Numerical Simulation of Drying of a Saturated Deformable Porous Media by the Lattice Boltzmann Method

A numerical study is reported here to investigate the drying of saturated deformable porous rectangular plate based on the Darcy–Brinkman extended model. All walls of the plate are maintained to a convective heat flux as well as the top and bottom faces are also subjected to a mass flux. The model for the energy transport is based on the local thermodynamic equilibrium between the fluid and the solid phases. The lattice Boltzmann method is used for solving the governing differential equations system. A comprehensive analysis of the influence of the Poisson’s coefficient, the Young’s modulus and the permeability on macroscopic fields is investigated throughout this work.     

Acoustics of Rotating Deformable Saturated Porous Media

We investigate wave propagation in elastic porous media which are saturated by incompressible viscous Newtonian fluids when the porous media are in rotation with respect to a Galilean frame. The model is obtained by upscaling the flow at the pore scale. We use the method of multiple scale expansions which gives rigorously the macroscopic behaviour without any prerequisite on the form of the macroscopic equations. For Kibel numbers A A(1), the acoustic filtration law resembles a Darcys law, but with a conductivity which depends on the wave frequency and on the angular velocity. The bulk momentum balance shows new inertial terms which account for the convective and Coriolis accelerations. Three dispersive waves are pointed out. An investigation in the inertial flow regime shows that the two pseudo-dilatational waves have a cut-off frequency.     

Radon Emanation in Partially Saturated Porous Media

Radon emanation which is the fraction of radon-222 atoms released in the connected pore space of a porous material, increases when the water content increases because of the low recoil range of this atom in water compared with air. This complex phenomenon is studied using reconstructed porous media and random packings where the phase distribution is obtained by a lattice Boltzmann technique incorporating interfacial tension and wetting. The influence of the pore structure, of the recoil range and of saturation, is systematically studied. The numerical results are in good agreement with data from uranium mine tailings.     

Osmotic Mechanism of Fracture Growth in Saturated Porous Media

Fracture growth in saturated porous bodies under the action of the osmotic pressure developed in the fracture by a solute for which the fracture surface represents a semipermeable membrane is considered. This mechanism of fracture growth, which follows directly from the basic laws of fracture mechanics and physical chemistry, should be a fairly general effect of significance in a number of geochemical and technological processes. In particular, the role of osmosis in well flushing and cementing processes was noted in study by N. G. Avetisyan, Choice of type of drill solution for drilling in unstable rocks, published in: Review Information. Drilling [in Russian], VNIIOENG (1983) and the mechanism was briefly discussed in monograph by A. Kh. Mirzadzhanzade and V. M. Entov, Drilling Hydrodynamics [in Russian], Nedra, Moscow (1985).In study by R. V. Gol'dshtein, V. M. Entov, and B. P. Pavlovskii, Model of the development of hydrogen fractures in metal, Dokl. Acad. Nauk SSSR, Vol. 237, 828 (1977) a comparable mathematical model was proposed for explaining the hydrogen embrittlement of metals. Finally, in study by J. P. Sargent and K. H. G. Ashbee, The contribution of osmosis to dimensional instability of adhesive joints, J. Adhesion, Vol. 17, 83 (1984) a very similar mechanism of fracture development in polymeric materials due to the osmotic splitting of internal joints as a result of the release in the joints of a substance dissolved in the solid polymer was discussed and visual observation data were given.The property of semipermeability of the fracture surface (permeability for water and impermeability for dissolved salts), which is fundamental to our study, is taken as a basic hypothesis and will not discussed in what follows. Many arguments could be advanced to show that natural semipermeable membranes can develop in rocks, especially in argillaceous ones. However, these arguments are not definite and clearly lie beyond the competence of the authors whose task is to trace the possible mechanical consequences of the presence of semipermeable membranes and draw them to the attention of the specialists.     

Wave Dynamics of Saturated Porous Media and Evolutionary Equations

Nonlinear wave dynamics of an elastically deformed saturated porous media is investigated following the Biot approach. Mathematical models under research are the Biot model and its generalization by consideration of viscous stresses inside liquids. Using two-scales and linear WKB methods, the classical Biot system is transformed to a first-order wave equation. To construct the solution of the other system, an asymptotic modified two-scales method is developed. Initial system of equations is transformed to a nonlinear generalized Korteweg–de Vries–Burgers equation for quick elastic wave. Distinctions of wave propagation in the context of the Biot model and its generalization are shown.     

NMR Measurements of Tortuosity in Partially Saturated Porous Media

The tortuosity (τ), defined in the present context as the ratio of the free diffusion coefficient to the restricted diffusion coefficient of a contained fluid, is an important but difficult to measure characteristic of a porous medium, particularly when it is partially saturated with water. We develop and apply methodology, based on nuclear magnetic resonance (NMR) pulsed field gradient techniques, to measure τ for various sandstone rock cores as a function of residual water fraction. The NMR methodology requires the use of bipolar pulsed field gradient stimulated echo pulse sequences to avoid systematic errors due to magnetic susceptibility differences and D₂O as a stationary immiscible water phase; this was selected as it provides no ¹H NMR signal. Tortuosity of the free pore space was successfully measured using liquid ethane as a probe fluid for three different sandstones over the full accessible range of residual water saturation. Generally, the tortuosity was observed to increase with residual water (D₂O) content; however, significant variations were observed between the different sandstones.     

