The analysis of a two-phase zone with condensation in a porous medium

The one-dimensional steady-state heat and mass transfer in a two-phase zone of a water-saturated porous medium is studied. The system consists of a sand-water-vapour mixture in a tube that is heated from above and cooled from below. Under certain conditions, a two-phase zone of both vapour and water exists in the middle of the tube. A model problem for the temperature and the liquid saturation profiles within this two-phase zone is formulated by allowing for an explicit temperature dependence for the saturation vapour pressure together with an explicit saturation dependence for the capillary pressure. A boundary-layer analysis is performed on this model in the asymptotic limit of a large vapour-pressure gradient. This asymptotic limit is similar to the large-activation-energy limit commonly used in combustion problems. In this limit, and in the outer region away from any boundary layers, it is shown that the temperature profile is slowly varying and that the corresponding saturation profile agrees very well with that obtained in the previous model of Udell [J. Heat Transfer 105 (1983) p. 485] where strict isothermal conditions were assumed. The condensation and evaporation occurring within the boundary layers near the edges of the two-phase zone is examined. Finally, an iterative method is described that allows the temperature profile in the two-phase zone to be coupled to the temperature profiles in the two single-phase zones consisting of either water or vapour. This allows for the computation of the locations of the edges of the two-phase zone within the tube. Numerical computations are performed with realistic values of the parameters.     

First-order indicators for the estimation of discrete fractures in porous media

Faults and geological barriers can drastically affect the flow patterns in porous media. Such fractures can be modelled as interfaces that interact with the surrounding matrix. We propose a new technique for the estimation of the location and hydrogeological properties of a small number of large fractures in a porous medium from given distributed pressure or flow data. At each iteration, the algorithm builds a short list of candidates by comparing fracture indicators. These indicators quantify at the first order the decrease of a data misfit function; they are cheap to compute. Then, the best candidate is picked up by minimization of the objective function for each candidate. Optimally driven by the fit to the data, the approach has the great advantage of not requiring remeshing, nor shape derivation. The stability of the algorithm is shown on a series of numerical examples representative of typical situations.     

In situ ozonation of anthracene in unsaturated porous media

Soil column experiments were conducted to investigate the effect of ozonation duration, contaminant content, particle size, moisture content, OH radical scavenger and soil organic matter on the removal of anthracene by in situ ozonation. In the whole study, the gas flow rate was 100 mL/min and concentration of gaseous ozone was 40 mg/L. The removal efficiency increased with the elapsed time, but the removal rate decreased in the range of 0–90 min. As anthracene content in sand decreased from 50 to 10 mg/kg, the removal efficiency increased from 42.1% to 62.0%, and ozone passed through soil column more rapidly. However, the ozone effectiveness reduced when anthracene content dropped. Small particle size provides a large interfacial area, which led to the high removal efficiency and long ozone breakthrough time in the column. The profile of residual anthracene in soil column varied more greatly at smaller particle size. The removal efficiency reduced when the moisture content rose from 0% to 9.1%. The ozone breakthrough time also decreased with the increasing moisture content. The presence of sodium bicarbonate or humic acid reduced the removal efficiency to some extent. GC–MS was employed in this study to determine 9,10-anthraquinone as the main ozonation product.     

A computational model for fracturing porous media

This paper presents a new computational model for simulating a fracturing process in a porous medium using the finite element method. Two independent numerical techniques are used for describing this process. The partition of unity method is used for describing the fracturing process, and the double porosity model is used for describing the resulting fluid flow. A key feature of the model is the coupling of these two independent numerical techniques, which provide the means for a better simulation of the involved physical and mechanical processes. The paper focuses on the numerical formulation of the model. The capability of the model is illustrated by means of numerical examples, which examine the behaviour of a 1D porous medium under different boundary conditions. The numerical results show that the very complicated physical and mechanical processes of the fracturing porous media can be simulated properly and efficiently. Copyright © 2006 John Wiley & Sons, Ltd.     

