Flow In Porous Materials Research Articles

The Generalized Inverse Computing Method of a Class of Block Matrix from Models for Flow in Porous Materials

The generalized inverse method of block matrix plays an effective and important role during the computing procedure of certain mathematical models. Some numerical methods for flow models in porous materials are discussed in this paper. Firstly, some partial differential equation models of flow in porous materials are given. Then a class of block matrix from the discrete systems of mathematic models by the multiscale finite element methods are analyzed. Finally, the generalized inverse of the two-by-two block matrix are obtained and the algorithm for computing the minus inverse is presented. The presented methods have an advantage of concise computing procedure for the simulation of models.

Liquid wicking behavior in paper-like materials: mathematical models and their emerging biomedical applications

Paper-like materials have found widespread applications in various fields, especially recently emerging applications in biomedicine as paper-based devices, where liquid wicking behavior plays a significant role. Although tremendous experimental evidence has indicated that fluid control is a key technology to improve the performance of these paper-based devices, the underlying mechanisms of liquid wicking behavior in paper-like materials remain unclear. Numerical and mathematical techniques provide effective strategy and great potential in understanding the liquid flowing process in the complex fibrous structure of paper-like materials. In this review, we first present the basic physical process and key factors of liquid wicking behavior in paper-like materials. Furthermore, we review various macroscopic and mesoscopic mathematical models on fluid flow in porous materials, focusing on each model’s advantages and challenges, and summarize their related biomedical applications. The aims are to better understand the underlying mechanisms of liquid wicking behavior in paper-like materials through mathematical models and to provide guidance in the design and optimization of paper-based biomedical devices.

Time-Dependent Model for Fluid Flow in Porous Materials with Multiple Pore Sizes.

An understanding of fluid transport through porous materials is critical for the development of lateral flow assays and analytical devices based on paper microfluidics. Models of fluid transport within porous materials often assume a single capillary pressure and permeability value for the material, implying that the material comprises a single pore size and that the porous material is fully saturated behind the visible wetted front. As a result, current models can lead to inaccuracies when modeling transport over long distances and/or times. A new transport model is presented that incorporates a range of pore sizes to more accurately predict the capillary transport of fluid in porous materials. The model effectively predicts the time-dependent saturation of rectangular strips of Whatman filter no. 1 paper using the manufacturer's data, published pore-size distribution measurements, and the fluid's properties.

A prospect for computing in porous materials research: Very large fluid flow simulations

Properties of porous materials, abundant both in nature and industry, have broad influences on societies via, e.g. oil recovery, erosion, and propagation of pollutants. The internal structure of many porous materials involves multiple scales which hinders research on the relation between structure and transport properties: typically laboratory experiments cannot distinguish contributions from individual scales while computer simulations cannot capture multiple scales due to limited capabilities. Thus the question arises how large domain sizes can in fact be simulated with modern computers. This question is here addressed using a realistic test case; it is demonstrated that current computing capabilities allow the direct pore-scale simulation of fluid flow in porous materials using system sizes far beyond what has been previously reported. The achieved system sizes allow the closing of some particular scale gaps in, e.g. soil and petroleum rock research. Specifically, a full steady-state fluid flow simulation in a porous material, represented with an unprecedented resolution for the given sample size, is reported: the simulation is executed on a CPU-based supercomputer and the 3D geometry involves 16,3843 lattice cells (around 590 billion of them are pore sites). Using half of this sample in a benchmark simulation on a GPU-based system, a sustained computational performance of 1.77 PFLOPS is observed. These advances expose new opportunities in porous materials research. The implementation techniques here utilized are standard except for the tailored high-performance data layouts as well as the indirect addressing scheme with a low memory overhead and the truly asynchronous data communication scheme in the case of CPU and GPU code versions, respectively.

An electrochemical-sensor system for real-time flow measurements in porous materials.

Flow monitoring in porous materials is critical for the engineering of paper-based microfluidic bioassays. Here, we present an electrochemical-sensor system that monitors the liquid flow in porous materials without affecting the real flow in paper-strip samples. The developed microfluidic sensor records an amperometric signal created by the solution movement mediated by paper wicking. This approach allows the in situ monitoring of the different hydrodynamic conditions of a specific paper geometry or composition. In addition, the method proposed in this work was employed to characterise the fluid flow of different nitrocellulose paper strips after oxygen-plasma treatment or dextran coating. The dextran fluid-flow modifiers were further used on the paper strip-based assays as means of signal enhancement. The proposed electrochemical-sensing method offers a valuable alternative to existing optical-based monitoring techniques for flow measurement in paper-based microfluidic systems.

