Compression-dependent permeability measurement for random soft porous media and its implications to lift generation

In the past decade, foundations have been laid for understanding the lift generation in a soft porous medium under rapid compaction (Feng and Weinbaum, 2000. Journal of Fluid Mechanics 422, 282–317; Wu et al., 2005b. Journal of Fluid Mechanics 542, 281–304; Wu et al., 2004a. Physical Review Letters 93(19), 194501; Barabadi et al., 2009. Journal of Heat Transfer 131(10), 101006-1–101006-12; Al-Chidiac et al., 2009. Journal of Porous Media 12(11), 1019–1035). One of the key parameters that affects the lift generation is the variation of the Darcy permeability as a function of compression. This critical problem is investigated in the current study using a novel experimental setup, namely a permeameter. Three different, soft, synthetic, fibrous, porous materials were chosen for the study. Their microstructures were characterized using a scanning electron microscope and a stereomicroscope. Their porosities were precisely measured using a water displacement method. By carefully controlling the air flow through the materials contained in a long Plexiglas tube of the permeameter, one obtained consistent results for the Darcy permeability of the tested material as a function of its porosity. Fluffing the porous materials caused disturbance of their microstructures thus variations in the permeability, especially in the high porosity range. The experimental data was curve-fitted and compared to established expressions. It showed that the Nogai Expression (Nogai and Ihara, 1978. Journal of Textile Machinery Society of Japan 31(12), T166–T170) provided the best fit for the change of permeability as a function of compression for the fibrous materials studied herein. The Carman–Kozeny equation, however, is only applicable for one of the fibrous materials. This finding is consistent with the theoretical predictions by Barabadi et al. (2009).     

Permeability of soft porous media under one-dimensional compaction

A novel experimental approach to measure permeability of porous material samples under variable longitudinal compaction has been developed. The material has a non-linear structural behavior and exhibits a small hysteresis during mechanical loading and unloading experiments. The new permeameter includes a piston moving inside a Plexiglas cylinder with controllable speed and a test section where the porous material sample is placed under compaction by two grids with adjustable positions. Time-dependent pressure was recorded at four different locations along the sample together with the velocity of the piston. Experiments with two different sample lengths have been performed at three different Reynolds numbers based on the apparatus diameter. The results show that pressure gradient and permeability data do not depend on initial uncompacted sample length. All experiments included measurements at various compaction ratios of the material followed by measurements during relaxation/expansion of the material. No hysteresis was observed in the pressure gradient and permeability data during compaction and expansion of the material for a wide range of compaction ratio. The effects of small velocity fluctuations due to variable friction of the moving piston with cylinder’s wall were also considered. These velocity fluctuations cause pressure fluctuations within the sample which are high close to the inlet part of the material sample and are reduced almost completely towards its outlet. However these pressure fluctuations when scaled with the corresponding mean pressure retained their time-dependent amplitude and phase unchanged along the material. These relative pressure fluctuations cancelled out the flow velocity fluctuations resulting insignificant fluctuations in permeability. It was found that permeability, which is a material property, is drastically reduced with increased compaction ratio of the material while its solid fraction changes substantially but its porosity remains practically unchanged. A comparison with the Cármán–Kozeny expression for random porous media was also examined. Cármán–Kozeny expression predicts qualitatively the reduction of permeability with compaction. However, the predicted values of permeability are very sensitive to the initial value of porosity.     

Non-Newtonian flow in porous media

In this article we present a review of the single-phase flow of non-Newtonian fluids in porous media. The four main approaches for describing the flow through porous media in general are examined and assessed in this context. These are: continuum models, bundle of tubes models, numerical methods and pore-scale network modeling.     

