Interface In Porous Medium Research Articles

The effect of pore size distribution on the fractal evaporative interface in porous media

This article aims to comprehensively analyze the heat and mass transfer and fractal evaporative interface in porous media with different pore size distribution through experiments and simulations of water. Weierstrass-Mandelbrot(W-M) function is used to establish a fractal evaporative interface based on fractal dimension and scaling parameter, which are determined by parameters of pore. The evaporative interface at the pore level is observed in the experiment with aluminum and nickel porous media, which shows reliability of model. The simulation results reveal that when the mass flow rate enlarges, the average Nusselt number, RMS and STD gradually grow, and the average temperature, vapor volume fraction, and velocity reduce, which indicates better thermal protection. As the initial temperature of the bottom improves, the trends in these variables are opposite except for STD, which means more irregular of evaporative interface. These findings have potential applications in transpiration cooling with high temperature in aerospace field and technologies requiring a stable evaporative interface, such as seawater desalination.

The Dynamics of Per- and Polyfluoroalkyl Substances (PFAS) at Interfaces in Porous Media: A Computational Roadmap from Nanoscale Molecular Dynamics Simulation to Macroscale Modeling.

Managing and remediating perfluoroalkyl and polyfluoroalkyl substance (PFAS) contaminated sites remains challenging. The major reasons are the complexity of geological media, partly unknown dynamics of the PFAS in different phases and at fluid-fluid and fluid-solid interfaces, and the presence of cocontaminants such as nonaqueous phase liquids (NAPLs). Critical knowledge gaps exist in understanding the behavior and fate of PFAS in vadose and saturated zones and in other porous media such as concrete and asphalt. The complexity of PFAS-surface interactions warrants the use of advanced characterization and computational tools to understand and quantify nanoscale behavior of the molecules. This can then be upscaled to the microscale to develop a constitutive relationship, in particular to distinguish between surface and bulk diffusion. The dominance of surface diffusion compared to bulk diffusion results in the solutocapillary Marangoni effect, which has not been considered while investigating the fate of PFAS. Without a deep understanding of these phenomena, derivation of constitutive relationships is challenging. The current Darcy scale mass-transfer models use constitutive relationships derived from either experiments or field measurements, which makes their applicability potentially limited. Here we review current efforts and propose a roadmap for developing Darcy scale transport equations for PFAS. We find that this needs to be based on systematic upscaling of both experimental and computational studies from nano- to microscales. We highlight recent efforts to undertake molecular dynamics simulations on problems with similar levels of complexity and explore the feasibility of conducting nanoscale simulations on PFAS dynamics at the interface of fluid pairs.

Prediction of relative permeability from capillary pressure based on the fractal capillary bundle model

The accurate prediction of relative permeability is one of the most important issues in the study of multiphase flow in porous media and is involved in many fields, such as geothermal energy development and petroleum engineering. Traditional models such as the Purcell model and Burdine model for predicting relative permeability from capillary pressure usually assume that the wetting phase (WP) flows in small pores and that the nonwetting phase (NWP) flows in large pores, which is a limiting assumption, such that these models cannot describe the process of WP being displaced by NWP. In this study, we propose a generalized theoretical model for calculating relative permeability based on the fluid distribution characteristics and the fractal capillary bundle model. The relative location α of the interface between NWP and WP is introduced to characterize the transport of the two-phase interface in porous media. The developed model was validated with relative permeability experimental data of gas–water/oil and compared with the Li model and the Brooks–Corey model. The comparison results show that the new model provides an improved match to experimental data than the Li model and the Brooks–Corey model. The sensitivity analysis results of the model show that tortuosity and pore size distribution play a key role in predicting relative permeability from the capillary pressure curve. The relative permeability of wetting phase decreases significantly with increasing fractal dimension of tortuosity and fractal dimension of pore size distribution. The effect of parameter α, which reflects fluid transport characteristics, on relative permeability of wetting phase is more pronounced in porous media with complex structures and low/ultralow permeability.