Hydromechanical Modelling of Experimentally Compacted Saturated Argillaceous Porous Media

In order to model the experimental compaction of clays as completely as possible, it is necessary to use the hydromechanical coupled three-dimensional theory for saturated porous media. The proposed formulation is based on elastoplasticity, more precisely on modified Cam-clay model. The identification of the parameters of the model is made by special oedometric experiments at steady state. The compaction experiments are simulated with accuracy in transient and steady states and complement those obtained in a recent study based only on steady state.     

Pore-Network Modeling of Isothermal Drying in Porous Media

In this paper we present numerical results obtained with a pore-network model for the drying of porous media that accounts for various processes at the pore scale. These include mass transfer by advection and diffusion in the gas phase, viscous flow in the liquid and gas phases and capillary effects at the liquid--gas interface. We extend our work by studying the effect of capillarity-induced flow in macroscopic liquid films that form at the pore walls as the liquid--gas interface recedes. A mathematical model that accounts for the effect of films on the drying rates and phase distribution patterns is presented. It is shown that film flow is a major transport mechanism in the drying of porous materials, its effect being dominant when capillarity controls the process, which is the case in typical applications.     

Thermodynamic Correction for Salts in Variably Saturated Porous Media

Using thermodynamic principles, the general relationship describing the equilibrium vapor content in the gas phase above a saline liquid and across a curved liquid–gas interface is developed. Since high salt concentration affects the intensive and extensive liquid properties, it is also necessary to account for these effects in liquid water content/liquid water pressure relationship curves so that experimentally derived curves for pure water may be useful for elevated salt concentrations. The appropriate thermodynamic relationships are derived to describe the salt effects on liquid and vapor properties. The resulting equations are valid for salt concentrations between zero and saturation, and for any temperatures that nominally occur in nearsurface geologic materials.     

Asymptotic Research of Nonlinear Wave Processes in Saturated Porous Media

The problem of nonlinear wave dynamics of a fluid-saturated porous medium is investigated. The mathematical model proposed is based on the classical Frenkel--Biot--Nikolaevskiy theory concerning elastic wave propagation and includes mass, momentum, energy conservation laws, as well as rheological and thermodynamic relations. The model describes nonlinear, dispersive, and dissipative medium. To solve the system of differential equations, an asymptotic modified two-scales method is developed and a Cauchy problem for initial equations system is transformed to a Cauchy problem for nonlinear generalized Korteweg--de Vries--Burgers equation for modulated quick wave amplitudes and an inhomogeneous set of equations for slow background motion. Stationary solutions of the derived evolutionary equation that have been constructed numerically reflect different regimes of elastic wave attenuation: diffusive, oscillating, and soliton-like.     

不可压饱和粘弹性多孔介质固结问题的Gurtin型变分原理

基于多孔介质理论,在固相骨架和孔隙流体微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,利用卷积积分的性质,本文首先建立了以固相骨架位移、孔隙流体相对速度和孔隙流体压力为宗量的流体饱和粘弹性多孔介质固结问题的一个Gurtin型变分原理.其次,利用Lagrange乘子法解除相关的变分约束条件,建立了流体饱和粘弹性多孔介质固结问题的若干广义Gurtin型变分原理,包括第三类的Hu-Washizu型变分原理.最后,简单讨论了等价初边值问题的相应变分原理.这些Gurtin型变分原理的建立不仅丰富了饱和粘弹性多孔介质的相关理论,而且为相关数值模拟方法,如有限元法、无网格法等的建立奠定了理论基础.     

Three-Dimensional Analytical Models for Virus Transport in Saturated Porous Media

Analytical models for virus transport in saturated, homogeneous porous media are developed. The models account for three-dimensional dispersion in a uniform flow field, and first-order inactivation of suspended and deposited viruses with different inactivation rate coefficients. Virus deposition onto solid particles is described by two different processes: nonequilibrium adsorption which is applicable to viruses behaving as solutes; and colloid filtration which is applicable to viruses behaving as colloids. The governing virus transport equations are solved analytically by employing Laplace/Fourier transform techniques. Instantaneous and continuous/periodic virus loadings from a point source are examined.     

Diffusion of Randon in Porous Media Saturated with Gels and Emulsions

The effective diffusion coefficient of radon was determined in polymer/silicate gels and clay suspension used as sealing materials in environmental protection. On the basis of the experimental findings, it was concluded that both materials drastically decrease the convective mass transport in porous media. Simultaneously, the effective diffusion coefficient was reduced significantly. Thus, the radon flux might be decreased by 5 to 6 orders of magnitude in porous systems originally having gas or low water saturation by injection of gel-forming materials or placement of clay suspensions. At high water saturation, however, the diffusion transport of radon can be slightly restricted in consolidated and unconsolidated porous media. The laboratory studies may firmly allow us to conclude that hydrogels and clay suspensions are prospective candidates in an integrated environmental technology to be used for restriction of radon migration in subsurface regions.     