The effect of solid conversion on travelling combustion waves in porous media

A system of nonlinear partial differential equations, which describe the combustion of a gas passing through a porous medium, is examined. This model provides a bridge between recent porous-medium combustion studies and more classical combustion models. In particular, the effect of solid conversion on the downstream temperature is determined for travelling-wave solutions to the system. In cases for which the solid matrix is a perfect catalyst, solely enhancing the exothermic chemical reaction, with zero mass exchange, it is proved that the downstream temperature must always exceed the upstream temperature. However, when the solid is allowed to react with the gas, travelling-wave solutions for which the up- and down-stream temperatures are equal may be realised. A key result of this work is then the investigation of physical processes and related parameter ranges that give rise to travelling wave solutions with equal up- and down-stream temperatures. Specifically, two critical wavespeeds c_i with 0 < c₁ < c₂ are identified. For c < c₁ the downstream temperature always exceeds that upstream, whilst for c > c₂ no bounded travelling-wave solutions exist. Behaviour in the region c₁ < c < c₂ is new: here solutions having equal up- and down-stream temperatures are realised. The two factors upon which this result depends are the inclusion into the model of solid conversion effects and the distinction between solid and gas temperatures. Thus the inclusion of a new physical process, that of heat storage in the solid varying as the reaction proceeds, allows the existence of a new type of travelling-wave solution. Further phenomena studied include the appearance of nonunique solutions (which are of a type that may be related to ignition processes) and degenerate solutions which terminate precisely when all the solid and gaseous fuel is used up. Parameter regimes for the existence of these various types of solutions are found and the stability of such solutions discussed.     

Numerical modelling of void inclusions in porous media

Numerical modelling of porous flow in a low‐permeability matrix with high‐permeability inclusions is a challenging task because the large ratio of permeabilities ill‐conditions the finite element system of equations. We propose a coupled model where Darcy flow is used for the porous matrix and potential flow is used for the inclusions. We discuss appropriate interface conditions in detail and show that the head drop in the inclusions can be prescribed in a very simple way. Algorithmic aspects are treated in full detail. Numerical examples show that this coupled approach precludes ill‐conditioning and is more efficient than heterogeneous Darcy flow. Copyright © 2003 John Wiley & Sons, Ltd.     

多孔介质冻结过程中温度变化的数值模拟

多数对多孔介质冻结过程的研究是建立模型借助于计算机技术给定数值解。笔者在借鉴现有数值模型的基础上，考虑多孔介质的内部特点，采用容积平均法建立数学模型，对无限大平板状多孔介质在第三类边界条件下发生的一维冻结过程中温度变化进行分析并加以实验验证。     

Proper stability in porous media based in a natural clay

In this work, the synthesis and characterisation of two aluminium pillared clays is introduced and their thermal, hydrothermal and chemical stability is studied. The source material was a Spanish clay with a high percentage of montmorillonite, called SerBca. This clay was pillared using two different methods with the same relationship metal/clay. Some differences in the characteristics were found, but both showed thermal and hydrothermal stability until 700 °C and chemical stability between pH values from 1.5 to 11. These characteristics make those materials appropriate to be used in processes such as heterogeneous catalysis, where those conditions are required. Received: 30 March 2000     

Influence of dielectrics with light absorption on the photonic bandgap of porous alumina photonic crystals

In this work, the influences of dielectrics with light absorption on the photonic bandgaps (PBGs) of porous alumina photonic crystals (PCs) were studied. Transmittance spectra of porous alumina PCs adsorbing ethanol showed that all the PBGs positions red-shifted; however, the transmittance of the PBG bottom showed different trends when the PBGs were located in different wavelength regions. In the near infrared region, liquid ethanol has strong light absorption, and, with the increase in adsorption, the PBG bottom transmittance of porous alumina PCs first increased and then decreased. However, in the visible light region, liquid ethanol has little light absorption, and thus, with the increase in adsorption, the PBG bottom transmittance of porous alumina PCs increased gradually all the time. Simulated results were consistent with the experimental results. The capillary condensation of organic vapors in the pores of porous alumina accounted for the change in the PBG bottom transmittance. The nonnegligible light absorption of the organic vapors was the cause of the decrease in the transmittance. The results for porous alumina PC adsorbing methanol, acetone, and toluene further confirmed the influences of light absorption on the PBG bottomed transmittance.

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恒压下树脂在双尺度多孔介质中的流动特性

基于复合材料液态模塑(LCM)工艺过程中存在半饱和区域的实验现象以及对预制体双尺度效应的逐步认识, 一些学者提出用沉浸模型来研究双尺度多孔介质的不饱和流动。通过体积均匀化方法描述了双尺度多孔介质复合材料液态模塑工艺模型的特征, 得到含有沉浸项的双尺度多孔介质的质量守恒方程, 并采用有限元法对方程进行数值求解, 通过具体算例计算了考虑双尺度效应时恒压树脂注射下不同时段的压力分布状态, 得到树脂在填充过程中流动前沿半饱和区域从出现到消失的过程, 采用不同注射压力进行模拟并比较。结果表明, 与单尺度多孔介质模型不同, 双尺度多孔介质模型更能反映实际树脂填充过程中出现的半饱和区域现象。     

