples.
In this paper, a simplified version of the approach outlined by Quiblier and the effectiveness of a modification to the reconstructed microstructures based on analysis of the hydraulic radius of the porous media are explored. Conductivities, permeabilities, and a critical pore diameter are all computed and used to evaluate the effectiveness of the reconstruction (original and modified) algorithms.