First, we discuss network models and techniques for determining the pore-scale properties and characteris-While network models of porous materials have traditionally been tics; second, we describe the regular and random porous constructed using regular or disordered lattices, recent developments allow the direct modeling of more realistic structures such as sphere media systems used to validate and evaluate the techpackings, microtomographic images, or computer-simulated materi-niques we are proposing; third, we present the improveals. One of the obstacles in these newer approaches is the generation ments made to two network generation techniques of network structures that are physically representative of the real based on their known limitations; fourth, we validate systems. In this paper, we present and compare two different algothese algorithms using regular packings; and finally, we rithms to extract pore network parameters from three-dimensional evaluate and compare the network representations of images of unconsolidated porous media systems. The first approach, random packings generated by these techniques. which utilizes a pixelized image of the pore space, is an extension to unconsolidated systems of a medial-axis based approach (MA). The second approach uses a modified Delaunay tessellation (MDT) of the BACKGROUND grain locations. The two algorithms are validated using theoretical Early models developed to account for pore-scale packings with known properties and then the networks generated properties idealized the pore space as collections of from random packing are compared. For the regular packings, both capillary tubes and provided simple analytical solutions methods are able to provide the correct pore network structure, including the number, size, and location of inscribed pore bodies, the num-to predict continuum-scale properties such as permeber, size, and location of inscribed pore throats, and the connectivity. ability. However, these models failed to incorporate the Despite the good agreement for the regular packings, there were interconnectivity of the pore space. Thus the idea of differences in both the spatial mapping and statistical distributions in representing the pore space as a two-or three-dimennetwork properties for the random packings. The discrepancies are sional network emerged from the pioneering work by attributed to the pixelization at low resolution, non-uniqueness of the Fatt (1956a,b,c). Due to the complexity of the poreinscribed pore-body locations, and differences in merging processes space morphology, the pore bodies and throats are usuused in the algorithms, and serve to highlight the difficulty in creating ally represented by simplified shapes. Pore bodies have a unique network from a complex, continuum pore space.
IntroductionNatural and manufactured fibrous materials are found in many processes of interest to chemical engineers, including the synthesis of composite materials, filtration, pulp and paper processing, biological transport phenomena, and the design and manufacture of adsorbent materials. Fluid transport is usually modeled using a continuum approach because of the length scales involved and the complexity of real pore structures. Continuum methods are very effective if appropriate averaged parameters are known or can be easily predicted. Oftentimes, however, these parameters can be found only through experiment, most notably in cases where the macroscopic parameters of interest depend strongly on porescale behavior. This limitation is important because it can prevent factors such as pore structure, wettability variations, or interface behavior from being explicitly incorporated into a model. A second concern in continuum modeling is the proper choice of scales. Averaged parameters contain implicitly assumed length scales, and a model must operate over similar scales. If the length scale for transport is too small, an averaged parameter is not meaningful. While this problem is rarely apparent for parameters such as porosity or flux, dispersion can exhibit so-called anomalous behavior that makes Ž the determination of characteristic lengths for dispersion co-. efficients difficult. At the other extreme, if the length scale in a model is large compared to the scale over which a parameter varies, then upscaling is required. This problem is common in numerical modeling, where the discretization scale Ž . such as the size of a finite element is large relative to the scale for permeability variations.The purpose of pore-scale modeling is to provide a link between microscopic properties of a porous medium and transport behavior at a larger scale. Pore-scale models are an important complement to continuum modeling because they Ž can be used to predict continuum parameters if they are . quantitative , and they provide a means for studying the scaling issues just mentioned. In an ideal modeling scenario, flow would be modeled at the pore scale using first principles, and the results would be used to generate averaged parameters for use at the continuum level. While this multiscale approach will probably become common in the future, a number of issues must be addressed before it becomes practical. One issue is the ability to consistently generate quantitative transport parameters using only basic morphologic information. This predictive capability has been demonstrated for Ž specific media such as sphere packs Bryant and Blunt, 1992;. Bryant et al., 1993a; Thompson and Fogler, 1997 , and cer-Ž tain consolidated rocks Bryant et al., 1993b; Bakke and Oren, . 1997 , but not for arbitrary types of media. A second issue is upscaling from the pore to the continuum level. The mathematical and numerical problems are quite challenging because of scaling, computational requirements, history dependence, and so on.In this article, we...
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