Equations of anomalous absorption onto swelling porous media

Absorption is a very common process which takes place on various types of materials ranging from porous media to new nano-materials and biological tissues. The majority of studies reported on absorption to date are concentrated on “rigid” porous media, which contradict the properties of real porous media which undergo swelling and shrinking changes. Here we present new absorption equations derived from a fractional diffusion-wave equation (fDWE) for absorption onto swelling porous media in a material coordinate. We show that the cumulative anomalous absorption is I(t) = St^β/2 and the absorption rate , where S is the anomalous sorptivity and β the order of fractional derivative in fDWE. Using published data on cumulative absorption against time, the two adsorption parameters are determined: β = 1.2448 and S = 2.7775 cm²/h. The value of β = 1.2448 implies that absorption onto this swelling porous media belong to the category of super-diffusion, which is a phenomenon unknown to us before. In comparison, the traditional absorption equations do not have such features. When S is determined, the anomalous diffusivity, D_m, is calculated using its relation with S. We expect that the proposed new absorption equations will be valuable for explaining new phenomena and processes encountered in broader disciplines of science and engineering applications.     

The heat and moisture transport properties of wet porous media

Existing methods for determining heat and moisture transport properties in porous media are briefly reviewed, and their merits and deficiencies are discussed. Emphasis is placed on research in developing new transient methods undertaken in China during the recent years. An attempt has been made to relate the coefficients in the heat and mass transfer equations with inherent properties of the liquid and matrix and then to predict these coefficients based on limited measurements.Invited paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 988, Gaithersburg, Maryland, U.S.A.     

Stabilized finite element methods with reduced integration techniques for miscible displacements in porous media

The objective of this work is to study some techniques to increase computational performance of stabilized finite element simulations of miscible displacements. We propose the use of a reduced integration technique for bilinear quadrilateral elements in the determination of the pressure and concentration fields. We also study the evaluation of pressure gradient (Darcy's velocity) by differentiation at super‐convergent points. Numerical examples are shown to validate our approach, accessing its efficiency and accuracy. Copyright © 2003 John Wiley & Sons, Ltd.     

Complex three‐dimensional microstructural permeability prediction of porous fibrous media with and without compaction

Much of the work in permeability prediction has so far been done with respect to the in‐plane properties. Guided by Darcy's law, the in‐plane permeabilities (i.e. Kxx and Kyy) have been well characterized by researchers both experimentally and, to some extent, analytically and numerically. Work on transverse or through thickness permeability, however, has been sparse. Owing to the fact that the limited length scale in the through thickness direction of most fibre preforms makes transverse permeability a difficult value to measure experimentally, the objective of the present development is to study the feasibility of applying the methodology proposed by the authors in a previous work for in‐plane permeability prediction to the estimation of transverse, as well as the in‐plane, permeability of a typical 3D woven fibre preform. The additional objective of this work is to present a preliminary study on the effects of fibre mat compression on the fibre preform permeability. Copyright © 2004 John Wiley & Sons, Ltd.     

Computational multiphase micro-periporomechanics for dynamic shear banding and fracturing of unsaturated porous media

Dynamic shearing banding and fracturing in unsaturated porous media are significant problems in engineering and science. This article proposes a multiphase micro-periporomechanics ( PPM) paradigm for modeling dynamic shear banding and fracturing in unsaturated porous media. Periporomechanics (PPM) is a nonlocal reformulation of classical poromechanics to model continuous and discontinuous deformation/fracture and fluid flow in porous media through a single framework. In PPM, a multiphase porous material is postulated as a collection of a finite number of mixed material points. The length scale in PPM that dictates the nonlocal interaction between material points is a mathematical object that lacks a direct physical meaning. As a novelty, in the coupled $$PPM, a microstructure-based material length scale is incorporated by considering micro-rotations of the solid skeleton following the Cosserat continuum theory for solids. As a new contribution, we reformulate the second-order work for detecting material instability and the energy-based crack criterion and J-integral for modeling fracturing in the $$PPM paradigm. The stabilized Cosserat PPM correspondence principle that mitigates the multiphase zero-energy mode instability is augmented to include unsaturated fluid flow. We have numerically implemented the novel $$PPM paradigm through a dual-way fractional-step algorithm in time and a hybrid Lagrangian–Eulerian meshfree method in space. Numerical examples are presented to demonstrate the robustness and efficacy of the proposed $$PPM paradigm for modeling shear banding and fracturing in unsaturated porous media.     

