Determination of permeability in fibrous porous media using the lattice Boltzmann method with application to PEM fuel cells

The lattice Boltzmann method (LBM) is used to simulate the flow through an idealized proton exchange membrane fuel cell (PEMFC) porous transport layer (PTL) geometry generated using a Monte Carlo method. Using the calculated flow field, Darcy's law is applied and the permeability is calculated. This process is applied in both through‐ and in‐plane directions of the paper as both of these permeability values are important in computational fluid dynamics models of PEMFCs. It is shown that the LBM can be used to determine permeability in a random porous media by solving the flow in the microstructure of the material. The permeability in the through‐ and in‐plane directions is shown to be different and the anisotropic nature of the geometry creates anisotropic permeability. It is also found that fiber arrangement plays a large role in the permeability of the PTL. New correlations are presented for in‐ and though‐plane permeabilities of fibrous porous media with (0.6<ε<0.8). Copyright © 2008 John Wiley & Sons, Ltd.     

On Calculating a Translational Flow Through a System of Circular or Spherical Layers with Different Permeabilities

The problem of finding the potential of a translational flow through a system of circular or spherical layers in a porous medium obeying Darcy's law is considered. The permeability coefficients change stepwise across the interface. The method is based on deriving special recurrence relations which give a rational dependence of the potentials on the permeability coefficients suitable for specific calculations.     

Incremental unknowns in three-dimensional stationary problem

The main purpose of this work is to set up the explicit matrix framework appropriate to three-dimensional partial differential equations by means of the incremental unknowns method. Multilevel schemes of the incremental unknowns are presented in the three space dimensions, and through numerical experiments, we confirm that the incremental unknowns method is efficient and the hierarchical preconditioning based on the incremental unknowns can be applied in a more general form.      

A new strip line broad-band measurement evaluation for determining the complex permeability of thin ferromagnetic films

In the present paper, a new method for determining the frequency dependent complex permeability of thin magnetic films, designed for measurements up to 5 GHz, is presented. The measurement technique described here was carried out by a one-port permeameter, which is based on a short-circuited strip line. The complex permeability was deduced by a new analytical approach from the measured reflection coefficient of a strip line (S₁₁) with and without a ferromagnetic film material inside. An adaptive error correction was applied in the measurement procedure. The spectral permeability of thin FeCoAlN films with an in-plane uniaxial anisotropy of μ₀^*H_a=3.2 mT induced by annealing at CMOS temperatures in a static magnetic field was investigated. The measurements were compared with a theoretical model taking the Landau–Lifshitz and eddy current theories into account. A resonant frequency of about 1.6 GHz was observed.     

Evolution of magnetic permeability and magneto-impedance effect in composite wires with insulator layer

CuBe/Insulator/NiCoP composite wire was prepared by electroless deposition on an insulated CuBe core with a diameter of 90 μm. The conversion relationship between the magneto-impedance and effective magnetic permeability of the composite wire was derived from an energy conversion model. The evolution of the magnetic permeability and the giant magneto-impedance (GMI) effect were investigated. The results show that a distinct GMI effect can be obtained at relatively low frequency. The largest GMI ratio is 240% at 600 kHz, and the maximal field sensitivity is 34%/Oe.     

Syntheses and gas transport properties of polyarylates based on isophthalic and terephthalic acids and mixtures of bisphenol A and 1, 1 bi‐2‐naphthol