Foam gel-casting preparation of SiC bonded ZrB2 porous ceramics for high-performance thermal insulation

Lightweight SiC-ZrB₂ porous ceramics is of great potential as thermal insulation material used in aerospace, chemical and energy industries. In this work, a series of SiC bonded ZrB₂ (SiC_b-ZrB₂) porous ceramics with porosity high up to 86.9% were prepared by a simple foam gel-casting method. The SiC_b-ZrB₂ porous ceramic prepared at 1573 K exhibited a low thermal conductivity of 0.280 W/(m?K) and a reasonable compressive strength of 0.52 MPa. It could maintain the original geometric shape and microstructure after a secondary heat treatment at 1473 K in inert atmosphere. When heating the samples with thickness of 30 mm for 12 min with an alcohol spray lamp (～1273 K), the temperatures of the cold sides of SiC_b-ZrB₂ ceramics were all lower than 432 K, demonstrating their exceptional insulation capabilities. The present work provides a simple route to produce robust and thermally-insulating non-oxide porous ceramics for use under high temperature.     

A research into thermal field in fluid-saturated porous media

Until now, the theory, methodology of investigations, and interpretation of thermometry data have been most completely developed for single-phase (oil, water, or gas) flows in formations. However, multiphase (oil+gas, oil+water, and oil+water+gas) flows in formations are more common in practice. This is primarily typical for fields featuring a high value of gas factor and saturation pressure, as well as for cases of formation tests at low values of bottom-hole pressure. Analysis of actual thermograms under these conditions has shown that the earlier-developed techniques for the cases of single-phase flows in the formation and the well cannot be applied here.This paper presents research data on the influence of the adiabatic and Joule-Thomson effects and the heat of fluid degassing on temperature field in porous medium.     

Novel NMR techniques for porous media research

Recent years have seen a significant progress in the study of porous media of natural and industrial sources. This paper provides a brief outline of the recent technical development of NMR in this area. These progresses are relevant for NMR applications in material characterization.     

Particulate clusters and permeability in porous media

The permeability of particulate colloidal titanium dioxide, P25, was investigated during sedimentation, permeation and filtration when suspended in water at a consistent ionic strength similar to tap water. Happel's cell model of permeability was used to determine the apparent particle size during these processes, and compared with the size of particle clusters measured using laser diffraction under identical ionic conditions and varying degree of shear. The primary particle size of the P25 was determined to be 28 nm, from consideration of the surface area and density of the particles, and the cluster size during permeation and filtration was close to 100 nm. During sedimentation the cluster size was determined to be close to 10 μm, which is the same size obtained by laser diffraction when measuring under conditions of low shear. Using the above two sizes (28 nm and 10 μm) as limits in Happel's permeability model it was possible to determine an ‘operating envelope’ of permeability that matched the experimentally measured values for the sedimentation, permeation and filtration processes.     

Characterization of impregnated particles via powder rheology

This work presents a specific application of a new powder rheometer prototype, for the characterization of liquid-impregnated particles which are used in chemical engineering for gas treatment on fixed beds. This new type of rheological characterization can provide useful information about the surface state of the particles and could contribute to the optimization of the impregnation process. The rheometer, consisting of a stress-imposed rheometer coupled with a vibrating cell, generates a Brownian-like motion at a macroscopic scale which makes the sample behave as a non-Newtonian condensed fluid, and allows rheological property measurements of powders which are very sensitive to changes on their surface. Their rheological behavior and its relationship with the impregnation ratio have been analyzed for several samples having different impregnation ratios, thanks to a free volume structural model taking into account the shear rate, the frictional stress, the granular pressure, the vibration frequency, the vibration energy, the free volume distribution and the mass of the samples. The resulting interpretation suggests a stepped kinetic of impregnation: first the liquid adsorbs on the surface of the silica matrix, then it fills progressively the pores, and finally it coats the outer surface of the particles.     