Gate elements at injection locations in numerical simulations of flow through porous media: applications to mold filling

Mold filling in polymer and composite processing is usually modelled as a special case of Darcy flow in porous media. The flow pattern and the time necessary to fill the mold depend on the ‘gate’ locations where resin is injected into the closed mold. In composite manufacturing, these are commonly outlets of small tubes transporting resin from a reservoir and their diameters are several orders of magnitude smaller than the mold dimensions. Similar size issue is also encountered in other applications of flow through porous media, such as oil and water pumping and drilling. Traditionally, these inlets are modelled by pressure or flow rate boundary condition as applied at a node of the finite element mesh that represents the injection gate. The omission of the inlet radius in the model results in a mathematical singularity as the mesh gets refined. The computed pressure or flow field depends on the mesh size and does not converge to the accurate solution, as the finite element mesh is refined. It is possible to deal with this phenomenon by modelling the inlet geometry more accurately but this approach is inefficient, as it requires additional degrees of freedom and, above all, significantly complicates the modelling process if the inlet location is not fixed a priori. This paper presents a more efficient alternate solution. It uses special ‘gate’ elements embedded in the mesh around the injection locations. Instead of adjusting the geometrical modelling of the injection location, the adjacent elements use modified shape functions to accurately model pressure field in the neighbourhood of small radial inlet. The proper pressure field shape‐functions for ‘gate’ elements based on linear finite elements are derived. The implementation in an existing mold filling simulation and how the ‘gate elements’ are automatically selected is described. An example to demonstrate the use of ‘gate’ elements and convergence towards the accurate solution with mesh refinement is presented. Copyright © 2004 John Wiley & Sons, Ltd.     

Elastic wave propagation in unsaturated porous media using hybrid‐Trefftz stress elements

The stress model of the hybrid‐Trefftz finite element is formulated for the analysis of elastodynamic problems defined on unsaturated porous media. The supporting mathematical model is the theory of mixtures with interfaces and considers the full coupling between the solid, fluid and gas phases, including the effect of seepage acceleration. Hybrid‐Trefftz stress elements use the free‐field regular solutions of the homogeneous Navier (or Beltrami) equation to construct the approximation of the generalized stresses in the domain of the element. The influence of non‐homogeneous terms in the Navier equation is modelled using solutions of the corresponding static problem. The resulting elements are highly convergent under p‐refinement and robust to both low and high excitation frequencies, as the trial functions embody relevant physical information on the modelled phenomenon. Copyright © 2013 John Wiley & Sons, Ltd.     

The relaxation effects of a saturated porous media using the generalized thermoviscoelasticity theory

In this paper, a model of the generalized thermoviscoelasticity for a saturated porous media is used. Taking the rheological properties of the volume into consideration, it is developed on the basis of the thermo-hydro-elastodynamic model proposed by the authors. The formulation is applied to the generalized porous thermoviscoelasticity theories: coupling theory, Lord-Shulman theory and Green-Lindsay theory. The general characteristic equations for arbitrary coordinate system are derived using a semi-analytical approach in the Laplace domain. Exact solutions of the saturated porous thermoviscoelastic media, with a cylindrical cavity that is subjected to a time dependent thermal load, are obtained in the absence of heat sources. Numerical results are illustrated graphically employing numerical method for inverting the Laplace transform. Comparisons are made with the results predicted by these theories and the classical theory. In addition, the influence of rheological parameters on the thermoviscoelastic property is analyzed.     

A consistent u‐p formulation for porous media with hysteresis

This paper presents a continuum formulation based on the theory of porous media for the mechanics of liquid unsaturated porous media. The hysteresis of the liquid retention model is carefully modelled, including the derivation of the corresponding consistent tangent moduli. The quadratic convergence of Newton's method for solving the highly nonlinear system with an implicit finite element code is demonstrated. A u‐p formulation is proposed where the time discretisation is carried out prior to the space discretisation. In this way, the derivation of all consistent moduli is fairly straightforward. Time integration is approximated with the Theta and Newmark's methods, and hence the fully coupled nonlinear dynamics of porous media is considered. It is shown that the liquid retention model requires also the consistent second‐order derivative for quadratic convergence. Some predictive simulations are presented illustrating the capabilities of the formulation, in particular to the modelling of complex porous media behaviour. Copyright © 2014 John Wiley & Sons, Ltd.