First-order approximate analytical expressions of oblique incident elastic wave at an interface of porous media saturated with a non-viscous fluid

The analysis technology of Amplitude Variation with Offset (AVO) is one of the important methods for oil and gas reservoir prediction. Zoeppritz equation and its approximations are the theoretical basis of AVO analysis, which assumes that the upper and lower media of a horizontal interface are single-phase media. Limited by this assumption, AVO analysis has limited prediction and identification accuracy for complex porous reservoirs. In view of this, the first-order approximate analytical expressions of oblique elastic wave at an interface of porous media are derived. Firstly, the incident and scattering characteristics of various waves at the interface of porous media are analyzed, and the displacement vectors generated by these elastic waves are described by exponential function. Secondly, the kinematic and dynamic boundary conditions at the interface of porous media are discussed. Thirdly, by substituting the displacement vectors of incident and scattered waves into boundary conditions, the exact analytical equation is derived. Then, considering the symmetry of scattering matrix in the equation, the exact analytical expressions of each scattered wave are obtained. Furthermore, under the assumptions of small incident angle, weak elasticity at an interface of porous media, and ignoring the second- and higher-order terms, the first-order approximate analytical expressions are derived. Establishing a model of sandstone porous media with different porosity in upper and lower media, the correctness of the approximate analytical expressions is verified, and the elastic wave response characteristics of lithology and pore fluids are analyzed.

Sorption of perfluoroalkyl ether carboxylic acids (PFECAs) at the air-water interface in porous media: Modeling perspectives

Perfluoroalkyl ether carboxylic acids (PFECAs) are a growing environmental concern, and thus their migration in unsaturated soils is receiving increased interest. In this study, sorption of four PFECAs at the air-water interface was measured in unsaturated sand columns under static (no flow) conditions following gravity drainage to assess the appropriateness of two commonly applied sorption models (Langmuir and Freundlich) in predicting interfacial uptake. This static method was employed to eliminate any potential artifacts due to flow bypassing and/or interfacial sorption kinetics that might occur in dynamic column experiments. The largest interfacial adsorption coefficient measured was 2.8 ± 1.6×10−5 m for ammonium perfluoro(2-methyl-3-oxahexanoate) (GenX). A commonly employed Langmuir-based model based on interfacial tension data substantially underpredicted GenX and nonafluoro-3,6-dioxaheptanoic acid (PFO2HpA) interfacial sorption measured at low (∼1,000 ng/L) aqueous concentrations in unsaturated sand columns, while a Freundlich-based model substantially overpredicted GenX and PFO2HpA interfacial sorption. These results highlight the need for improved interfacial modeling approaches to predict PFECA fate and transport at relatively low concentrations in unsaturated media.

The Influence of Bimodal Heterogeneity on Viscous Fingering of a Miscible Interface in Porous Media

The flow regimes and the dynamics of the front in miscible displacements are controlled by the interactions between the mechanisms of instability involved in such processes. The instabilities may be driven by unfavorable gravity or mobility ratios or by the heterogeneity of the medium providing favorable paths for the more mobile fluid. In this work, the effect of porous medium heterogeneity with two scales of permeability variations on the frontal instability and fluid mixing have been investigated. The base mode of permeability variations has a smaller wavelength and higher frequency while the imposed mode has a larger wavelength. The effect of such a bimodal heterogeneity on the growth of mixing zone length (MZL) has been studied and the development of the previously recognized flow regimes in layered porous media have been examined. Compared to the unimodal medium comprising the base wave, in the bimodal cases with large contrast between the wavelengths of the two periodic profiles the dominance of each wave length at a different time scale predictably enhances the growth of fingers in the early and late stages. Interestingly and less intuitively, even in cases with close wave numbers between the combined modes faster growth of the mixing zone length is observed. In such cases, the coherence of equal layers in a unimodal layered medium is disturbed by the second wave number resulting in fading of the lateral diffusion regime. However, bimodal heterogeneity may attenuate the instability compared to the unimodal system with the imposed wave’s frequency.

The role of a porous wall on the solute dispersion in a concentric annulus

We studied the role of a porous wall on the dispersion of a solute in an annular space in the presence of a pressure-driven flow. The continuity of concentration and mass flux at the annulus–porous medium interface is used to handle the interaction between the two media. The Reynolds decomposition technique and the cross-sectional averaging method are used to derive a reduced-order advective–dispersive transport model with the associated equivalent diffusion and advection terms. The resultant dispersion and advection coefficients for an annulus with a porous wall are fully characterized as a function of the inner solid core radius of the annulus. The findings reveal that dispersion is retarded in the presence of the inner core in an annulus for both porous and non-porous outer walls. The results also indicate that the transition to a fully advective regime occurs at higher Peclet numbers for an annulus with a porous outer wall. The results suggest that dispersion and advection in an annulus can be controlled by proper selection of the inner core diameter. We also identified the inner core size where the solute dispersion in an annulus with a porous wall is minimum compared to a non-porous boundary. The developed model and insights find applications in many engineering processes where a fluid containing a solute in an annulus interacts with a surrounding porous medium.