The Local Geometry of Gas Injection into Saturated Homogeneous Porous Media

The injection of gases into liquid saturated porous media is of theoretical and practical interest (e.g., air sparging for the removal of volatile organic compounds from contaminated aquifer sediments). The influence of the rate of gas delivery and the vertical distance from the source are developed. The concept of a “near-injection region” is presented in which the pressure gradients exceed buoyant gradients and thus exhibits largely radial flow. The near-injection size is shown to have an area required to carry the injected gas flow under unit gradient. The parabolic movement of gas outside of this area which has often been observed is explained as reflecting the sum of many realizations of gas channels following random lateral movements as they precede upward independent of flux. These concepts are confirmed through comparison with published and experimental data of air injection into slabs consisting of saturated sands of a range of textures.     

Quasi-Static and Dynamic Behavior of Saturated Porous Media with Incompressible Constituents

In this paper the field equations governing the dynamic response of a fluid-saturated elastic porous medium are analyzed and built up for the study of quasi-static and dynamical problems like the consolidation problem and wave propagation. The two constituents are assumed to be incompressible. A numerical solution is derived by means of the standard Galerkin procedure and the finite element method.     

Dynamics of Viscous Entrapped Saturated Zones in Partially Wetted Porous Media

As a typical multiphase fluid flow process, drainage in porous media is of fundamental interest both in nature and in industrial applications. During drainage processes in unsaturated soils and porous media in general, saturated regions, or clusters, in which a liquid phase fully occupies the pore space between solid grains, affect the relative permeability and effective stress of the system. Here, we experimentally study drainage processes in unsaturated granular media as a model porous system. The distribution of saturated clusters is analysed by optical imaging under different drainage conditions, with pore-scale information from Voronoi and Delaunay tessellation used to characterise the topology of saturated cluster distributions. By employing statistical analyses, we describe the observed spatial and temporal evolution of multiphase flow and fluid entrapment in granular media. Results indicate that the distributions of both the crystallised cell size and pore size are positively correlated to the spatial and temporal distribution of saturated cluster sizes. The saturated cluster size is found to follow a lognormal distribution, in which the generalised Bond number (\( Bo^{*} \)) correlates negatively to the scale parameter (μ) and positively to the shape parameter (σ). With further consideration of the total surface energy obtained based on liquid–air interfaces, we were able to include additional grain-scale information in the constitutive modelling of unsaturated soils using both the degree of saturation and generalised Bond number. These findings can be used to connect pore-scale behaviour with overall hydro-mechanical characteristics in granular systems.     

Effect of Efflorescence Formation on Drying Kinetics of Porous Media

We study experimentally the evaporation of an aqueous NaCl solution with efflorescence formation in hydrophilic or hydrophobic two-dimensional model porous media. The efflorescence formation only marginally affects the invasion patterns but greatly modifies the drying kinetics compared to pure water. Two mechanisms are identified for explaining the impact of efflorescence formation on drying kinetics. It is shown that the efflorescence contributes to increase the evaporation rate compared to drying with pure water, a surprising result since the water activity is reduced in the presence of dissolved salt. This effect is explained by the efflorescence liquid capillary pumping effect associated with the porous nature of the efflorescence. Then, we identify a second phase where the efflorescence dries out and acts as a vapour diffusion barrier, leading to a dramatic reduction of evaporation rate.     

Modeling Chemotactic Waves in Saturated Porous Media using Adaptive Mesh Refinement

Bacterial transport is heavily influenced by chemical gradients and interfaces that exist in the subsurface. The main aim of this article is to describe a method of simulating the propagation of a traveling bacterial wave in a contaminated region and the resulting degradation of the contaminant. The presence of the chemotactic term and the relatively small bacterial diffusion means that the wave contains a very sharp wavefront. We, therefore, use an upwind conservative numerical scheme to obtain accurate and numerically stable solutions. The accuracy of the method is verified by comparisons with an exact one-dimensional solution of a simplified problem to give the same wavespeed. The method is then used to simulate the propagation of a realistic chemotactic wave in one dimension. We then use adaptive mesh refinement (AMR) to compute the propagation of chemotactic waves in two dimensions using the simplified model calibrated to give the same wavespeed as the full model.     

Dispersion and Dispersivity Tensors in Saturated Porous Media with Uniaxial Symmetry

The coefficient of dispersion, D _ij , and the dispersivity, a _ijkl , appear in the expression for the flux of a solute in saturated flow through porous media. We present a detailed analysis of these tensors in an axially symmetric porous medium, e.g., a stratified porous medium, with alternating layers, and show that in such a medium, the dispersivity is governed by six independent moduli. We present also the constraints that have to be satisfied by these moduli. We also show that at least two independent experiments are required in order to obtain the values of these coefficients for any three-dimensional porous medium domain.