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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

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.

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.