Polyarylates based on isophthalic (IA) and terephthalic (TA) acids and an equimolar mixture of the diols Bisphenol A (BPA) and 1,1 bi‐2‐naphthol (BN) were synthesized to produce BPA‐BN/IA and BPA‐BN/TA polymers and to measure their gas permeability coefficients, P(i), at several pressures and 35 °C, to the gases O₂, N₂, CH₄, and CO₂. For the BPA‐BN/IA membranes, at a 2 atm up‐stream pressure, the P(O₂) and P(CO₂) are 0.93 and 4.0 Barrers with O₂/N₂ and CO₂/CH₄ ideal separation factors of 6.7 and 27. For the BPA‐BN/TA, at a 2 atm up‐stream pressure, the P(O₂) and P(CO₂) are 2.0 and 9.9 Barrers with O₂/N₂ and CO₂/CH₄ ideal separation factors of 5.6 and 21. Comparing the selectivity–permeability balance of properties shown by the BPA/TA membranes with that shown by the copolymer BPA‐BN/TA, the balance moves in the direction of higher selectivity and lower permeability because of the incorporation of BN, which is a more rigid monomer than BPA. However, when the balance of properties for the pair O₂/N₂ shown by BPA‐BN/TA is compared with the one shown by other membranes such as those based on mixtures of diols and diacids, that is the bisphenol A‐naphthalene/I‐T polymers reported in the literature, the balance moves up and to the right of the typical selectivity–permeability trade‐off observed in the BPA‐polyarylate family. Thus, simultaneous incorporations of flexible and rigid monomers in both the diols and the diacids lead to more productive and more selective membranes. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 256–263, 2006     

非对称开口六边形谐振单环的微波透射特性

受自然界树型结构的启发，设计了分叉树型微结构单元，用电路板刻蚀技术制作了非对称开口六边形谐振单环及其组合结构.采用计算机模拟和实验研究了单个和多个谐振环在微波段(7—12 GHz)的电磁响应行为.研究结果表明：该结构具有负磁导率特性，开口谐振环几何尺寸影响环的磁谐振频率；两环环间距较小时出现二次谐振；带高级分支的辐射状环列相对于不带分支环列透射峰向低频移动.实验和模拟结果相符. 关键词： 负磁导率 开口谐振环 透射率     

Relative Permeabilities for Strictly Hyperbolic Models of Three-Phase Flow in Porous Media

Traditional mathematical models of multiphase flow in porous media use a straightforward extension of Darcys equation. The key element of these models is the appropriate formulation of the relative permeability functions. It is well known that for one-dimensional flow of three immiscible incompressible fluids, when capillarity is neglected, most relative permeability models used today give rise to regions in the saturation space with elliptic behavior (the so-called elliptic regions). We believe that this behavior is not physical, but rather the result of an incomplete mathematical model. In this paper we identify necessary conditions that must be satisfied by the relative permeability functions, so that the system of equations describing three-phase flow is strictly hyperbolic everywhere in the saturation triangle. These conditions seem to be in good agreement with pore-scale physics and experimental data.     

The use of renormalization for calculating effective permeability

There is a need in the numerical simulation of reservoir performance to use average permeability values for the grid blocks. The permeability distributions to be averaged over are based on samples taken from cores and from logs using correlations between permeabilities and porosities and from other sources. It is necessary to use a suitable effective value determined from this sample. The effective value is a single value for an equivalent homogeneous block. Conventionally, this effective value has been determined from a simple estimate such as the geometric mean or a detailed numerical solution of the single phase flow equation.If the permeability fluctuations are small then perturbation theory or effective medium theory (EMT) give reliable estimates of the effective permeability. However, for systems with a more severe permeability variation or for those with a finite fraction of nonreservoir rock all the simple estimates are invalid as well as EMT and perturbation theory.This paper describes a real-space renormalization technique which leads to better estimates than the simpler methods and is able to resolve details on a much finer scale than conventional numerical solution. Conventional simulation here refers to finite difference (or element) techniques for solving the single phase pressure equation. This requires the pressure and permeability at every grid point to be stored. Hence, these methods are limited in their resolution by the amount of data that can be stored in core. Although virtual memory techniques may be used they increase computer time. The renormalization method involves averaging over small regions of the reservoir first to form a new averaged permeability distribution with a lower variance than the original. This pre-averaging may be repeated until a stable estimate is found. Examples are given to show that this is in excellent agreement with computationally more expensive numerical solution but significantly different from simple estimates such as the geometric mean.     

Effects of Relative Permeability History Dependence on Two-Phase Flow in Porous Media

Hysteresis phenomena in multi-phase flow in porous media has been recognized by many researchers and widely believed to have significant effects on the flow. In an attempt to account for these effects, a theoretical model for history-dependent relative permeabilities is considered. This model is incorporated into 1-D two-phase nondiffusive flow system and the corresponding flow is predicted. Flow history is observed to have a notable impact on the saturation profile and fluids breakthrough.