Pore-scale modeling of fluid transport in disordered fibrous materials

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.

[1]  L. E. Scriven,et al.  Percolation and conduction on Voronoi and triangular networks: a case study in topological disorder , 1984 .

[2]  A. Ladd,et al.  Simulation of low-Reynolds-number flow via a time-independent lattice-Boltzmann method. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Kishore K. Mohanty,et al.  Network Modeling of Non-Darcy Flow Through Porous Media , 1998 .

[4]  Keith W. Jones,et al.  Synchrotron computed microtomography of porous media: Topology and transports. , 1994, Physical review letters.

[5]  Clayton J. Radke,et al.  Laminar flow of a wetting liquid along the corners of a predominantly gas-occupied noncircular pore , 1988 .

[6]  Muhammad Sahimi,et al.  Transient Diffusion and Conduction in Heterogeneous Media: Beyond the Classical Effective-Medium Approximation , 1997 .

[7]  Joel Koplik,et al.  Creeping flow in two-dimensional networks , 1982, Journal of Fluid Mechanics.

[8]  David S. Clague,et al.  A numerical calculation of the hydraulic permeability of three-dimensional disordered fibrous media , 1997 .

[9]  Steven L. Bryant,et al.  Network model evaluation of permeability and spatial correlation in a real random sphere packing , 1993 .

[10]  W. E. Soll,et al.  Pore level imaging of fluid transport using synchrotron X-ray microtomography , 1996 .

[11]  R. E. Larson,et al.  Microscopic flow near the surface of two-dimensional porous media. Part 2. Transverse flow , 1987, Journal of Fluid Mechanics.

[12]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[13]  Andreas Acrivos,et al.  Slow flow past periodic arrays of cylinders with application to heat transfer , 1982 .

[14]  Muhammad Sahimi,et al.  Pore network simulation of imbibition into paper during coating: I. Model development , 2001 .

[15]  Markus Hilpert,et al.  Pore-morphology-based simulation of drainage in totally wetting porous media , 2001 .

[16]  C. Ross Ethier,et al.  Flow through mixed fibrous porous materials , 1991 .

[17]  Bryant,et al.  Prediction of relative permeability in simple porous media. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[18]  H. Scott Fogler,et al.  Modeling flow in disordered packed beds from pore‐scale fluid mechanics , 1997 .

[19]  Chen,et al.  Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Dewei Qi Microstructural model for a three-dimensional fiber network , 1997 .

[21]  I. Fatt The Network Model of Porous Media , 1956 .

[22]  Martin J. Blunt,et al.  Development of a pore network simulation model to study nonaqueous phase liquid dissolution , 2000 .

[23]  Cesar Zarcone,et al.  Numerical models and experiments on immiscible displacements in porous media , 1988, Journal of Fluid Mechanics.

[24]  J. Drummond,et al.  Laminar viscous flow through regular arrays of parallel solid cylinders , 1984 .

[25]  Madalena M. Dias,et al.  Network models for two-phase flow in porous media Part 2. Motion of oil ganglia , 1986, Journal of Fluid Mechanics.

[26]  D. F. James,et al.  The permeability of fibrous porous media , 1986 .

[27]  J. L. Finney,et al.  Random packings and the structure of simple liquids. I. The geometry of random close packing , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[28]  H. S. Fogler,et al.  Pore evolution and channel formation during flow and reaction in porous media , 1988 .

[29]  Cass T. Miller,et al.  Pore‐Scale Modeling of Nonwetting‐Phase Residual in Porous Media , 1995 .

[30]  Donald G. Baird,et al.  An Impregnation Model for the Preparation of Thermoplastic Prepregs , 1992 .

[31]  Martin J. Blunt,et al.  Relative permeabilities from two- and three-dimensional pore-scale network modelling , 1991 .

[32]  D. F. James,et al.  The hydrodynamic resistance of hyaluronic acid and its contribution to tissue permeability. , 1982, Biorheology.

[33]  P. A. Goode,et al.  Momentum transfer across fluid-fluid interfaces in porous media: A network model , 1993 .

[34]  Steven L. Bryant,et al.  Physically representative network models of transport in porous media , 1993 .

[35]  Kristian Mogensen,et al.  A Dynamic Two-Phase Pore-Scale Model of Imbibition , 1998 .

[36]  W. B. Lindquist,et al.  Medial axis analysis of void structure in three-dimensional tomographic images of porous media , 1996 .

[37]  S. Bakke,et al.  3-D Pore-Scale Modelling of Sandstones and Flow Simulations in the Pore Networks , 1997 .

[38]  Friedrich Löffler,et al.  Realistic modelling of the behaviour of fibrous filters through consideration of filter structure , 1994 .

[39]  A. Sangani,et al.  INCLUSION OF LUBRICATION FORCES IN DYNAMIC SIMULATIONS , 1994 .

[40]  C.-W. Park,et al.  A predictive model for the removal of colloidal particles in fibrous filter media , 1999 .

[41]  H. Scott Fogler,et al.  Influence of Transport and Reaction on Wormhole Formation in Porous Media , 1998 .

[42]  van der Erik Giessen,et al.  A numerical study of large deformations of low-density elastomeric open-cell foams , 1998 .

[43]  J. Higdon,et al.  Permeability of three-dimensional models of fibrous porous media , 1996, Journal of Fluid Mechanics.

[44]  J. Koplik,et al.  Conductivity and permeability from microgeometry , 1984 .

[45]  Daniel H. Rothman,et al.  Lattice‐Boltzmann studies of immiscible two‐phase flow through porous media , 1993 .

[46]  H. Scott Fogler,et al.  Pore-scale model for fluid injection and in situ gelation in porous media , 1998 .

[47]  Guangli Liu,et al.  A domain decomposition method for modelling Stokes flow in porous materials , 2002 .

[48]  Anthony J. C. Ladd,et al.  Moderate Reynolds number flows through periodic and random arrays of aligned cylinders , 1996, Journal of Fluid Mechanics.

[49]  Y. Termonia,et al.  Permeability of sheets of nonwoven fibrous media , 1998 .

[50]  F. Dullien Porous Media: Fluid Transport and Pore Structure , 1979 .

[51]  T. Dąbroś,et al.  A singularity method for calculating hydrodynamic forces and particle velocities in low-Reynolds-number flows , 1985, Journal of Fluid Mechanics.

[52]  Ashok Shantilal Sangani,et al.  Transport Processes in Random Arrays of Cylinders. II. Viscous Flow , 1988 .

[53]  T. J. Lasseter,et al.  Two-phase flow in random network models of porous media , 1985 .

[54]  D. Qi,et al.  Numerical experiments on paper-fluid interaction — permeability of a three-dimensional anisotropic fibre network , 1996, Journal of Materials Science.

[55]  Ioannis Chatzis,et al.  Permeability and electrical conductivity of porous media from 3D stochastic replicas of the microstructure , 2000 .