A multiphase porous medium transport model with distributed sublimation front to simulate vacuum freeze drying

A porous medium transport model with a distributed sublimation front is developed for low pressure freeze drying of beef by radiant surface heating and volumetric microwave heating. The model incorporates the importance of Knudsen flow in porous materials during low pressure freeze drying. This effort is part of fundamental physics-based framework building for simulating food and biomaterial processes involving rapid evaporation/sublimation. Temperature, pressure and ice saturation histories were computed. Drying rates and spatial temperature profiles showed excellent agreement with literature experimental data. Sublimation front width, a novel result, is seen to increase as ice saturation decreases, justifying the importance of this distributed sublimation formulation in contrast with the sharp sublimation front commonly employed in literature. The insulation effect of the gas fraction in the pores is observed by the slow movement of the sublimation front in ‘thick’ samples. Effects of porosity, initial ice saturation and microwave heating are illustrated.

A combined numerical and experimental framework for determining permeability properties of the arterial media.

The medial layer of the arterial wall may play an important role in the regulation of water and solute transport across the wall. In particular, a high medial resistance to transport could cause accumulation of lipid-carrying molecules in the inner wall. In this study, the water transport properties of medial tissue were characterised in a numerical model, utilising experimentally obtained data for the medial microstructure and the relative permeability of different constituents. For the model, a new solver for flow in porous materials, based on a high-order splitting scheme, was implemented in the spectral/hp element library nektar++ and validated. The data were obtained by immersing excised aortic bifurcations in a solution of fluorescent protein tracer and subsequently imaging them with a confocal microscope. Cuboidal regions of interest were selected in which the microstructure and relative permeability of different structures were transformed to a computational mesh. Impermeable objects were treated fictitiously in the numerical scheme. On this cube, a pressure drop was applied in the three coordinate directions and the principal components of the permeability tensor were determined. The reconstructed images demonstrated the arrangement of elastic lamellae and interspersed smooth muscle cells in rat aortic media; the distribution and alignment of the smooth muscle cells varied spatially within the extracellular matrix. The numerical simulations highlighted that the heterogeneity of the medial structure is important in determining local water transport properties of the tissue, resulting in regional and directional variation of the permeability tensor. A major factor in this variation is the alignment and density of smooth muscle cells in the media, particularly adjacent to the adventitial layer.

A novel three-dimensional element free Galerkin (EFG) code for simulating two-phase fluid flow in porous materials

Abstract In the past few decades, numerical simulation of multiphase flow systems has received increasing attention because of its importance in various fields of science and engineering. In this paper, a three-dimensional numerical model is developed for the analysis of simultaneous flow of two fluids through porous media. The numerical approach is fairly new based on the element-free Galerkin (EFG) method. The EFG is a type of mesh-less method which has rarely been used in the field of flow in porous media. The weak forms of the governing partial differential equations are derived by applying the weighted residual method and Galerkin technique. The penalty method is utilized for imposition of the essential boundary conditions. To create the discrete equation system, the EFG shape functions are used for spatial discretization of pore fluid pressures and a fully implicit scheme is employed for temporal discretization. The obtained numerical results indicate that the EFG method has the capability to substitute the classical FE and FD approaches from the accuracy point of view, provided that the efficiency of the EFG is improved. The developed EFG code can be used as a robust numerical tool for simulating two-phase flow processes in the subsurface layers in various engineering disciplines.

A pore network model for simulating non-ideal gas flow in micro- and nano-porous materials

The capability to simulate real gas flow in porous materials with micro- and nano-meter-scale pores is of importance in many applications, such as gas extraction from shale reservoirs, and the design of gas-based fuel cells. A node-bond pore-network flow model (PNFM) has been developed for gas flow where it is the only fluid phase. The flow conductance equation includes the usual Darcy flow terms, and additional terms that capture the contributions from slip flow to Knudsen diffusion. With respect to the case for a non-ideal gas, the extra contributions, which are necessary, to the coefficients of the Darcy and Knudsen terms, are expressed in terms of reduced temperature and pressure, using van der Waals’s two-parameter principle of corresponding states. Analysis on cylindrical pores shows that the coefficient deviates from that of the non-ideal gas case by more than 80% in the Darcy term, while between −80% and 150% in the Knudsen term, when the physical states approach to the critical state of the fluid. Although the deviations become smaller when the states are away from the critical state, they remain relatively large even at conditions relevant to practical applications. The model was applied to a pore network of a realistic 3D shale model to show slippage and Knudsen effects on the predicted permeability and the sensitivity to pore sizes. Simulations were carried out for methane under the operational conditions of typical shale-gas reservoirs, and nitrogen under the conditions of laboratory experiments. The results show that the ratio of gas and Darcy permeability correlates positively and strongly with the pore size but inversely with the gas pressure and Tangential Momentum Accommodation Coefficient (TMAC) in the slip term, which can impact gas permeability disproportionally. The results are in favour of controlling the rate of gas depressurisation to avoid early depletion in shale gas production. The methane permeability is shown to be 30% greater, relatively, than that when the ideal gas law is applied, even under normal field operational conditions, while the nitrogen permeability can only approximate the methane permeability within a certain range of field operational conditions when the slip flow is not dominating.

