Comparison of Network Generation Techniques for Unconsolidated Porous Media

First, we discuss network models and techniques for determining the pore-scale properties and characterisWhile 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 materiniques 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 numto 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 twoor 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. been represented by spheres or cubes, while pore throats have been represented by cylinders or other ducts with non-circular cross-sections. Although netW and solute transport and the distribution work models can be twoor threedimensional, twoof phases in subsurface systems are directly redimensional networks have significant limitations in lated to the geometry and the topology of the pore space how they represent the interconnectivity of real threeand can have a strong influence on continuum scale dimensional media (Chatzis and Dullien, 1977). Comproperties. While many processes related to site assessmon three-dimensional networks are random (e.g., ment and remediation are usually studied using a continLowry and Miller, 1995) or cubic lattices with coordinauum approach, pore-scale modeling is considered a powtion number of six (or smaller if bonds are removed). erful tool to better understand the physical processes In actual porous media systems, however, the connectivinvolved and to determine macroscale constitutive relaity is distributed, and can have values larger than six tionships that can be difficult to obtain experimentally. (Kwiecien et al., 1990). One solution to this problem is The most critical part of constructing a network model to use physically representative networks, which do not is the identification of the pore structure. This can be employ an underlying lattice but instead, map the true done using either using computer-generated porous mepore structure of a medium onto a network (Bryant et dia systems or through the use of non-destructive imal., 1993a). Consequently, they retain more completely aging techniques (e.g., synchrotron microtomography). the true pore morphology and any inherent spatial corThe significant challenge lies in the generation of netrelations. work structures that are physically representative of the Network models have been used to study a wide range real materials of interest. of single and multiphase flow processes including relaIn this paper we present the development of and tive permeability (Blunt and King, 1990, Rajaram et compare two improved techniques for generating physial., 1997, Fischer and Celia, 1999); the effect of pore cally realistic network models of granular porous media. structure on relative permeability and capillary pressure hysteresis in two phase systems (Jerauld and Salter, R. Al-Raoush and C.S. Willson, Dep. of Civil and Environmental 1990); prediction of permeability (Bryant et al., 1993a); Engineering, Louisiana State Univ., Baton Rouge, LA 70808; K. Thompson, Dep. of Chemical Engineering, Louisiana State Univ., investigation of the functional relationship between capBaton Rouge, LA 70808. Received 6 June 2002. *Corresponding auillary pressure, saturation, and interfacial areas (Reeves thor ([email protected]). and Celia, 1996); prediction of permeabilities and resiPublished in Soil Sci. Soc. Am. J. 67:1687–1700 (2003).  Soil Science Society of America Abbreviations: MA, medial-axis based approach; MDT, modified Delaunay tessellation. 677 S. Segoe Rd., Madison, WI 53711 USA