Lattice Boltzmann Simulation of Multicomponent Porous Media Flows With Chemical Reaction

Flows with chemical reactions in porous media are fundamental phenomena encountered in many natural, industrial, and scientific areas. For such flows, most existing studies use continuum assumptions and focus on volume-averaged properties on macroscopic scales. Considering the complex porous structures and fluid–solid interactions in realistic situations, this study develops a sophisticated lattice Boltzmann (LB) model for simulating reactive flows in porous media on the pore scale. In the present model, separate LB equations are built for multicomponent flows and chemical species evolutions, source terms are derived for heat and mass transfer, boundary schemes are formulated for surface reaction, and correction terms are introduced for temperature-dependent density. Thus, the present LB model offers a capability to capture pore-scale information of compressible/incompressible fluid motions, homogeneous reaction between miscible fluids, and heterogeneous reaction at the fluid–solid interface in porous media. Different scenarios of density fingering with homogeneous reaction are investigated, with effects of viscosity contrast being clarified. Furthermore, by introducing thermal flows, the solid coke combustion is modeled in porous media. During coke combustion, fluid viscosity is affected by heat and mass transfer, which results in unstable combustion fronts.

An Analytical Solution of Wave Motion in a Transversely Isotropic Poroelastic Half-Space Underlying a Liquid Layer

In this paper, an analytical method is developed for the axisymmetric dynamic response of a finite thickness liquid layer overlying a transversely isotropic porous solid half-space due to body waves. Potential functions and integral transforms are used together to handle the equations of wave motion in two media. The time-harmonic excitation with axisymmetric shape is assumed to be distributed in the interface of liquid and porous media. Green’s functions of stress and displacement are derived as closed-form integral expressions. Demonstration of the effect of the liquid thickness, degree of material anisotropy, and frequency of excitation on the dynamic response is considered here. Numerical results for a uniform distributed disk load are comprised with the existing elastic and poroelastic solutions to illustrate the quality of the method. The results of the current paper can be used in analysis and modelling the rigid or flexible foundations in marine structures.

Analytical solution of flows in porous media for transpiration cooling applications

Abstract

The Characteristics of Reflection and Transmission Coefficients of Porous Medium Saturated with an Ideal Fluid

The underground rock is composed of rock skeleton and pore fluids. When seismic waves propagate in underground medium, it will show complicated change influenced by pore and pore fluids in rocks. It is very important to study the characteristics of reflection and trans- mission coefficients of seismic waves at the interface and to analyze the properties of the lithology and pore fluids of porous medium, which can reveal the oil and gas bearing in underground medium. Based on the relationship among wave functions, displacement and stress in porous medium, the equation of reflection and transmission coefficients at the interface of porous medium saturated with an ideal fluid is derived. A geological model with sandstone porous medium in the top layer and mudstone porous medium in the bottom layer, the rock skeleton parameters of which vary with porosities, is established. Based on the equation and the model, the variation of reflection and transmission coefficients with the incident angle at the interface of porous medium is studied under the conditions of dif- ferent pore fluids filling and different porosities. The study shows that the existence of the pore and pore fluids will impede the reflected and transmitted abilities of seismic waves at the interface of porous medium. Combining with the theory of rock physics and well data, the porosities and pore fluids of porous medium can be identified qualitatively by studying the variation of the reflected fast P- and SV- waves with incident angle. The values of reflection and transmission coefficients of slow P-wave are very small, but the variation of that is relatively large due to the influence of the pore and pore fluids.