RETRACTED ARTICLE: Numerical analysis of multiphase flow in porous material

RETRACTED ARTICLE: Numerical analysis of multiphase flow in porous material

Comparison of Four Thermo-Mechanical Models for Simulating Reactive Flow in Porous Materials

The objective of this paper is to present numerical simulations of combustion of an air/methane mixture in porous materials using a model that considers the intra-pore levels of turbulent kinetic energy. Transport equations are written in their time-and-volume-averaged form and a volume-based statistical turbulence model is applied to simulate turbulence generation due to the porous matrix. Four different thermo-mechanical models are compared, namely Laminar, Laminar with Radiation Transport, Turbulent, Turbulent with Radiation Transport. Combustion is modeled via a unique simple closure. Preliminary testing results indicate that a substantially different temperature distribution is obtained depending on the model used. In addition, for high excess air peak gas temperature are reduced.

A Numerical Approach for Non-Linear Moisture Flow in Porous Materials with Account to Sorption Hysteresis

A numerical approach for moisture transport in porous materials like concrete is presented. The model considers mass balance equations for the vapour phase and the water phase in the material together with constitutive equations for the mass flows and for the exchange of mass between the two phases. History-dependent sorption behaviour is introduced by considering scanning curves between the bounding desorption and absorption curves. The method, therefore, makes it possible to calculate equilibrium water contents for arbitrary relative humidity variations at every material point considered. The scanning curves for different wetting and drying conditions are constructed by using third degree polynomial expressions. The three coefficients describing the scanning curves is determined for each wetting and drying case by assuming a relation between the slope of boundary sorption curve and the scanning curve at the point where the moisture response enters the scanning domain. Furthermore, assuming that the slope of the scanning curve is the same as the boundary curve at the junction point, that is, at the point where the scanning curve hits the boundary curve once leaving the scanning domain, a complete cyclic behaviour can be considered. A finite element approach is described, which is capable of solving the non-linear coupled equation system. The numerical calculation is based on a Taylor expansion of the residual of the stated problem together with the establishment of a Newton-Raphson equilibrium iteration scheme within the time steps. Examples are presented illustrating the performance and potential of the model. Two different types of measurements on moisture content profiles in concrete are used to verify the relevance of the novel proposed model for moisture transport and sorption. It is shown that a good match between experimental results and model predictions can be obtained by fitting the included material constants and parameters.

Plastic flow of porous materials in friction contact area

The paper considers the instantaneous stress-strain state in an infinite hollow porous plastic cylinder subjected to simultaneous radial compression and twisting by shear stresses applied to the cylinder surface. It is assumed that the cylinder material obeys a cylindrical yield criterion and associated flow rule. The asymptotic behavior of the equivalent strain rate near the maximum friction surface is studied. It is shown that the distribution of this quantity follows the inverse square root rule near the maximum friction surface. It is noted that the same dependence is observed in the case of incompressible perfect rigid-plastic material. The strain rate intensity factor is found and is compared to that derived from the corresponding perfect rigid-plastic solution.

Measurement of Physical Characteristics of Particle Beds for Drying

Among physical characteristics of porous materials, properties related to liquid flow in porous materials play a critical role in the prediction of drying curves. In the present work, a simple experimental method was developed to simultaneously measure the capillary pressure and the relative permeability of particle beds by a simple drainage method. The observed data of permeability at low saturation of less than 70% was in fair agreement with a range of two lines that were predicted from the Campbell model. The purpose of the development of the present drainage method along with the drying method described in a previous paper is to provide a group of physical properties which are needed for prediction of drying curves by use of minimal measurement devices.

Analysis of moisture flow in porous materials using microfocus X-ray radiography

Microfocus X-ray projection is presented as an accurate experimental technique for measuring moisture transport processes in porous materials. The technique has evolved from the better-known medical technique. Compared to classical γ-ray and NMR-techniques it allows an instant and accurate determination of the two-dimensional transient moisture content profiles. A calibration procedure is presented to optimise the resolution in moisture content by choosing an adequate sample thickness in relation to the energy of the X-ray source. To illustrate the capabilities of the X-ray projection method, examples of two-dimensional liquid water uptake in homogeneous, heterogeneous, micro- and macro-fractured materials are presented.