泡沫分离技术及其发展现状

探讨了泡沫分离技术的原理、泡沫分离设备及泡沫分离技术的研究进展。泡沫分离过程的性能受很多因素的影响 ,例如 ,进料液浓度、气泡尺寸、气体流量、泡沫的排液、进料位置、聚并、温度等。阐述了现有的几种新技术 ,如低重力条件操作、通过压力梯度而提高分离效率。此外 ,还简要介绍了泡沫分离塔中传质单元数和传质单元高度的概念。     

Nonlinear, multicomponent, mass transport in porous media

In this paper we consider multicomponent mass transport in porous media for non-dilute solutions. This process is described by coupled, nonlinear transport equations that must be spatially smoothed in order to be useful. This spatial smoothing, or upscaling, is achieved by the method of volume averaging for the case of negligible adsorption, desorption, and heterogeneous reaction. For pure diffusion, the results demonstrate that a single tortuosity tensor applies to the transport of all species. When convective transport is important, the process becomes much more complex and it is difficult to generalize about the behavior of the various dispersion tensors.     

A synchronous cellular automaton model of mass transport in porous media

In this work we present a fully synchronous coarse grained cellular automaton model for large-scale simulations at molecular level. The model is based on Margolus partitioning scheme, which was generalized as to describe quantitatively diffusion, adsorption and directed flow in porous media. Our aim is to create conceptually simple and computationally efficient framework to model the mass transport in porous materials with large representative volume. This work focuses on the fundamental aspects of the generalized Margolus cellular automaton. We exemplify the model by solving several diffusion problems, studying the monolayer adsorption, chromatography on disordered porous structures and chemical transformation in a system with phase separation. The results indicate that the model reflects the essential features of these phenomena. Absence of round-off errors, fully synchronous way of implementation, autonomous physically meaningful time scale and ease-to-handle boundary conditions make this model a promising framework for study various transport phenomena in porous structures.     

Parametric investigations of premixed methane-air combustion in two-section porous media by numerical simulation

Motivated by detailed designs of industrial porous burners published in patents, the combustion of methane-air mixtures in a two-section porous burner has been studied numerically. The software FLUENT is used to solve a two-dimensional transient mathematical model of the combustion. In order to reveal the reality of the combustion in porous media, the user defined function (UDF) is used to extend the ability of FLUENT and enable two-dimensional distributions of temperature and velocity to be obtained. Some operating or property parameters, which mainly affect the functions and quality of the industrial burner design, such as the inlet velocity of the reactants, the equivalence ratio, the extinction coefficient and the thermal conductivity of porous media, have been investigated. The results show that the contours of temperature and velocity change considerably at the interface of the porous media and near the wall, the gas temperature at the low inlet velocity limit is higher than that for the high velocity limit, the thermal conductivity in the upstream section has more influence on the temperature than that in the downstream section and finally, the temperature profiles of both the gas and the porous skeleton vary considerably with changes of the radiative extinction coefficient of the large-pore porous media.     

Role of entropy generation on thermal management during natural convection in porous square cavities with distributed heat sources

Material processing by thermal convection may be carried out in an energy efficient way based on the second law of thermodynamics. In the current work, the entropy generation in porous square cavities with distributed heat sources during laminar natural convection has been studied. Four different configurations of discretely heated cavities are considered for the study based on the location of the heat sources on the walls of the cavities. The governing equations are solved using Galerkin finite element method. The entropy generation terms are evaluated using finite element basis sets and the derivatives at particular nodes are estimated based on the functions within adjacent elements. Simulations are performed for the range of Darcy number, Da=10⁻⁶–10⁻³ and Rayleigh number, Ra=10³–10⁶ for various fluids (Prandtl number, Pr=0.015,0.7,10 and 1000). A detailed analysis on the effect of Da on entropy generation due to heat transfer (S_θ) and fluid friction (S_ψ) based on their local distribution in various cases is presented. The maximum values of S_θ are found to occur near the hot–cold junctions while the maximum values of S_ψ are found at various locations on the walls of the cavity depending on the circulation cells in various configurations. Significant S_ψ is also observed in the interior regions due to the friction between counter rotating circulation cells. The dominance of S_ψ is found to be high for higher Pr fluids. The total entropy generation rate (S_total) is found to increase with Da and the average Bejan number (Be_av) is found to be less than 0.5, indicating the dominance of fluid friction irreversibility at higher Da in all cases for various fluids. Finally, the thermal mixing, temperature uniformity has been correlated with S_total and Be_av for all distributed heating cases and the thermal management via enhanced thermal mixing vs optimal entropy production for efficient thermal processing of various fluids in porous media are proposed.     