The Nonlinear Instability of a Cylindrical Interface Between Two Hydromagnetic Darcian Flows

This paper investigates the nonlinear instability of an interface between two magnetic fluids separated by a cylindrical interface in porous media. The system is influenced by a uniform axial magnetic field. The magnetic field intensities allow a presence of surface currents at the interface. The transfer of mass and heat across the interface is considered. The solutions of linearized equations of motion, under the appropriate nonlinear boundary conditions, lead to a nonlinear characteristic equation that is governed the behavior of the interface deflection. Drawing on the linear stability theory, Routh–Hurwitz’s criteria are utilized to judge the stability criteria. The coupling of Laplace transforms and Homotopy perturbation techniques are adopted to obtain an approximate analytical solution of the interface profile. The nonlinear stability analysis resulted in two levels of solvability conditions. By means of these conditions, a Ginzburg–Landau equation is conducted. The latter equation represented the nonlinear stability configuration. The magnetic field intensity was plotted versus the wave number of the surface waves. Therefore, the stability picture was divided into stable and as well as unstable regions. Subsequently, the influence of the various physical parameters was addressed.

Anomalous imbibition of non-Newtonian fluids in porous media

The imbibition of a complex fluid in porous media often exhibits anomalous behavior, which is dominated by multiple time-spatial scales. In this work, a spatiotemporal fractional imbibition model (SFIM) is proposed to capture anomalous imbibition. The anomalous exponent and the non-Newtonian index of SFIM are introduced to characterize the heterogeneity of porous media and the nonlocality of the non-Newtonian fluid. It is found that the anomalous exponent is inversely proportional to the fractal dimension of tortuosity. The non-Newtonian index unveils the radius variation due to the interaction between the non-Newtonian fluid and the interface of porous media. In addition, the proposed model is superior to the Lucas-Washburn model (LWM) with respect to the experimental data of oil and epoxy resin. This work is provided as a preliminary probe into a study on anomalous imbibition via fractional calculus.

Stability analysis of an interface between immiscible liquids in Hele-Shaw flow in the presence of a magnetic field

• Magnetic fluid interface in porous media. • Field stabilizing fingers. • Surface tension inhibits small scales. • Nonlinear regime of fingers interface. Hydrodynamic instabilities may occur when a viscous fluid is driven by a less viscous one through a porous medium . These penetrations are common in enhanced oil recovery , dendrite formation and aquifer flow. Recent studies have shown that the use of magnetic suspensions allow the external control of the instability. The problem is nonlinear and some further improvements of both theory and experimental observations are still needed and continue being a current source of investigation. In this paper we present a generalized Darcy law formulation in order to examine the growth of finger instabilities as a magnetic field is applied to the interface between the fluids in a Hele-Shaw cell. A new linear stability analysis is performed in the presence of magnetic effects and provides a stability criterion in terms of the non-dimensional physical parameters of the examined flow and the wavenumber of the finger disturbances. The interfacial tension inhibits small wavelength instabilities. The magnetic field contributes to the interface stability for moderate wavelength as it is applied parallel to the liquid-interface. In particular, we find an explicit expression, as a function of the susceptibility, for a critical angle between the interface and the magnetic field direction, in which its effect on the interface is neutral. We have developed a new asymptotic solution for the flow problem in a weak nonlinear regime. The first correction captures the second order nonlinear effects of the magnetic field, which tends to align the fingers with the field orientation and have a destabilizing effect. The analysis predicts that the non-linear effects at second order can counterbalance the first order stabilizing effect of a parallel magnetic field which results in a loss of effectiveness for controlling the investigated finger instabilities. The relevant physical parameters for controlling these finger instabilities are clearly identified by our non-dimensional analysis.

Inertial and Darcy’s Terms Ratio in Boundary Layer at Fluid–Porous Medium Interface

The study considers the forced boundary-layer flow overlying the Darcy–Brinkman porous medium and gives a quantitative analysis of the nonlinear inertial terms in the Brinkman filtration equation. The inertial terms are shown to be larger than the Darcy’s drag near the porous medium interface. The applicability range of boundary-layer approach is determined. It is suitable in high-permeable media with moderate velocities of an external flow. If it is slow enough, the inertial terms can be omitted in spite of interface effect. On the other hand, fast external flow produces the filtration with large pore-scale Reynolds number; therefore, the Forchheimer’s drag should be taken into account. It is shown the Brinkman term as well as inertial terms have a significant role in boundary-layer formation within the porous medium.