Diffusion and Chemical Reaction in the Porous Structures of Solid Oxide Fuel Cells

The Rolls-Royce integrated-planar solid oxide fuel cell (IP-SOFC) consists of ceramic modules with electrochemical cells printed on the outer surfaces. The cathodes are supplied with oxygen from air flowing over the outside of the module and the anodes are supplied with fuel diffusing from the internal gas channels. Natural gas is reformed into hydrogen in a separate reformer module of similar design except that the fuel cells are replaced by a reforming catalyst layer. The performance of the modules is intrinsically linked to the behavior of the gas flows within their porous structures. The multi-component convective-diffusive flows are simulated using a new theory of flow in porous material, the cylindrical pore interpolation model. The effects of the catalyzed methane reforming and water-gas shift chemical reactions are also considered using appropriate kinetic models. It is found that the shift reaction, which is catalyzed by the anode material, has certain beneficial effects on the fuel cell module performance. The shift reaction enables the fuel cells to make effective use of carbon monoxide as a fuel when the supplied fuel has become depleted of hydrogen. In the reformer module the kinetics of the reaction make it difficult to sustain a high methane conversion rate. Although the analysis is based on IP-SOFC geometry, the modeling approach and general conclusions are applicable to other types of SOFCs.

Supercritical fluid flow in porous media: modeling and simulation

The present work aims the modeling and simulation of supercritical fluid flow through porous media. This type of flow appears in several situations of interest in applied science and engineering, as the supercritical flow in porous materials employed in chromatography, supercritical extraction and petroleum reservoirs. The fluid is constituted of one pure substance, the flow is monophasic, highly compressible and isothermal. The porous media is isotropic, possibly heterogeneous, with rectangular format and the flow is two-dimensional. The heterogeneities of porous media are modeled by a simple power law, which describes the relationship between permeability and porosity. The modeling of the hydrodynamic phenomena incorporates the Darcy's law and the equation of mass conservation. Appropriated correlations are used to model, in a realistic form, the density and the viscosity of the fluid. A conservative finite-difference scheme is used in the discretization of the differential equations. The nonlinearity is treated by Newton method, together with the conjugate gradient method. The results of the simulation for pressure and mobility of supercritical and liquid propane flowing through porous media are presented, analyzed and graphically depicted.

Inertial effects and diffusion

Fick’s law of diffusion is equivalent to an equation of motion for an ideal substance in which the thermodynamic driving force is assumed to be balanced by a drag force proportional to drift velocity. Neglect of the inertial force required by Newton’s second law leads to anomalous short-time predictions such as infinite speeds of propagation. Resolution of the propagation anomaly for chemical diffusion is considered for three applications: Knudsen flow in porous materials, interstitial diffusion in elastic solids, and interstitial diffusion in viscoelastic solids. The transients associated with inertial effects for the first two cases occur at very short-times and are typically of little practical significance. Diffusion in viscoelastic solids appears as a possible exception based on observations of linear transport kinetics in ordinary timescales. The constitutive equations for the Maxwell model lead to the prediction that solute-induced dilatations propagate according to the telegraph equation, a widely proposed correction for avoiding the propagation anomaly in standard diffusion theory. The telegraph equation is not universally valid, however. In the case of Knudsen flow, for example, inertial effects give rise to an additional term related to material convection.

On Two-Phasic Flow Problems in Elasto-Plastic Porous Materials

In the present contribution, the formulation of the governing equations of coupled flow and deformation processes in porous materials is based on the well-founded Theory of Porous Media (TPM) [2, 3]. Embedded in this concept, the model under consideration represents a triphasic medium of a cohesive-frictional elasto-plastic solid skeleton and a binary pore-fluid, which is composed of a materially incompressible wetting phase (here water) and a materially compressible non-wetting phase (here air). The unsaturated domain (saturation in terms of liquid saturation) of the porous medium is included in the model by the application of a suitable capillary-pressure-saturation relation, which takes into account the interaction of the solid skeleton and the two pore-fluids. Furthermore, the interaction is described by Darcy's filter law including a relative permeability, which depends on the deformation of the pore space and the degree of saturation.

On perfectly plastic flow in porous material

Experimental observations suggest that for perfectly-plastic materials containing pores, the (small) strain at which significant macroscopic yielding occurs is relatively insensitive to porosity, for volume fractions below approximately 15–20% (although the yield stress drops significantly with increasing porosity). Another observation is that, at these porosity levels, the stress–strain curve remains approximately linear almost up to the yield point. Based on these observations, Sevostianov and Kachanov constructed yield surfaces that explicitly reflect the shapes of the pores and their orientation. The underlying microscale mechanism is that local plastic “pockets” near pores blunt the stress concentrations; as a result, they remain limited in size and well contained in the elastic field until they connect and almost the entire matrix plasticizes within a narrow interval of stresses that can be idealized as the yield point. The present paper provides direct insight into the micromechanics of poroplasticity through direct microscale numerical simulation. Besides confirming the basic microscale mechanism, these simulations reveal that the reduction of the macroscopic poroplastic yield stress is approximated quite closely by 1−v2 times the dense nonporous yield stress, where v2 is the volume fraction of the pores.