Gas transport in tight porous media: Gas kinetic approach

We describe the flow of gas in a porous medium in the kinetic regime, where the viscous flow structure is not formed in separate pores. Special attention is paid to the dense kinetic regime, where the interactions within the gas are as important as the interaction with the porous medium. The transport law for this regime is derived by means of the gas kinetic theory, in the framework of the model of “heavy gas in light one”. The computations of the gas kinetic theory are confirmed by the dimension analysis and a simplified derivation revealing the considerations behind the kinetic derivation. The role of the thermal gradient in the transport law is clarified.     

多孔泡沫金属及其在化工设备中的应用

介绍了多孔泡沫金属的结构特征与力学、热物理、渗透、电学和声学等性能,重点讨论了它在化工生产装置中的应用状况,并对其在研究中存在的问题和应用前景作了评述。     

CAPILLARY NETWORK MODELS FOR TRANSPORT IN PACKED BEDS: CONSIDERATIONS OF PORE ASPECT RATIO

The conventional analysts for the estimation of the tortuosity factor for transport in porous media is modified here to account for the effect of pore aspect ratio. Structural models of the porous medium are also constructed for calculating the aspect ratio as a function of porosity. Comparison of the model predictions with the extensive data of Currie (1960) for the effective diffusivity of hydrogen in packed beds shows good agreement with a network model of randomly oriented intersecting pores for porosities upto about 50 percent, which is the region of practical interest. The predictions based on this network model are also found to be in better agreement with the data of Currie than earlier expressions developed Tor unconsolidated and grainy media.     

Simulation of micro- and macro-transport in a packed bed of porous adsorbents by lattice Boltzmann methods

In this study we report 3D simulation of concentration profiles in a fixed bed packed with spherical porous adsorbents using lattice Boltzmann methods (LBMs). The lattice models have been developed to investigate evolution of concentration profiles due to inter- and intra-particle mass transport in an adsorber having small tube-to-sphere diameter (d_t/d_p) ratios. The multi-scaling feature of LBMs permits full 3D simulation of concentration profiles both in the bed voids and within the pores of the adsorbents without using any empirical correlations or without making 1D or 2D approximations that are usually made in traditional numerical methods. The model simulation is carried out for varying packing arrangements and small to large pore diffusivities. The simulation results show significant concentration gradients for small pore diffusivities and large particle size, which must be considered in predicting breakthrough and adsorption times for a tubular adsorber having d_t/d_p<10. The model predicted breakthrough curves are validated with the experimental data obtained by tomography technique in a tubular adsorber packed with zeolite particles.     

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.     

Instability due to wettability alteration in displacements through porous media

Wettability of some petroleum reservoir rocks can be altered by changing the brine composition, e.g., lowering salinity or adding surfactants. Wettability alteration can mobilize stranded oil and enhance oil recovery. Analytical solutions for 1D tertiary low-salinity floods show two saturation shocks one of which is associated with an adverse mobility ratio. The adverse mobility ratio across this shock is not very large, about 1.5-3 in the cases considered. As the viscosity ratio increases, the width of the oil bank decreases and one of the shocks disappears at a high viscosity ratio (>10). The remaining shock at high viscosity ratio is stable. A viscous fingering model is applied to describe the flow instability in relatively homogeneous multi-dimensional porous media. It shows that the viscous fingering is mild and the breakthrough of low-salinity injectant is only 11-31% faster than in the 1D flow. Numerical simulation of these displacements in 2D permeability fields show that the fingering model approximates the average saturation profile if the standard deviation in permeability heterogeneity is low. Fingering behavior depends mostly on permeability standard deviation, but not on correlation length for the spherical variogram model used in this study. Low-salinity floods are expected to be mildly unstable due to the low mobility ratio at adverse saturation shocks.