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Microtomography is an emerging technique for particle and particulate-materials characterization. To use this technology effectively, robust and accurate computational algorithms are needed to compute relevant particle properties, including particle surface area and particle-particle contact area. However, the most accurate algorithms that have been developed for computing the exposed (void/solid) surface area in a microtomography image cannot be used directly for computing surface areas or particle-particle contact areas for individual particles in a dense packing. This paper presents an algorithm for extracting particle contact areas from a digitized, segmented image of a packed granular material, which in turn can be used to find individual particle surface areas (even if the complete surfaces are not exposed because of contacts in the packing). Results show that small errors in the binary surface-area computations are magnified in the course of determining particle contact areas; the total error in the computation depends mainly on the size of the contact area in voxel units.

Network modeling has been performed to obtain quantitative and predictive results of the flow of yield-stress fluids in packed beds. Physically representative networks were used as the basis for the modeling, which have a one-to-one correspondence to computer-generated packed beds of spheres. The networks are able to account for the interconnectivity, heterogeneity, and converging/diverging geometry that are inherent in porous media. The approach can be used to model a wide range of non-Newtonian fluids, but the emphasis is for yield-stress fluids that can be represented using a Bingham model. For these fluids, a threshold pressure gradient is required to initiate flow, and flow at low pressure gradients is characterized by critical percolation behavior. Quantitative results of superficial velocity vs. pressure gradient are presented, and are compared to traditional bundle-of-tubes models, as well as limited experimental data available in the literature. Important differences are observed between the network model and the constitutive models. These are attributed mainly to heterogeneity and converging/diverging geometry, which are not accounted for in the semiempirical models. Comparison to experimental data is good for certain fluids. In other cases, the modeling suggests that effects other than fluid rheology may also have affected flow, such as adsorption or filtration. © 2004 American Institute of Chemical Engineers AIChE J, 50: 3034–3048, 2004

While network models of porous materials have traditionally been constructed using regular or disordered lattices, recent developments allow the direct modeling of more realistic structures such as sphere packings, microtomographic images, or computer-simulated materials. One of the obstacles in these newer approaches is the generation of network structures that are physically representative of the real systems. In this paper, we present and compare two different algorithms to extract pore network parameters from three-dimensional images of unconsolidated porous media systems. The first approach, 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 grain locations. The two algorithms are validated using theoretical packings with known properties and then the networks generated from random packing are compared. For the regular packings, both methods are able to provide the correct pore network structure, including the number, size, and location of inscribed pore bodies, the number, size, and location of inscribed pore throats, and the connectivity. Despite the good agreement for the regular packings, there were differences in both the spatial mapping and statistical distributions in network properties for the random packings. The discrepancies are attributed to the pixelization at low resolution, non-uniqueness of the inscribed pore-body locations, and differences in merging processes used in the algorithms, and serve to highlight the difficulty in creating a unique network from a complex, continuum pore space.

The modeling of fluid transport in fibrous materials is important for many applications. Most models operate at the continuum level, which requires an a priori knowledge of spatially averaged transport parameters. Alternatively, highly detailed models, in which the momentum equations are solved directly, require major simplifying assumptions. Thus, it is desirable to use intermediate-level techniques that model transport using first principles, but that are appropriate for real engineering processes. In this work, pore-scale network modeling is adapted for fibrous materials and tested for a large range of fibrous structures and solid volume fractions. A novel technique is used to generate prototype network structures from Voronoi diagrams. The Voronoi networks are coupled with two different multiphase flow algorithms, enabling the modeling of various displacement processes relevant to engineering. Permeability predictions agree well with known values. Effects of dynamics, wettability, and material structure on displacement were studied. This modeling technique not only allows for better quantification of how microscale properties affect macroscopic transport, but helps reduce the number of experiments required to predict continuum transport parameters for various materials and processes.

An algorithm is presented for constructing three-dimensional Delaunay tessellations in periodic domains. Applications include mesh generation for periodic transport problems and geometric decomposition for modelling particulate structures. The algorithm is a point insertion technique, and although the general framework is similar to point insertion in a convex hull, a number of new issues are introduced by periodicity. These issues are discussed in detail in the context of the computational algorithm. Examples are given for the tessellation of random points and random sphere packings. Performance data for the algorithm are also presented. These data show an empirical scaling of the computation time with size of O(N1.11) and tessellation rates of 7000–14000 tetrahedrons per second for the problems studied (up to 105 points). A breakdown of the performance is given, which shows the computational load is shared most heavily by two specific parts of the point-insertion procedure. Copyright © 2002 John Wiley & Sons, Ltd.

An algorithm is presented for solving the Stokes equation in large disordered two-dimensional porous domains. It is applied to random packings of discs, but the geometry can be essentially arbitrary. The approach includes the subdivision of the domain and a subsequent application of boundary integral equations to the subdomains. This gives a block diagonal matrix with sparse off-block components that arise from shared variables on internal subdomain boundaries. The global problem is solved using a biconjugate gradient routine with preconditioning. Results show that the effectiveness of the preconditioner is strongly affected by the subdomain structure, from which a methodology is proposed for the domain decomposition step. A minimum is observed in the solution time versus subdomain size, which is governed by the time required for preconditioning, the time for vector multiplications in the biconjugate gradient routine, the iterative convergence rate and issues related to memory allocation. The method is demonstrated on various domains including a random 1000-particle domain. The solution can be used for efficient recovery of point velocities, which is discussed in the context of stochastic modelling of solute transport

Network models are an effective means of incorporating pore-scale heterogeneity into flow models of porous materials. The drawback to these models used to be the inability to obtain quantitative macroscopic parameters representing larger (experimental-scale) media. However, recently developed modeling techniques, combined with more widely available computational resources, make the simulation of macroscopic parameters from a network approach viable. A network model for the slow flow of an incompressible fluid in disordered packed beds is presented. Fundamental fluid mechanics equations are solved at the pore scale and then translated to macroscopic behaviour using a network approach. The results reproduce experimental permeabilities and show excellent quantitative fits to residence time distributions for mechanical dispersion in real beds. Simulations of the RTD are of special interest, because they are definitive links between pore-scale flow behavior and macroscopic responses.