Study of migration and deposition of micro particles in porous media by Lattice-Boltzmann Method

The direct-forcing immersed boundary-lattice Boltzmann (IB-LBM) method is used to simulate the migration and deposition of micro particles at the interface of porous media. Single particle deposition and double particles drafting, kissing and tumbling (DKT) motion was respectively simulated to validate the calculation program by comparing with the previous calculation results. Based on this, the effects of the concentration and density of suspended particles on the deposition characteristics were studied. The results indicate that the amount of micro particles deposited in porous media increases as particle density increases. When the particle concentration is constant, the larger the particle density, the earlier the clogging occurs. Besides, micro particles with small concentration are easily migrated through the interfaces into the porous medium, and the amount of particle deposition is not positively related to the particle concentration.

Role of air‐water interfaces in colloid transport in porous media: A review

AbstractAir‐water interfaces play an important role in unsaturated porous media, giving rise to phenomena like capillarity. Less recognized and understood are interactions of colloids with the air‐water interface in porous media and the implications of these interactions for fate and transport of colloids. In this review, we discuss how colloids, both suspended in the aqueous phase and attached at pore walls, interact with air‐water interfaces in porous media. We discuss the theory of colloid/air‐water interface interactions, based on the different forces acting between colloids and the air‐water interface (DLVO, hydrophobic, capillary forces) and based on thermodynamic considerations (Gibbs free energy). Subsurface colloids are usually electrostatically repelled from the air‐water interface because most subsurface colloids and the air‐water are negatively charged. However, hydrophobic interactions can lead to attraction to the air‐water interface. When colloids are at the air‐water interface, capillary forces are usually dominant over other forces. Moving air‐water interfaces are effective in mobilizing and transporting colloids from surfaces. Thermodynamic considerations show that, for a colloid, the air‐water interface is the favored state as compared with the suspension phase, except for hydrophilic colloids in the nanometer size range. Experimental evidence indicates that colloid mobilization in soils often occurs through macropores, although matrix transport is also prevalent in absence of macropores. Moving air‐water interfaces, e.g., occurring during infiltration, imbibition, or drainage, have been shown to scour colloids from surfaces and translocate colloids. Colloids can also be pinned to surfaces by thin water films and capillary menisci at the air‐water‐solid interface line, causing colloid retention and immobilization. Air‐water interfaces thus can both mobilize or immobilize colloids in porous media, depending on hydrodynamics and colloid and surface chemistry.

Reflected wave by the first interface of rigid porous medium at Darcy’s regime

In this paper, reflection waves by the first interface of porous medium having rigid frame is considered. The method presented in this work is based on a temporal model of the direct problem in which a simplified expression of the reflection coefficient at the Darcy’s regime (low frequency range) is established using equivalent fluid model, this expression depends only on the porosity and the viscous permeability (or the flow resistivity) of the medium. The simulated reflected wave is obtained in time domain by convolution between the reflected operator and the incident field. Experimental results are given for samples of air-saturated plastic foams and compared with theoretical predictions.

Analysis of electroosmotic characters in fractal porous media

Electroosmotic flow (EOF) in porous media has very important applications in various scientific and engineering fields. In this article, a fractal model for the height difference caused by the EOFs in porous media is developed based on the fractal theory of porous media and on the electrokinetic flow in capillaries, whose tortuosity is taken into account. The proposed model indicates that the height difference is a function of the physical properties of electrolyte solutions, micro-structural parameters of porous media, zeta potential on the solid surface and Debye thickness near the solid–liquid interface in porous media. Factors influencing the height difference are also analyzed. The model predictions show the same variation tendencies with the available experimental data reported in literature. It is found that the proposed fractal model is superior to the hydraulic radius model in terms of dealing with transport in porous media.

On dispersive propagation of surface waves in patchy saturated porous media

Frequency-dependent velocity and attenuation for Rayleigh-wave propagation along a vacuum/patchy saturated porous medium interface are investigated in the low frequency band (0.1–1000 Hz). Conventional patchy saturation models for compressional waves are extended to account for Rayleigh wave propagation along a free surface. The mesoscopic interaction of fluid and solid phases, as a dominant loss mechanism in patchy saturated media, significantly affects Rayleigh-wave propagation and attenuation. Researches on the dispersion characteristics at low frequencies with different gas fractions in patchy saturated media also demonstrate a strong correlation between the Rayleigh-wave mode and the fast compressional wave. Especially, the strongest attenuation with the maximum value of 1/Q for Rayleigh waves are obtained in the frequency range of 1–200 Hz. Numerical results show that the significant dependence of velocity and attenuation on frequencies and gas fractions presents a distinctive dynamical response of Rayleigh waves in the time domain.